TSTP Solution File: SYN393^4.004 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYN393^4.004 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 11:57:13 EDT 2024
% Result : Theorem 37.78s 5.16s
% Output : Refutation 37.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN393^4.004 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.37 % Computer : n008.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 3 17:58:23 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.16/0.37 This is a TH0_THM_EQU_NAR problem
% 0.16/0.37 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.C36a6lzdu4/Vampire---4.8_19757
% 0.16/0.39 % (20017)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.16/0.39 % (20016)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.16/0.39 % (20018)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 Vampire---4 for (2999ds/27Mi)
% 0.16/0.39 % (20019)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.16/0.39 % (20021)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.16/0.39 % (20020)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.16/0.39 % (20022)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.16/0.39 % (20023)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.16/0.39 % (20019)Instruction limit reached!
% 0.16/0.39 % (20019)------------------------------
% 0.16/0.39 % (20019)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (20019)Termination reason: Unknown
% 0.16/0.39 % (20020)Instruction limit reached!
% 0.16/0.39 % (20020)------------------------------
% 0.16/0.39 % (20020)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (20020)Termination reason: Unknown
% 0.16/0.39 % (20020)Termination phase: Property scanning
% 0.16/0.39
% 0.16/0.39 % (20020)Memory used [KB]: 1023
% 0.16/0.39 % (20020)Time elapsed: 0.003 s
% 0.16/0.39 % (20020)Instructions burned: 3 (million)
% 0.16/0.39 % (20020)------------------------------
% 0.16/0.39 % (20020)------------------------------
% 0.16/0.39 % (20019)Termination phase: Naming
% 0.16/0.39
% 0.16/0.39 % (20019)Memory used [KB]: 1023
% 0.16/0.39 % (20019)Time elapsed: 0.004 s
% 0.16/0.39 % (20019)Instructions burned: 3 (million)
% 0.16/0.39 % (20019)------------------------------
% 0.16/0.39 % (20019)------------------------------
% 0.16/0.39 % (20023)Instruction limit reached!
% 0.16/0.39 % (20023)------------------------------
% 0.16/0.39 % (20023)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (20023)Termination reason: Unknown
% 0.16/0.39 % (20023)Termination phase: Property scanning
% 0.16/0.39
% 0.16/0.39 % (20023)Memory used [KB]: 1023
% 0.16/0.39 % (20023)Time elapsed: 0.004 s
% 0.16/0.39 % (20023)Instructions burned: 3 (million)
% 0.16/0.39 % (20023)------------------------------
% 0.16/0.39 % (20023)------------------------------
% 0.16/0.39 % (20017)Instruction limit reached!
% 0.16/0.39 % (20017)------------------------------
% 0.16/0.39 % (20017)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (20017)Termination reason: Unknown
% 0.16/0.39 % (20017)Termination phase: Property scanning
% 0.16/0.39
% 0.16/0.39 % (20017)Memory used [KB]: 1023
% 0.16/0.39 % (20017)Time elapsed: 0.004 s
% 0.16/0.39 % (20017)Instructions burned: 5 (million)
% 0.16/0.39 % (20017)------------------------------
% 0.16/0.39 % (20017)------------------------------
% 0.16/0.39 % (20021)Refutation not found, incomplete strategy
% 0.16/0.39 % (20021)------------------------------
% 0.16/0.39 % (20021)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (20021)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.39
% 0.16/0.39
% 0.16/0.39 % (20021)Memory used [KB]: 5500
% 0.16/0.39 % (20021)Time elapsed: 0.005 s
% 0.16/0.39 % (20021)Instructions burned: 4 (million)
% 0.16/0.39 % (20021)------------------------------
% 0.16/0.39 % (20021)------------------------------
% 0.16/0.40 % (20022)Instruction limit reached!
% 0.16/0.40 % (20022)------------------------------
% 0.16/0.40 % (20022)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (20022)Termination reason: Unknown
% 0.16/0.40 % (20022)Termination phase: Saturation
% 0.16/0.40
% 0.16/0.40 % (20022)Memory used [KB]: 5500
% 0.16/0.40 % (20022)Time elapsed: 0.010 s
% 0.16/0.40 % (20022)Instructions burned: 18 (million)
% 0.16/0.40 % (20022)------------------------------
% 0.16/0.40 % (20022)------------------------------
% 0.16/0.40 % (20018)Instruction limit reached!
% 0.16/0.40 % (20018)------------------------------
% 0.16/0.40 % (20018)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (20018)Termination reason: Unknown
% 0.16/0.40 % (20018)Termination phase: Saturation
% 0.16/0.40
% 0.16/0.40 % (20018)Memory used [KB]: 5628
% 0.16/0.40 % (20018)Time elapsed: 0.013 s
% 0.16/0.40 % (20018)Instructions burned: 29 (million)
% 0.16/0.40 % (20018)------------------------------
% 0.16/0.40 % (20018)------------------------------
% 0.16/0.41 % (20024)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on Vampire---4 for (2999ds/37Mi)
% 0.16/0.41 % (20025)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 Vampire---4 for (2999ds/15Mi)
% 0.16/0.41 % (20026)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.16/0.41 % (20027)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on Vampire---4 for (2999ds/1041Mi)
% 0.16/0.41 % (20028)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.16/0.41 % (20026)Instruction limit reached!
% 0.16/0.41 % (20026)------------------------------
% 0.16/0.41 % (20026)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (20026)Termination reason: Unknown
% 0.16/0.41 % (20026)Termination phase: Function definition elimination
% 0.16/0.41
% 0.16/0.41 % (20026)Memory used [KB]: 1023
% 0.16/0.41 % (20026)Time elapsed: 0.004 s
% 0.16/0.41 % (20026)Instructions burned: 4 (million)
% 0.16/0.41 % (20026)------------------------------
% 0.16/0.41 % (20026)------------------------------
% 0.16/0.41 % (20028)Instruction limit reached!
% 0.16/0.41 % (20028)------------------------------
% 0.16/0.41 % (20028)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (20028)Termination reason: Unknown
% 0.16/0.41 % (20028)Termination phase: Property scanning
% 0.16/0.41
% 0.16/0.41 % (20028)Memory used [KB]: 1023
% 0.16/0.41 % (20028)Time elapsed: 0.006 s
% 0.16/0.41 % (20028)Instructions burned: 8 (million)
% 0.16/0.41 % (20028)------------------------------
% 0.16/0.41 % (20028)------------------------------
% 0.16/0.41 % (20029)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.16/0.41 % (20025)Instruction limit reached!
% 0.16/0.41 % (20025)------------------------------
% 0.16/0.41 % (20025)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (20025)Termination reason: Unknown
% 0.16/0.41 % (20025)Termination phase: Saturation
% 0.16/0.41
% 0.16/0.41 % (20025)Memory used [KB]: 5500
% 0.16/0.41 % (20025)Time elapsed: 0.009 s
% 0.16/0.41 % (20025)Instructions burned: 17 (million)
% 0.16/0.41 % (20025)------------------------------
% 0.16/0.41 % (20025)------------------------------
% 0.16/0.42 % (20030)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.16/0.42 % (20030)Instruction limit reached!
% 0.16/0.42 % (20030)------------------------------
% 0.16/0.42 % (20030)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (20030)Termination reason: Unknown
% 0.16/0.42 % (20030)Termination phase: SInE selection
% 0.16/0.42
% 0.16/0.42 % (20030)Memory used [KB]: 1023
% 0.16/0.42 % (20030)Time elapsed: 0.003 s
% 0.16/0.42 % (20030)Instructions burned: 3 (million)
% 0.16/0.42 % (20030)------------------------------
% 0.16/0.42 % (20030)------------------------------
% 0.16/0.42 % (20024)Instruction limit reached!
% 0.16/0.42 % (20024)------------------------------
% 0.16/0.42 % (20024)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (20024)Termination reason: Unknown
% 0.16/0.42 % (20024)Termination phase: Saturation
% 0.16/0.42
% 0.16/0.42 % (20024)Memory used [KB]: 5628
% 0.16/0.42 % (20024)Time elapsed: 0.017 s
% 0.16/0.42 % (20024)Instructions burned: 39 (million)
% 0.16/0.42 % (20024)------------------------------
% 0.16/0.42 % (20024)------------------------------
% 0.16/0.42 % (20031)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.16/0.42 % (20029)Instruction limit reached!
% 0.16/0.42 % (20029)------------------------------
% 0.16/0.42 % (20029)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (20029)Termination reason: Unknown
% 0.16/0.42 % (20029)Termination phase: Saturation
% 0.16/0.42
% 0.16/0.42 % (20029)Memory used [KB]: 5884
% 0.16/0.42 % (20029)Time elapsed: 0.013 s
% 0.16/0.42 % (20029)Instructions burned: 17 (million)
% 0.16/0.42 % (20029)------------------------------
% 0.16/0.42 % (20029)------------------------------
% 0.16/0.43 % (20031)Instruction limit reached!
% 0.16/0.43 % (20031)------------------------------
% 0.16/0.43 % (20031)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.43 % (20031)Termination reason: Unknown
% 0.16/0.43 % (20031)Termination phase: Property scanning
% 0.16/0.43
% 0.16/0.43 % (20031)Memory used [KB]: 1023
% 0.16/0.43 % (20031)Time elapsed: 0.004 s
% 0.16/0.43 % (20031)Instructions burned: 4 (million)
% 0.16/0.43 % (20031)------------------------------
% 0.16/0.43 % (20031)------------------------------
% 0.16/0.43 % (20032)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.16/0.43 % (20033)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.16/0.43 % (20032)Instruction limit reached!
% 0.16/0.43 % (20032)------------------------------
% 0.16/0.43 % (20032)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.43 % (20032)Termination reason: Unknown
% 0.16/0.43 % (20032)Termination phase: Property scanning
% 0.16/0.43
% 0.16/0.43 % (20032)Memory used [KB]: 1023
% 0.16/0.43 % (20033)Instruction limit reached!
% 0.16/0.43 % (20033)------------------------------
% 0.16/0.43 % (20033)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.43 % (20033)Termination reason: Unknown
% 0.16/0.43 % (20033)Termination phase: Function definition elimination
% 0.16/0.43
% 0.16/0.43 % (20033)Memory used [KB]: 1023
% 0.16/0.43 % (20033)Time elapsed: 0.004 s
% 0.16/0.43 % (20033)Instructions burned: 4 (million)
% 0.16/0.43 % (20033)------------------------------
% 0.16/0.43 % (20033)------------------------------
% 0.16/0.43 % (20032)Time elapsed: 0.005 s
% 0.16/0.43 % (20032)Instructions burned: 7 (million)
% 0.16/0.43 % (20032)------------------------------
% 0.16/0.43 % (20032)------------------------------
% 0.16/0.43 % (20034)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.16/0.44 % (20034)Instruction limit reached!
% 0.16/0.44 % (20034)------------------------------
% 0.16/0.44 % (20034)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.44 % (20034)Termination reason: Unknown
% 0.16/0.44 % (20034)Termination phase: Property scanning
% 0.16/0.44
% 0.16/0.44 % (20034)Memory used [KB]: 1023
% 0.16/0.44 % (20034)Time elapsed: 0.004 s
% 0.16/0.44 % (20034)Instructions burned: 4 (million)
% 0.16/0.44 % (20034)------------------------------
% 0.16/0.44 % (20034)------------------------------
% 0.16/0.44 % (20035)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.16/0.44 % (20036)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on Vampire---4 for (2999ds/710Mi)
% 0.16/0.44 % (20037)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.16/0.44 % (20037)Instruction limit reached!
% 0.16/0.44 % (20037)------------------------------
% 0.16/0.44 % (20037)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.44 % (20037)Termination reason: Unknown
% 0.16/0.44 % (20037)Termination phase: Property scanning
% 0.16/0.44
% 0.16/0.44 % (20037)Memory used [KB]: 1023
% 0.16/0.44 % (20037)Time elapsed: 0.005 s
% 0.16/0.44 % (20037)Instructions burned: 6 (million)
% 0.16/0.44 % (20037)------------------------------
% 0.16/0.44 % (20037)------------------------------
% 0.23/0.44 % (20036)Refutation not found, incomplete strategy
% 0.23/0.44 % (20036)------------------------------
% 0.23/0.44 % (20036)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.44 % (20036)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.44
% 0.23/0.44
% 0.23/0.44 % (20036)Memory used [KB]: 5628
% 0.23/0.44 % (20036)Time elapsed: 0.007 s
% 0.23/0.44 % (20036)Instructions burned: 8 (million)
% 0.23/0.44 % (20036)------------------------------
% 0.23/0.44 % (20036)------------------------------
% 0.23/0.45 % (20039)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on Vampire---4 for (2999ds/21Mi)
% 0.23/0.45 % (20038)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 Vampire---4 for (2999ds/902Mi)
% 0.23/0.45 % (20035)Instruction limit reached!
% 0.23/0.45 % (20035)------------------------------
% 0.23/0.45 % (20035)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.45 % (20035)Termination reason: Unknown
% 0.23/0.45 % (20035)Termination phase: Saturation
% 0.23/0.45
% 0.23/0.45 % (20035)Memory used [KB]: 5628
% 0.23/0.45 % (20035)Time elapsed: 0.035 s
% 0.23/0.45 % (20035)Instructions burned: 18 (million)
% 0.23/0.45 % (20035)------------------------------
% 0.23/0.45 % (20035)------------------------------
% 0.23/0.45 % (20040)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on Vampire---4 for (2999ds/5Mi)
% 0.23/0.45 % (20038)Refutation not found, incomplete strategy
% 0.23/0.45 % (20038)------------------------------
% 0.23/0.45 % (20038)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.45 % (20038)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.45
% 0.23/0.45
% 0.23/0.45 % (20038)Memory used [KB]: 5500
% 0.23/0.45 % (20038)Time elapsed: 0.005 s
% 0.23/0.45 % (20038)Instructions burned: 5 (million)
% 0.23/0.45 % (20038)------------------------------
% 0.23/0.45 % (20038)------------------------------
% 0.23/0.45 % (20040)Instruction limit reached!
% 0.23/0.45 % (20040)------------------------------
% 0.23/0.45 % (20040)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.45 % (20040)Termination reason: Unknown
% 0.23/0.45 % (20040)Termination phase: Property scanning
% 0.23/0.45
% 0.23/0.45 % (20040)Memory used [KB]: 1023
% 0.23/0.45 % (20040)Time elapsed: 0.004 s
% 0.23/0.45 % (20040)Instructions burned: 5 (million)
% 0.23/0.45 % (20040)------------------------------
% 0.23/0.45 % (20040)------------------------------
% 0.23/0.45 % (20039)Instruction limit reached!
% 0.23/0.45 % (20039)------------------------------
% 0.23/0.45 % (20039)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.45 % (20039)Termination reason: Unknown
% 0.23/0.45 % (20039)Termination phase: Saturation
% 0.23/0.45
% 0.23/0.45 % (20039)Memory used [KB]: 5628
% 0.23/0.45 % (20039)Time elapsed: 0.011 s
% 0.23/0.45 % (20039)Instructions burned: 22 (million)
% 0.23/0.45 % (20039)------------------------------
% 0.23/0.45 % (20039)------------------------------
% 0.23/0.46 % (20041)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.23/0.46 % (20042)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on Vampire---4 for (2999ds/377Mi)
% 0.23/0.46 % (20041)Refutation not found, incomplete strategy
% 0.23/0.46 % (20041)------------------------------
% 0.23/0.46 % (20041)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.46 % (20041)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.46
% 0.23/0.46
% 0.23/0.46 % (20041)Memory used [KB]: 5500
% 0.23/0.46 % (20041)Time elapsed: 0.005 s
% 0.23/0.46 % (20041)Instructions burned: 5 (million)
% 0.23/0.46 % (20041)------------------------------
% 0.23/0.46 % (20041)------------------------------
% 0.23/0.46 % (20043)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 Vampire---4 for (2999ds/779Mi)
% 0.23/0.47 % (20044)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on Vampire---4 for (2999ds/19Mi)
% 0.23/0.47 % (20045)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on Vampire---4 for (2999ds/879Mi)
% 0.23/0.47 % (20044)Refutation not found, incomplete strategy
% 0.23/0.47 % (20044)------------------------------
% 0.23/0.47 % (20044)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.47 % (20044)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.47
% 0.23/0.47
% 0.23/0.47 % (20044)Memory used [KB]: 5500
% 0.23/0.47 % (20044)Time elapsed: 0.004 s
% 0.23/0.47 % (20044)Instructions burned: 4 (million)
% 0.23/0.47 % (20044)------------------------------
% 0.23/0.47 % (20044)------------------------------
% 0.23/0.47 % (20046)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (2999ds/17Mi)
% 0.23/0.48 % (20046)Instruction limit reached!
% 0.23/0.48 % (20046)------------------------------
% 0.23/0.48 % (20046)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.48 % (20046)Termination reason: Unknown
% 0.23/0.48 % (20046)Termination phase: Saturation
% 0.23/0.48
% 0.23/0.48 % (20046)Memory used [KB]: 5500
% 0.23/0.48 % (20046)Time elapsed: 0.009 s
% 0.23/0.48 % (20046)Instructions burned: 17 (million)
% 0.23/0.48 % (20046)------------------------------
% 0.23/0.48 % (20046)------------------------------
% 0.23/0.48 % (20047)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.23/0.48 % (20016)Instruction limit reached!
% 0.23/0.48 % (20016)------------------------------
% 0.23/0.48 % (20016)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.48 % (20016)Termination reason: Unknown
% 0.23/0.48 % (20016)Termination phase: Saturation
% 0.23/0.48
% 0.23/0.48 % (20016)Memory used [KB]: 6140
% 0.23/0.48 % (20016)Time elapsed: 0.088 s
% 0.23/0.48 % (20016)Instructions burned: 183 (million)
% 0.23/0.48 % (20016)------------------------------
% 0.23/0.48 % (20016)------------------------------
% 0.23/0.48 % (20047)Instruction limit reached!
% 0.23/0.48 % (20047)------------------------------
% 0.23/0.48 % (20047)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.48 % (20047)Termination reason: Unknown
% 0.23/0.48 % (20047)Termination phase: Property scanning
% 0.23/0.48
% 0.23/0.48 % (20047)Memory used [KB]: 1023
% 0.23/0.48 % (20047)Time elapsed: 0.004 s
% 0.23/0.48 % (20047)Instructions burned: 4 (million)
% 0.23/0.48 % (20047)------------------------------
% 0.23/0.48 % (20047)------------------------------
% 0.23/0.48 % (20048)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on Vampire---4 for (2999ds/30Mi)
% 0.23/0.49 % (20049)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on Vampire---4 for (2999ds/127Mi)
% 0.23/0.49 % (20050)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on Vampire---4 for (2999ds/100Mi)
% 0.23/0.49 % (20051)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 Vampire---4 for (2998ds/3Mi)
% 0.23/0.50 % (20048)Instruction limit reached!
% 0.23/0.50 % (20048)------------------------------
% 0.23/0.50 % (20048)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.50 % (20048)Termination reason: Unknown
% 0.23/0.50 % (20048)Termination phase: Saturation
% 0.23/0.50
% 0.23/0.50 % (20048)Memory used [KB]: 5628
% 0.23/0.50 % (20048)Time elapsed: 0.014 s
% 0.23/0.50 % (20048)Instructions burned: 30 (million)
% 0.23/0.50 % (20048)------------------------------
% 0.23/0.50 % (20048)------------------------------
% 0.23/0.50 % (20051)Instruction limit reached!
% 0.23/0.50 % (20051)------------------------------
% 0.23/0.50 % (20051)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.50 % (20051)Termination reason: Unknown
% 0.23/0.50 % (20051)Termination phase: Property scanning
% 0.23/0.50
% 0.23/0.50 % (20051)Memory used [KB]: 1023
% 0.23/0.50 % (20051)Time elapsed: 0.003 s
% 0.23/0.50 % (20051)Instructions burned: 5 (million)
% 0.23/0.50 % (20051)------------------------------
% 0.23/0.50 % (20051)------------------------------
% 0.23/0.51 % (20054)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 Vampire---4 for (2998ds/20Mi)
% 0.23/0.51 % (20054)Refutation not found, incomplete strategy
% 0.23/0.51 % (20054)------------------------------
% 0.23/0.51 % (20054)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.51 % (20054)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.51
% 0.23/0.51
% 0.23/0.51 % (20054)Memory used [KB]: 5500
% 0.23/0.51 % (20054)Time elapsed: 0.003 s
% 0.23/0.51 % (20054)Instructions burned: 5 (million)
% 0.23/0.51 % (20054)------------------------------
% 0.23/0.51 % (20054)------------------------------
% 0.23/0.51 % (20055)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on Vampire---4 for (2998ds/86Mi)
% 0.23/0.52 % (20056)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 Vampire---4 for (2998ds/107Mi)
% 0.23/0.53 % (20049)Instruction limit reached!
% 0.23/0.53 % (20049)------------------------------
% 0.23/0.53 % (20049)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.53 % (20049)Termination reason: Unknown
% 0.23/0.53 % (20049)Termination phase: Saturation
% 0.23/0.53
% 0.23/0.53 % (20049)Memory used [KB]: 6012
% 0.23/0.53 % (20049)Time elapsed: 0.041 s
% 0.23/0.53 % (20049)Instructions burned: 128 (million)
% 0.23/0.53 % (20049)------------------------------
% 0.23/0.53 % (20049)------------------------------
% 0.23/0.54 % (20056)Refutation not found, incomplete strategy
% 0.23/0.54 % (20056)------------------------------
% 0.23/0.54 % (20056)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.54 % (20056)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.54
% 0.23/0.54
% 0.23/0.54 % (20056)Memory used [KB]: 5628
% 0.23/0.54 % (20056)Time elapsed: 0.017 s
% 0.23/0.54 % (20056)Instructions burned: 36 (million)
% 0.23/0.54 % (20056)------------------------------
% 0.23/0.54 % (20056)------------------------------
% 0.23/0.54 % (20050)Instruction limit reached!
% 0.23/0.54 % (20050)------------------------------
% 0.23/0.54 % (20050)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.54 % (20050)Termination reason: Unknown
% 0.23/0.54 % (20050)Termination phase: Saturation
% 0.23/0.54
% 0.23/0.54 % (20050)Memory used [KB]: 5628
% 0.23/0.54 % (20050)Time elapsed: 0.047 s
% 0.23/0.54 % (20050)Instructions burned: 100 (million)
% 0.23/0.54 % (20050)------------------------------
% 0.23/0.54 % (20050)------------------------------
% 0.23/0.54 % (20055)Instruction limit reached!
% 0.23/0.54 % (20055)------------------------------
% 0.23/0.54 % (20055)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.54 % (20055)Termination reason: Unknown
% 0.23/0.54 % (20055)Termination phase: Saturation
% 0.23/0.54
% 0.23/0.54 % (20055)Memory used [KB]: 5628
% 0.23/0.54 % (20055)Time elapsed: 0.034 s
% 0.23/0.54 % (20055)Instructions burned: 87 (million)
% 0.23/0.54 % (20055)------------------------------
% 0.23/0.54 % (20055)------------------------------
% 1.48/0.55 % (20065)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on Vampire---4 for (2998ds/448Mi)
% 1.48/0.55 % (20066)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 Vampire---4 for (2998ds/46Mi)
% 1.48/0.55 % (20064)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 Vampire---4 for (2998ds/39Mi)
% 1.48/0.55 % (20067)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on Vampire---4 for (2998ds/98Mi)
% 1.48/0.56 % (20064)Instruction limit reached!
% 1.48/0.56 % (20064)------------------------------
% 1.48/0.56 % (20064)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.48/0.56 % (20064)Termination reason: Unknown
% 1.48/0.56 % (20064)Termination phase: Saturation
% 1.48/0.56
% 1.48/0.56 % (20064)Memory used [KB]: 5628
% 1.48/0.56 % (20064)Time elapsed: 0.010 s
% 1.48/0.56 % (20064)Instructions burned: 41 (million)
% 1.48/0.56 % (20064)------------------------------
% 1.48/0.56 % (20064)------------------------------
% 1.58/0.57 % (20068)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 Vampire---4 for (2998ds/507Mi)
% 1.58/0.57 % (20066)Instruction limit reached!
% 1.58/0.57 % (20066)------------------------------
% 1.58/0.57 % (20066)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.58/0.57 % (20066)Termination reason: Unknown
% 1.58/0.57 % (20066)Termination phase: Saturation
% 1.58/0.57
% 1.58/0.57 % (20066)Memory used [KB]: 5756
% 1.58/0.57 % (20066)Time elapsed: 0.020 s
% 1.58/0.57 % (20066)Instructions burned: 48 (million)
% 1.58/0.57 % (20066)------------------------------
% 1.58/0.57 % (20066)------------------------------
% 1.58/0.57 % (20067)Instruction limit reached!
% 1.58/0.57 % (20067)------------------------------
% 1.58/0.57 % (20067)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.58/0.57 % (20067)Termination reason: Unknown
% 1.58/0.57 % (20067)Termination phase: Saturation
% 1.58/0.57
% 1.58/0.57 % (20067)Memory used [KB]: 1151
% 1.58/0.57 % (20067)Time elapsed: 0.025 s
% 1.58/0.57 % (20067)Instructions burned: 98 (million)
% 1.58/0.57 % (20067)------------------------------
% 1.58/0.57 % (20067)------------------------------
% 1.58/0.58 % (20069)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on Vampire---4 for (2998ds/149Mi)
% 1.58/0.58 % (20068)Refutation not found, incomplete strategy
% 1.58/0.58 % (20068)------------------------------
% 1.58/0.58 % (20068)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.58/0.58 % (20068)Termination reason: Refutation not found, incomplete strategy
% 1.58/0.58
% 1.58/0.58
% 1.58/0.58 % (20068)Memory used [KB]: 5628
% 1.58/0.58 % (20068)Time elapsed: 0.015 s
% 1.58/0.58 % (20068)Instructions burned: 60 (million)
% 1.58/0.58 % (20068)------------------------------
% 1.58/0.58 % (20068)------------------------------
% 1.58/0.58 % (20070)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on Vampire---4 for (2998ds/39Mi)
% 1.58/0.59 % (20042)Instruction limit reached!
% 1.58/0.59 % (20042)------------------------------
% 1.58/0.59 % (20042)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.58/0.59 % (20042)Termination reason: Unknown
% 1.58/0.59 % (20042)Termination phase: Saturation
% 1.58/0.59
% 1.58/0.59 % (20042)Memory used [KB]: 6652
% 1.58/0.59 % (20042)Time elapsed: 0.131 s
% 1.58/0.59 % (20042)Instructions burned: 379 (million)
% 1.58/0.59 % (20042)------------------------------
% 1.58/0.59 % (20042)------------------------------
% 1.58/0.59 % (20071)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 Vampire---4 for (2998ds/6Mi)
% 1.58/0.59 % (20071)Instruction limit reached!
% 1.58/0.59 % (20071)------------------------------
% 1.58/0.59 % (20071)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.58/0.59 % (20071)Termination reason: Unknown
% 1.58/0.59 % (20071)Termination phase: Property scanning
% 1.58/0.59
% 1.58/0.59 % (20071)Memory used [KB]: 1023
% 1.58/0.59 % (20071)Time elapsed: 0.003 s
% 1.58/0.59 % (20071)Instructions burned: 8 (million)
% 1.58/0.59 % (20071)------------------------------
% 1.58/0.59 % (20071)------------------------------
% 1.58/0.59 % (20070)Instruction limit reached!
% 1.58/0.59 % (20070)------------------------------
% 1.58/0.59 % (20070)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.58/0.59 % (20070)Termination reason: Unknown
% 1.58/0.59 % (20070)Termination phase: Saturation
% 1.58/0.59
% 1.58/0.59 % (20070)Memory used [KB]: 5628
% 1.58/0.59 % (20070)Time elapsed: 0.010 s
% 1.58/0.59 % (20070)Instructions burned: 42 (million)
% 1.58/0.59 % (20070)------------------------------
% 1.58/0.59 % (20070)------------------------------
% 1.58/0.60 % (20072)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 Vampire---4 for (2997ds/1087Mi)
% 1.58/0.60 % (20073)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on Vampire---4 for (2997ds/47Mi)
% 1.58/0.60 % (20074)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on Vampire---4 for (2997ds/44Mi)
% 1.58/0.60 % (20072)Refutation not found, incomplete strategy
% 1.58/0.60 % (20072)------------------------------
% 1.58/0.60 % (20072)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.58/0.60 % (20072)Termination reason: Refutation not found, incomplete strategy
% 1.58/0.60
% 1.58/0.60
% 1.58/0.60 % (20072)Memory used [KB]: 5628
% 1.58/0.60 % (20072)Time elapsed: 0.004 s
% 1.58/0.60 % (20072)Instructions burned: 9 (million)
% 1.58/0.60 % (20072)------------------------------
% 1.58/0.60 % (20072)------------------------------
% 1.58/0.61 % (20073)Instruction limit reached!
% 1.58/0.61 % (20073)------------------------------
% 1.58/0.61 % (20073)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.58/0.61 % (20073)Termination reason: Unknown
% 1.58/0.61 % (20073)Termination phase: Saturation
% 1.58/0.61
% 1.58/0.61 % (20073)Memory used [KB]: 5628
% 1.58/0.61 % (20073)Time elapsed: 0.011 s
% 1.58/0.61 % (20075)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 Vampire---4 for (2997ds/432Mi)
% 1.58/0.61 % (20073)Instructions burned: 47 (million)
% 1.58/0.61 % (20073)------------------------------
% 1.58/0.61 % (20073)------------------------------
% 1.58/0.61 % (20074)Instruction limit reached!
% 1.58/0.61 % (20074)------------------------------
% 1.58/0.61 % (20074)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.58/0.61 % (20074)Termination reason: Unknown
% 1.58/0.61 % (20074)Termination phase: Saturation
% 1.58/0.61
% 1.58/0.61 % (20074)Memory used [KB]: 1151
% 1.58/0.61 % (20074)Time elapsed: 0.011 s
% 1.58/0.61 % (20074)Instructions burned: 46 (million)
% 1.58/0.61 % (20074)------------------------------
% 1.58/0.61 % (20074)------------------------------
% 1.58/0.62 % (20079)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on Vampire---4 for (2997ds/62Mi)
% 1.58/0.62 % (20080)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 Vampire---4 for (2997ds/31Mi)
% 1.58/0.63 % (20080)Instruction limit reached!
% 1.58/0.63 % (20080)------------------------------
% 1.58/0.63 % (20080)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.58/0.63 % (20080)Termination reason: Unknown
% 1.58/0.63 % (20080)Termination phase: Saturation
% 1.58/0.63
% 1.58/0.63 % (20080)Memory used [KB]: 5628
% 1.58/0.63 % (20080)Time elapsed: 0.008 s
% 1.58/0.63 % (20080)Instructions burned: 31 (million)
% 1.58/0.63 % (20080)------------------------------
% 1.58/0.63 % (20080)------------------------------
% 1.58/0.63 % (20069)Instruction limit reached!
% 1.58/0.63 % (20069)------------------------------
% 1.58/0.63 % (20069)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.58/0.63 % (20069)Termination reason: Unknown
% 1.58/0.63 % (20069)Termination phase: Saturation
% 1.58/0.63
% 1.58/0.63 % (20069)Memory used [KB]: 6012
% 1.58/0.63 % (20069)Time elapsed: 0.055 s
% 1.58/0.63 % (20069)Instructions burned: 150 (million)
% 1.58/0.63 % (20069)------------------------------
% 1.58/0.63 % (20069)------------------------------
% 1.58/0.63 % (20079)Instruction limit reached!
% 1.58/0.63 % (20079)------------------------------
% 1.58/0.63 % (20079)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.58/0.63 % (20079)Termination reason: Unknown
% 1.58/0.63 % (20079)Termination phase: Saturation
% 1.58/0.63
% 1.58/0.63 % (20079)Memory used [KB]: 5756
% 1.58/0.63 % (20079)Time elapsed: 0.016 s
% 1.58/0.63 % (20079)Instructions burned: 62 (million)
% 1.58/0.63 % (20079)------------------------------
% 1.58/0.63 % (20079)------------------------------
% 1.58/0.63 % (20088)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on Vampire---4 for (2997ds/96Mi)
% 2.09/0.64 % (20090)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 Vampire---4 for (2997ds/453Mi)
% 2.09/0.64 % (20092)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on Vampire---4 for (2997ds/71Mi)
% 2.09/0.66 % (20088)Instruction limit reached!
% 2.09/0.66 % (20088)------------------------------
% 2.09/0.66 % (20088)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.09/0.66 % (20088)Termination reason: Unknown
% 2.09/0.66 % (20088)Termination phase: Saturation
% 2.09/0.66
% 2.09/0.66 % (20088)Memory used [KB]: 5756
% 2.09/0.66 % (20088)Time elapsed: 0.024 s
% 2.09/0.66 % (20088)Instructions burned: 98 (million)
% 2.09/0.66 % (20088)------------------------------
% 2.09/0.66 % (20088)------------------------------
% 2.09/0.66 % (20092)Instruction limit reached!
% 2.09/0.66 % (20092)------------------------------
% 2.09/0.66 % (20092)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.09/0.66 % (20092)Termination reason: Unknown
% 2.09/0.66 % (20092)Termination phase: Saturation
% 2.09/0.66
% 2.09/0.66 % (20092)Memory used [KB]: 5756
% 2.09/0.66 % (20092)Time elapsed: 0.020 s
% 2.09/0.66 % (20092)Instructions burned: 72 (million)
% 2.09/0.66 % (20092)------------------------------
% 2.09/0.66 % (20092)------------------------------
% 2.09/0.67 % (20104)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on Vampire---4 for (2997ds/83Mi)
% 2.23/0.67 % (20104)Refutation not found, incomplete strategy
% 2.23/0.67 % (20104)------------------------------
% 2.23/0.67 % (20104)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.23/0.67 % (20104)Termination reason: Refutation not found, incomplete strategy
% 2.23/0.67
% 2.23/0.67
% 2.23/0.67 % (20104)Memory used [KB]: 5500
% 2.23/0.67 % (20104)Time elapsed: 0.002 s
% 2.23/0.67 % (20104)Instructions burned: 4 (million)
% 2.23/0.67 % (20104)------------------------------
% 2.23/0.67 % (20104)------------------------------
% 2.23/0.67 % (20106)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on Vampire---4 for (2997ds/11Mi)
% 2.23/0.67 % (20106)Instruction limit reached!
% 2.23/0.67 % (20106)------------------------------
% 2.23/0.67 % (20106)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.23/0.67 % (20106)Termination reason: Unknown
% 2.23/0.67 % (20106)Termination phase: Saturation
% 2.23/0.67
% 2.23/0.67 % (20106)Memory used [KB]: 5500
% 2.23/0.67 % (20106)Time elapsed: 0.004 s
% 2.23/0.67 % (20106)Instructions burned: 13 (million)
% 2.23/0.67 % (20106)------------------------------
% 2.23/0.67 % (20106)------------------------------
% 2.23/0.68 % (20110)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on Vampire---4 for (2997ds/41Mi)
% 2.23/0.68 % (20065)Instruction limit reached!
% 2.23/0.68 % (20065)------------------------------
% 2.23/0.68 % (20065)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.23/0.68 % (20065)Termination reason: Unknown
% 2.23/0.68 % (20065)Termination phase: Saturation
% 2.23/0.68
% 2.23/0.68 % (20065)Memory used [KB]: 6012
% 2.23/0.68 % (20065)Time elapsed: 0.131 s
% 2.23/0.68 % (20065)Instructions burned: 451 (million)
% 2.23/0.68 % (20065)------------------------------
% 2.23/0.68 % (20065)------------------------------
% 2.23/0.68 % (20112)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2997ds/6Mi)
% 2.23/0.68 % (20112)Instruction limit reached!
% 2.23/0.68 % (20112)------------------------------
% 2.23/0.68 % (20112)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.23/0.68 % (20112)Termination reason: Unknown
% 2.23/0.68 % (20112)Termination phase: Property scanning
% 2.23/0.68
% 2.23/0.68 % (20112)Memory used [KB]: 1023
% 2.23/0.68 % (20112)Time elapsed: 0.003 s
% 2.23/0.68 % (20112)Instructions burned: 8 (million)
% 2.23/0.68 % (20112)------------------------------
% 2.23/0.68 % (20112)------------------------------
% 2.23/0.68 % (20110)Instruction limit reached!
% 2.23/0.68 % (20110)------------------------------
% 2.23/0.68 % (20110)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.23/0.68 % (20110)Termination reason: Unknown
% 2.23/0.68 % (20110)Termination phase: Saturation
% 2.23/0.68
% 2.23/0.68 % (20110)Memory used [KB]: 5628
% 2.23/0.68 % (20110)Time elapsed: 0.010 s
% 2.23/0.68 % (20110)Instructions burned: 43 (million)
% 2.23/0.68 % (20110)------------------------------
% 2.23/0.68 % (20110)------------------------------
% 2.23/0.68 % (20117)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on Vampire---4 for (2997ds/150Mi)
% 2.23/0.69 % (20121)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on Vampire---4 for (2997ds/343Mi)
% 2.23/0.69 % (20123)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 Vampire---4 for (2997ds/109Mi)
% 2.23/0.70 % (20121)Refutation not found, incomplete strategy
% 2.23/0.70 % (20121)------------------------------
% 2.23/0.70 % (20121)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.23/0.70 % (20121)Termination reason: Refutation not found, incomplete strategy
% 2.23/0.70
% 2.23/0.70
% 2.23/0.70 % (20121)Memory used [KB]: 5628
% 2.23/0.70 % (20121)Time elapsed: 0.007 s
% 2.23/0.70 % (20121)Instructions burned: 22 (million)
% 2.23/0.70 % (20121)------------------------------
% 2.23/0.70 % (20121)------------------------------
% 2.23/0.70 % (20117)Refutation not found, incomplete strategy
% 2.23/0.70 % (20117)------------------------------
% 2.23/0.70 % (20117)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.23/0.70 % (20117)Termination reason: Refutation not found, incomplete strategy
% 2.23/0.70
% 2.23/0.70
% 2.23/0.70 % (20117)Memory used [KB]: 5628
% 2.23/0.70 % (20117)Time elapsed: 0.012 s
% 2.23/0.70 % (20117)Instructions burned: 51 (million)
% 2.23/0.70 % (20117)------------------------------
% 2.23/0.70 % (20117)------------------------------
% 2.23/0.71 % (20128)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 Vampire---4 for (2996ds/253Mi)
% 2.23/0.71 % (20129)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on Vampire---4 for (2996ds/140Mi)
% 2.23/0.71 % (20128)Refutation not found, incomplete strategy
% 2.23/0.71 % (20128)------------------------------
% 2.23/0.71 % (20128)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.23/0.71 % (20128)Termination reason: Refutation not found, incomplete strategy
% 2.23/0.71
% 2.23/0.71
% 2.23/0.71 % (20128)Memory used [KB]: 5500
% 2.23/0.71 % (20128)Time elapsed: 0.002 s
% 2.23/0.71 % (20128)Instructions burned: 3 (million)
% 2.23/0.71 % (20128)------------------------------
% 2.23/0.71 % (20128)------------------------------
% 2.23/0.71 % (20129)Refutation not found, incomplete strategy
% 2.23/0.71 % (20129)------------------------------
% 2.23/0.71 % (20129)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.23/0.71 % (20129)Termination reason: Refutation not found, incomplete strategy
% 2.23/0.71
% 2.23/0.71
% 2.23/0.71 % (20129)Memory used [KB]: 5628
% 2.23/0.71 % (20129)Time elapsed: 0.003 s
% 2.23/0.71 % (20129)Instructions burned: 6 (million)
% 2.23/0.71 % (20129)------------------------------
% 2.23/0.71 % (20129)------------------------------
% 2.23/0.72 % (20134)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 Vampire---4 for (2996ds/614Mi)
% 2.23/0.72 % (20135)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 Vampire---4 for (2996ds/202Mi)
% 2.23/0.72 % (20135)Refutation not found, incomplete strategy
% 2.23/0.72 % (20135)------------------------------
% 2.23/0.72 % (20135)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.23/0.72 % (20135)Termination reason: Refutation not found, incomplete strategy
% 2.23/0.72
% 2.23/0.72
% 2.23/0.72 % (20135)Memory used [KB]: 5500
% 2.23/0.72 % (20135)Time elapsed: 0.002 s
% 2.23/0.72 % (20135)Instructions burned: 3 (million)
% 2.23/0.72 % (20135)------------------------------
% 2.23/0.72 % (20135)------------------------------
% 2.23/0.72 % (20123)Instruction limit reached!
% 2.23/0.72 % (20123)------------------------------
% 2.23/0.72 % (20123)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.23/0.72 % (20123)Termination reason: Unknown
% 2.23/0.72 % (20123)Termination phase: Saturation
% 2.23/0.72
% 2.23/0.72 % (20123)Memory used [KB]: 5756
% 2.23/0.72 % (20123)Time elapsed: 0.028 s
% 2.23/0.72 % (20123)Instructions burned: 111 (million)
% 2.23/0.72 % (20123)------------------------------
% 2.23/0.72 % (20123)------------------------------
% 2.72/0.73 % (20142)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 Vampire---4 for (2996ds/339Mi)
% 2.72/0.73 % (20043)Instruction limit reached!
% 2.72/0.73 % (20043)------------------------------
% 2.72/0.73 % (20043)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.72/0.73 % (20043)Termination reason: Unknown
% 2.72/0.73 % (20043)Termination phase: Saturation
% 2.72/0.73
% 2.72/0.73 % (20043)Memory used [KB]: 6652
% 2.72/0.73 % (20043)Time elapsed: 0.266 s
% 2.72/0.73 % (20043)Instructions burned: 779 (million)
% 2.72/0.73 % (20043)------------------------------
% 2.72/0.73 % (20043)------------------------------
% 2.72/0.73 % (20143)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 Vampire---4 for (2996ds/283Mi)
% 2.72/0.74 % (20147)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on Vampire---4 for (2996ds/134Mi)
% 2.72/0.74 % (20075)Instruction limit reached!
% 2.72/0.74 % (20075)------------------------------
% 2.72/0.74 % (20075)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.72/0.74 % (20075)Termination reason: Unknown
% 2.72/0.74 % (20075)Termination phase: Saturation
% 2.72/0.74
% 2.72/0.74 % (20075)Memory used [KB]: 2046
% 2.72/0.74 % (20075)Time elapsed: 0.135 s
% 2.72/0.74 % (20075)Instructions burned: 433 (million)
% 2.72/0.74 % (20075)------------------------------
% 2.72/0.74 % (20075)------------------------------
% 2.72/0.75 % (20152)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on Vampire---4 for (2996ds/298Mi)
% 2.92/0.76 % (20090)Instruction limit reached!
% 2.92/0.76 % (20090)------------------------------
% 2.92/0.76 % (20090)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.92/0.76 % (20090)Termination reason: Unknown
% 2.92/0.76 % (20090)Termination phase: Saturation
% 2.92/0.76
% 2.92/0.76 % (20090)Memory used [KB]: 6140
% 2.92/0.76 % (20090)Time elapsed: 0.122 s
% 2.92/0.76 % (20090)Instructions burned: 453 (million)
% 2.92/0.76 % (20090)------------------------------
% 2.92/0.76 % (20090)------------------------------
% 2.92/0.77 % (20160)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on Vampire---4 for (2996ds/192Mi)
% 2.92/0.77 % (20045)Instruction limit reached!
% 2.92/0.77 % (20045)------------------------------
% 2.92/0.77 % (20045)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.92/0.77 % (20045)Termination reason: Unknown
% 2.92/0.77 % (20045)Termination phase: Saturation
% 2.92/0.77
% 2.92/0.77 % (20045)Memory used [KB]: 8699
% 2.92/0.77 % (20045)Time elapsed: 0.301 s
% 2.92/0.77 % (20045)Instructions burned: 881 (million)
% 2.92/0.77 % (20045)------------------------------
% 2.92/0.77 % (20045)------------------------------
% 2.92/0.77 % (20147)Instruction limit reached!
% 2.92/0.77 % (20147)------------------------------
% 2.92/0.77 % (20147)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.92/0.77 % (20147)Termination reason: Unknown
% 2.92/0.77 % (20147)Termination phase: Saturation
% 2.92/0.77
% 2.92/0.77 % (20147)Memory used [KB]: 5756
% 2.92/0.77 % (20147)Time elapsed: 0.036 s
% 2.92/0.77 % (20147)Instructions burned: 136 (million)
% 2.92/0.77 % (20147)------------------------------
% 2.92/0.77 % (20147)------------------------------
% 2.92/0.78 % (20171)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 Vampire---4 for (2996ds/258Mi)
% 2.92/0.78 % (20172)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on Vampire---4 for (2996ds/90Mi)
% 2.92/0.79 % (20027)Instruction limit reached!
% 2.92/0.79 % (20027)------------------------------
% 2.92/0.79 % (20027)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.92/0.79 % (20027)Termination reason: Unknown
% 2.92/0.79 % (20027)Termination phase: Saturation
% 2.92/0.79
% 2.92/0.79 % (20027)Memory used [KB]: 8187
% 2.92/0.79 % (20027)Time elapsed: 0.389 s
% 2.92/0.80 % (20027)Instructions burned: 1042 (million)
% 2.92/0.80 % (20027)------------------------------
% 2.92/0.80 % (20027)------------------------------
% 2.92/0.80 % (20189)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on Vampire---4 for (2995ds/231Mi)
% 2.92/0.81 % (20143)Instruction limit reached!
% 2.92/0.81 % (20143)------------------------------
% 2.92/0.81 % (20143)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.92/0.81 % (20143)Termination reason: Unknown
% 2.92/0.81 % (20143)Termination phase: Saturation
% 2.92/0.81
% 2.92/0.81 % (20143)Memory used [KB]: 6012
% 2.92/0.81 % (20143)Time elapsed: 0.103 s
% 2.92/0.81 % (20143)Instructions burned: 284 (million)
% 2.92/0.81 % (20143)------------------------------
% 2.92/0.81 % (20143)------------------------------
% 2.92/0.81 % (20172)Instruction limit reached!
% 2.92/0.81 % (20172)------------------------------
% 2.92/0.81 % (20172)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.92/0.81 % (20172)Termination reason: Unknown
% 2.92/0.81 % (20172)Termination phase: Saturation
% 2.92/0.81
% 2.92/0.81 % (20172)Memory used [KB]: 5884
% 2.92/0.81 % (20172)Time elapsed: 0.035 s
% 2.92/0.81 % (20172)Instructions burned: 90 (million)
% 2.92/0.81 % (20172)------------------------------
% 2.92/0.81 % (20172)------------------------------
% 2.92/0.82 % (20197)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 Vampire---4 for (2995ds/458Mi)
% 2.92/0.82 % (20160)Instruction limit reached!
% 2.92/0.82 % (20160)------------------------------
% 2.92/0.82 % (20160)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.92/0.82 % (20160)Termination reason: Unknown
% 2.92/0.82 % (20160)Termination phase: Saturation
% 2.92/0.82
% 2.92/0.82 % (20160)Memory used [KB]: 6140
% 2.92/0.82 % (20160)Time elapsed: 0.054 s
% 2.92/0.82 % (20160)Instructions burned: 193 (million)
% 2.92/0.82 % (20160)------------------------------
% 2.92/0.82 % (20160)------------------------------
% 2.92/0.82 % (20201)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 Vampire---4 for (2995ds/31Mi)
% 3.35/0.83 % (20142)Instruction limit reached!
% 3.35/0.83 % (20142)------------------------------
% 3.35/0.83 % (20142)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.35/0.83 % (20142)Termination reason: Unknown
% 3.35/0.83 % (20142)Termination phase: Saturation
% 3.35/0.83
% 3.35/0.83 % (20142)Memory used [KB]: 6396
% 3.35/0.83 % (20142)Time elapsed: 0.101 s
% 3.35/0.83 % (20142)Instructions burned: 340 (million)
% 3.35/0.83 % (20142)------------------------------
% 3.35/0.83 % (20142)------------------------------
% 3.35/0.83 % (20206)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on Vampire---4 for (2995ds/297Mi)
% 3.35/0.83 % (20201)Instruction limit reached!
% 3.35/0.83 % (20201)------------------------------
% 3.35/0.83 % (20201)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.35/0.83 % (20201)Termination reason: Unknown
% 3.35/0.83 % (20201)Termination phase: Saturation
% 3.35/0.83
% 3.35/0.83 % (20201)Memory used [KB]: 5628
% 3.35/0.83 % (20201)Time elapsed: 0.008 s
% 3.35/0.83 % (20201)Instructions burned: 31 (million)
% 3.35/0.83 % (20201)------------------------------
% 3.35/0.83 % (20201)------------------------------
% 3.35/0.83 % (20206)Refutation not found, incomplete strategy
% 3.35/0.83 % (20206)------------------------------
% 3.35/0.83 % (20206)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.35/0.83 % (20206)Termination reason: Refutation not found, incomplete strategy
% 3.35/0.83
% 3.35/0.83
% 3.35/0.83 % (20206)Memory used [KB]: 5500
% 3.35/0.83 % (20206)Time elapsed: 0.003 s
% 3.35/0.83 % (20206)Instructions burned: 5 (million)
% 3.35/0.83 % (20206)------------------------------
% 3.35/0.83 % (20206)------------------------------
% 3.35/0.84 % (20215)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 Vampire---4 for (2995ds/987Mi)
% 3.35/0.84 % (20217)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on Vampire---4 for (2995ds/182Mi)
% 3.35/0.84 % (20152)Instruction limit reached!
% 3.35/0.84 % (20152)------------------------------
% 3.35/0.84 % (20152)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.35/0.84 % (20152)Termination reason: Unknown
% 3.35/0.84 % (20152)Termination phase: Saturation
% 3.35/0.84
% 3.35/0.84 % (20152)Memory used [KB]: 6396
% 3.35/0.84 % (20152)Time elapsed: 0.089 s
% 3.35/0.84 % (20152)Instructions burned: 300 (million)
% 3.35/0.84 % (20152)------------------------------
% 3.35/0.84 % (20152)------------------------------
% 3.35/0.84 % (20219)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on Vampire---4 for (2995ds/182Mi)
% 3.35/0.85 % (20225)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on Vampire---4 for (2995ds/154Mi)
% 3.35/0.85 % (20171)Instruction limit reached!
% 3.35/0.85 % (20171)------------------------------
% 3.35/0.85 % (20171)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.35/0.85 % (20171)Termination reason: Unknown
% 3.35/0.85 % (20171)Termination phase: Saturation
% 3.35/0.85
% 3.35/0.85 % (20171)Memory used [KB]: 6268
% 3.35/0.85 % (20171)Time elapsed: 0.075 s
% 3.35/0.85 % (20171)Instructions burned: 259 (million)
% 3.35/0.85 % (20171)------------------------------
% 3.35/0.85 % (20171)------------------------------
% 3.35/0.86 % (20229)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 Vampire---4 for (2995ds/79Mi)
% 3.67/0.87 % (20134)Instruction limit reached!
% 3.67/0.87 % (20134)------------------------------
% 3.67/0.87 % (20134)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.67/0.87 % (20134)Termination reason: Unknown
% 3.67/0.87 % (20134)Termination phase: Saturation
% 3.67/0.87
% 3.67/0.87 % (20134)Memory used [KB]: 6908
% 3.67/0.87 % (20134)Time elapsed: 0.160 s
% 3.67/0.87 % (20134)Instructions burned: 617 (million)
% 3.67/0.87 % (20134)------------------------------
% 3.67/0.87 % (20134)------------------------------
% 3.67/0.88 % (20229)Instruction limit reached!
% 3.67/0.88 % (20229)------------------------------
% 3.67/0.88 % (20229)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.67/0.88 % (20229)Termination reason: Unknown
% 3.67/0.88 % (20229)Termination phase: Saturation
% 3.67/0.88
% 3.67/0.88 % (20229)Memory used [KB]: 5628
% 3.67/0.88 % (20229)Time elapsed: 0.019 s
% 3.67/0.88 % (20229)Instructions burned: 79 (million)
% 3.67/0.88 % (20229)------------------------------
% 3.67/0.88 % (20229)------------------------------
% 3.67/0.88 % (20244)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 Vampire---4 for (2995ds/216Mi)
% 3.67/0.89 % (20189)Instruction limit reached!
% 3.67/0.89 % (20189)------------------------------
% 3.67/0.89 % (20189)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.67/0.89 % (20189)Termination reason: Unknown
% 3.67/0.89 % (20189)Termination phase: Saturation
% 3.67/0.89
% 3.67/0.89 % (20189)Memory used [KB]: 6652
% 3.67/0.89 % (20189)Time elapsed: 0.083 s
% 3.67/0.89 % (20189)Instructions burned: 231 (million)
% 3.67/0.89 % (20189)------------------------------
% 3.67/0.89 % (20189)------------------------------
% 3.67/0.89 % (20217)Instruction limit reached!
% 3.67/0.89 % (20217)------------------------------
% 3.67/0.89 % (20217)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.67/0.89 % (20246)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on Vampire---4 for (2995ds/114Mi)
% 3.67/0.89 % (20217)Termination reason: Unknown
% 3.67/0.89 % (20217)Termination phase: Saturation
% 3.67/0.89
% 3.67/0.89 % (20217)Memory used [KB]: 6140
% 3.67/0.89 % (20217)Time elapsed: 0.051 s
% 3.67/0.89 % (20217)Instructions burned: 182 (million)
% 3.67/0.89 % (20217)------------------------------
% 3.67/0.89 % (20217)------------------------------
% 3.67/0.89 % (20225)Instruction limit reached!
% 3.67/0.89 % (20225)------------------------------
% 3.67/0.89 % (20225)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.67/0.89 % (20225)Termination reason: Unknown
% 3.67/0.89 % (20225)Termination phase: Saturation
% 3.67/0.89
% 3.67/0.89 % (20225)Memory used [KB]: 5884
% 3.67/0.89 % (20225)Time elapsed: 0.042 s
% 3.67/0.89 % (20225)Instructions burned: 156 (million)
% 3.67/0.89 % (20225)------------------------------
% 3.67/0.89 % (20225)------------------------------
% 3.67/0.89 % (20248)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on Vampire---4 for (2994ds/922Mi)
% 3.67/0.90 % (20249)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on Vampire---4 for (2994ds/182Mi)
% 3.67/0.90 % (20252)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on Vampire---4 for (2994ds/164Mi)
% 3.67/0.90 % (20252)Refutation not found, incomplete strategy
% 3.67/0.90 % (20252)------------------------------
% 3.67/0.90 % (20252)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.67/0.90 % (20252)Termination reason: Refutation not found, incomplete strategy
% 3.67/0.90
% 3.67/0.90
% 3.67/0.90 % (20252)Memory used [KB]: 1023
% 3.67/0.90 % (20252)Time elapsed: 0.003 s
% 3.67/0.90 % (20252)Instructions burned: 3 (million)
% 3.67/0.90 % (20252)------------------------------
% 3.67/0.90 % (20252)------------------------------
% 3.67/0.90 % (20246)Refutation not found, incomplete strategy
% 3.67/0.90 % (20246)------------------------------
% 3.67/0.90 % (20246)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.67/0.90 % (20246)Termination reason: Refutation not found, incomplete strategy
% 3.67/0.90
% 3.67/0.90
% 3.67/0.90 % (20246)Memory used [KB]: 5628
% 3.67/0.90 % (20246)Time elapsed: 0.013 s
% 3.67/0.90 % (20246)Instructions burned: 56 (million)
% 3.67/0.90 % (20246)------------------------------
% 3.67/0.90 % (20246)------------------------------
% 3.67/0.90 % (20219)Instruction limit reached!
% 3.67/0.90 % (20219)------------------------------
% 3.67/0.90 % (20219)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.67/0.90 % (20219)Termination reason: Unknown
% 3.67/0.90 % (20219)Termination phase: Saturation
% 3.67/0.90
% 3.67/0.90 % (20219)Memory used [KB]: 5884
% 3.67/0.90 % (20219)Time elapsed: 0.065 s
% 3.67/0.90 % (20219)Instructions burned: 182 (million)
% 3.67/0.90 % (20219)------------------------------
% 3.67/0.90 % (20219)------------------------------
% 3.67/0.91 % (20244)Refutation not found, incomplete strategy
% 3.67/0.91 % (20244)------------------------------
% 3.67/0.91 % (20244)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.67/0.91 % (20244)Termination reason: Refutation not found, incomplete strategy
% 3.67/0.91
% 3.67/0.91
% 3.67/0.91 % (20244)Memory used [KB]: 5628
% 3.67/0.91 % (20244)Time elapsed: 0.024 s
% 3.67/0.91 % (20244)Instructions burned: 101 (million)
% 3.67/0.91 % (20244)------------------------------
% 3.67/0.91 % (20244)------------------------------
% 3.67/0.91 % (20257)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 Vampire---4 for (2994ds/50Mi)
% 3.67/0.91 % (20258)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on Vampire---4 for (2994ds/368Mi)
% 3.67/0.91 % (20260)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on Vampire---4 for (2994ds/1021Mi)
% 3.67/0.91 % (20261)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 Vampire---4 for (2994ds/267Mi)
% 3.67/0.92 % (20257)Instruction limit reached!
% 3.67/0.92 % (20257)------------------------------
% 3.67/0.92 % (20257)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.67/0.92 % (20257)Termination reason: Unknown
% 3.67/0.92 % (20257)Termination phase: Saturation
% 3.67/0.92
% 3.67/0.92 % (20257)Memory used [KB]: 10106
% 3.67/0.92 % (20257)Time elapsed: 0.012 s
% 3.67/0.92 % (20257)Instructions burned: 52 (million)
% 3.67/0.92 % (20257)------------------------------
% 3.67/0.92 % (20257)------------------------------
% 3.67/0.92 % (20267)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on Vampire---4 for (2994ds/204Mi)
% 4.21/0.94 % (20249)Instruction limit reached!
% 4.21/0.94 % (20249)------------------------------
% 4.21/0.94 % (20249)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.21/0.94 % (20249)Termination reason: Unknown
% 4.21/0.94 % (20249)Termination phase: Saturation
% 4.21/0.94
% 4.21/0.94 % (20249)Memory used [KB]: 5756
% 4.21/0.94 % (20249)Time elapsed: 0.047 s
% 4.21/0.94 % (20249)Instructions burned: 185 (million)
% 4.21/0.94 % (20249)------------------------------
% 4.21/0.94 % (20249)------------------------------
% 4.21/0.94 % (20197)Instruction limit reached!
% 4.21/0.94 % (20197)------------------------------
% 4.21/0.94 % (20197)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.21/0.94 % (20197)Termination reason: Unknown
% 4.21/0.94 % (20197)Termination phase: Saturation
% 4.21/0.94
% 4.21/0.94 % (20197)Memory used [KB]: 7291
% 4.21/0.94 % (20197)Time elapsed: 0.127 s
% 4.21/0.94 % (20197)Instructions burned: 458 (million)
% 4.21/0.94 % (20197)------------------------------
% 4.21/0.94 % (20197)------------------------------
% 4.21/0.95 % (20272)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 Vampire---4 for (2994ds/26Mi)
% 4.21/0.95 % (20273)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 Vampire---4 for (2994ds/53Mi)
% 4.21/0.96 % (20272)Instruction limit reached!
% 4.21/0.96 % (20272)------------------------------
% 4.21/0.96 % (20272)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.21/0.96 % (20272)Termination reason: Unknown
% 4.21/0.96 % (20272)Termination phase: Saturation
% 4.21/0.96
% 4.21/0.96 % (20272)Memory used [KB]: 5756
% 4.21/0.96 % (20272)Time elapsed: 0.010 s
% 4.21/0.96 % (20272)Instructions burned: 26 (million)
% 4.21/0.96 % (20272)------------------------------
% 4.21/0.96 % (20272)------------------------------
% 4.21/0.96 % (20273)Instruction limit reached!
% 4.21/0.96 % (20273)------------------------------
% 4.21/0.96 % (20273)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.21/0.96 % (20273)Termination reason: Unknown
% 4.21/0.96 % (20273)Termination phase: Saturation
% 4.21/0.96
% 4.21/0.96 % (20273)Memory used [KB]: 5628
% 4.21/0.96 % (20273)Time elapsed: 0.012 s
% 4.21/0.96 % (20273)Instructions burned: 53 (million)
% 4.21/0.96 % (20273)------------------------------
% 4.21/0.96 % (20273)------------------------------
% 4.21/0.96 % (20274)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 Vampire---4 for (2994ds/4436Mi)
% 4.44/0.97 % (20275)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on Vampire---4 for (2994ds/1539Mi)
% 4.44/0.97 % (20274)Refutation not found, incomplete strategy
% 4.44/0.97 % (20274)------------------------------
% 4.44/0.97 % (20274)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.44/0.97 % (20274)Termination reason: Refutation not found, incomplete strategy
% 4.44/0.97
% 4.44/0.97
% 4.44/0.97 % (20274)Memory used [KB]: 5628
% 4.44/0.97 % (20274)Time elapsed: 0.004 s
% 4.44/0.97 % (20274)Instructions burned: 9 (million)
% 4.44/0.97 % (20274)------------------------------
% 4.44/0.97 % (20274)------------------------------
% 4.44/0.98 % (20279)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 Vampire---4 for (2994ds/408Mi)
% 4.44/0.98 % (20267)Instruction limit reached!
% 4.44/0.98 % (20267)------------------------------
% 4.44/0.98 % (20267)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.44/0.98 % (20267)Termination reason: Unknown
% 4.44/0.98 % (20267)Termination phase: Saturation
% 4.44/0.98
% 4.44/0.98 % (20267)Memory used [KB]: 6140
% 4.44/0.98 % (20267)Time elapsed: 0.052 s
% 4.44/0.98 % (20267)Instructions burned: 204 (million)
% 4.44/0.98 % (20267)------------------------------
% 4.44/0.98 % (20267)------------------------------
% 4.44/0.98 % (20261)Instruction limit reached!
% 4.44/0.98 % (20261)------------------------------
% 4.44/0.98 % (20261)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.44/0.98 % (20261)Termination reason: Unknown
% 4.44/0.98 % (20261)Termination phase: Saturation
% 4.44/0.98
% 4.44/0.98 % (20261)Memory used [KB]: 6012
% 4.44/0.98 % (20261)Time elapsed: 0.069 s
% 4.44/0.98 % (20261)Instructions burned: 268 (million)
% 4.44/0.98 % (20261)------------------------------
% 4.44/0.98 % (20261)------------------------------
% 4.44/0.98 % (20285)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 Vampire---4 for (2994ds/5205Mi)
% 4.44/0.99 % (20288)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 Vampire---4 for (2994ds/1913Mi)
% 4.44/1.00 % (20288)Refutation not found, incomplete strategy
% 4.44/1.00 % (20288)------------------------------
% 4.44/1.00 % (20288)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.44/1.00 % (20288)Termination reason: Refutation not found, incomplete strategy
% 4.44/1.00
% 4.44/1.00
% 4.44/1.00 % (20288)Memory used [KB]: 1151
% 4.44/1.00 % (20288)Time elapsed: 0.010 s
% 4.44/1.00 % (20288)Instructions burned: 37 (million)
% 4.44/1.00 % (20288)------------------------------
% 4.44/1.00 % (20288)------------------------------
% 4.44/1.00 % (20258)Instruction limit reached!
% 4.44/1.00 % (20258)------------------------------
% 4.44/1.00 % (20258)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.44/1.00 % (20258)Termination reason: Unknown
% 4.44/1.00 % (20258)Termination phase: Saturation
% 4.44/1.00
% 4.44/1.00 % (20258)Memory used [KB]: 6908
% 4.44/1.00 % (20258)Time elapsed: 0.096 s
% 4.44/1.00 % (20258)Instructions burned: 371 (million)
% 4.44/1.00 % (20258)------------------------------
% 4.44/1.00 % (20258)------------------------------
% 4.44/1.01 % (20293)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on Vampire---4 for (2993ds/4350Mi)
% 4.44/1.01 % (20295)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 Vampire---4 for (2993ds/68Mi)
% 4.44/1.02 % (20295)Instruction limit reached!
% 4.44/1.02 % (20295)------------------------------
% 4.44/1.02 % (20295)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.44/1.02 % (20295)Termination reason: Unknown
% 4.44/1.02 % (20295)Termination phase: Saturation
% 4.44/1.02
% 4.44/1.02 % (20295)Memory used [KB]: 5628
% 4.44/1.02 % (20295)Time elapsed: 0.016 s
% 4.44/1.02 % (20295)Instructions burned: 72 (million)
% 4.44/1.02 % (20295)------------------------------
% 4.44/1.02 % (20295)------------------------------
% 4.72/1.03 % (20304)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on Vampire---4 for (2993ds/358Mi)
% 4.72/1.04 % (20304)Refutation not found, incomplete strategy
% 4.72/1.04 % (20304)------------------------------
% 4.72/1.04 % (20304)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.72/1.04 % (20304)Termination reason: Refutation not found, incomplete strategy
% 4.72/1.04
% 4.72/1.04
% 4.72/1.04 % (20304)Memory used [KB]: 5628
% 4.72/1.04 % (20304)Time elapsed: 0.009 s
% 4.72/1.04 % (20304)Instructions burned: 32 (million)
% 4.72/1.04 % (20304)------------------------------
% 4.72/1.04 % (20304)------------------------------
% 4.72/1.05 % (20311)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 Vampire---4 for (2993ds/31Mi)
% 4.72/1.05 % (20311)Instruction limit reached!
% 4.72/1.05 % (20311)------------------------------
% 4.72/1.05 % (20311)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.72/1.05 % (20311)Termination reason: Unknown
% 4.72/1.05 % (20311)Termination phase: Saturation
% 4.72/1.05
% 4.72/1.05 % (20311)Memory used [KB]: 5628
% 4.72/1.05 % (20311)Time elapsed: 0.008 s
% 4.72/1.05 % (20311)Instructions burned: 33 (million)
% 4.72/1.05 % (20311)------------------------------
% 4.72/1.05 % (20311)------------------------------
% 5.65/1.07 % (20315)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on Vampire---4 for (2993ds/279Mi)
% 5.65/1.10 % (20279)Instruction limit reached!
% 5.65/1.10 % (20279)------------------------------
% 5.65/1.10 % (20279)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.65/1.10 % (20279)Termination reason: Unknown
% 5.65/1.10 % (20279)Termination phase: Saturation
% 5.65/1.10
% 5.65/1.10 % (20279)Memory used [KB]: 7036
% 5.65/1.10 % (20279)Time elapsed: 0.128 s
% 5.65/1.10 % (20279)Instructions burned: 409 (million)
% 5.65/1.10 % (20279)------------------------------
% 5.65/1.10 % (20279)------------------------------
% 5.65/1.11 % (20343)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on Vampire---4 for (2992ds/258Mi)
% 5.65/1.13 % (20215)Instruction limit reached!
% 5.65/1.13 % (20215)------------------------------
% 5.65/1.13 % (20215)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.65/1.13 % (20215)Termination reason: Unknown
% 5.65/1.13 % (20215)Termination phase: Saturation
% 5.65/1.13
% 5.65/1.13 % (20215)Memory used [KB]: 7291
% 5.65/1.13 % (20215)Time elapsed: 0.293 s
% 5.65/1.13 % (20215)Instructions burned: 989 (million)
% 5.65/1.13 % (20215)------------------------------
% 5.65/1.13 % (20215)------------------------------
% 5.65/1.14 % (20355)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 Vampire---4 for (2992ds/26Mi)
% 6.17/1.14 % (20248)Instruction limit reached!
% 6.17/1.14 % (20248)------------------------------
% 6.17/1.14 % (20248)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.17/1.14 % (20248)Termination reason: Unknown
% 6.17/1.14 % (20248)Termination phase: Saturation
% 6.17/1.14
% 6.17/1.14 % (20248)Memory used [KB]: 9210
% 6.17/1.14 % (20248)Time elapsed: 0.251 s
% 6.17/1.14 % (20248)Instructions burned: 924 (million)
% 6.17/1.14 % (20248)------------------------------
% 6.17/1.14 % (20248)------------------------------
% 6.17/1.15 % (20355)Instruction limit reached!
% 6.17/1.15 % (20355)------------------------------
% 6.17/1.15 % (20355)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.17/1.15 % (20355)Termination reason: Unknown
% 6.17/1.15 % (20355)Termination phase: Saturation
% 6.17/1.15
% 6.17/1.15 % (20355)Memory used [KB]: 5756
% 6.17/1.15 % (20355)Time elapsed: 0.011 s
% 6.17/1.15 % (20355)Instructions burned: 28 (million)
% 6.17/1.15 % (20355)------------------------------
% 6.17/1.15 % (20355)------------------------------
% 6.17/1.15 % (20315)Instruction limit reached!
% 6.17/1.15 % (20315)------------------------------
% 6.17/1.15 % (20315)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.17/1.15 % (20315)Termination reason: Unknown
% 6.17/1.15 % (20315)Termination phase: Saturation
% 6.17/1.15
% 6.17/1.15 % (20315)Memory used [KB]: 5884
% 6.17/1.15 % (20315)Time elapsed: 0.078 s
% 6.17/1.15 % (20315)Instructions burned: 279 (million)
% 6.17/1.15 % (20315)------------------------------
% 6.17/1.15 % (20315)------------------------------
% 6.17/1.15 % (20359)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 Vampire---4 for (2992ds/995Mi)
% 6.17/1.15 % (20360)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 Vampire---4 for (2992ds/373Mi)
% 6.17/1.16 % (20361)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 Vampire---4 for (2992ds/253Mi)
% 6.38/1.19 % (20260)Instruction limit reached!
% 6.38/1.19 % (20260)------------------------------
% 6.38/1.19 % (20260)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.38/1.19 % (20260)Termination reason: Unknown
% 6.38/1.19 % (20260)Termination phase: Saturation
% 6.38/1.19
% 6.38/1.19 % (20260)Memory used [KB]: 9594
% 6.38/1.19 % (20260)Time elapsed: 0.280 s
% 6.38/1.19 % (20260)Instructions burned: 1021 (million)
% 6.38/1.19 % (20260)------------------------------
% 6.38/1.19 % (20260)------------------------------
% 6.38/1.19 % (20343)Instruction limit reached!
% 6.38/1.19 % (20343)------------------------------
% 6.38/1.19 % (20343)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.38/1.19 % (20343)Termination reason: Unknown
% 6.38/1.19 % (20343)Termination phase: Saturation
% 6.38/1.19
% 6.38/1.19 % (20343)Memory used [KB]: 6268
% 6.38/1.19 % (20343)Time elapsed: 0.086 s
% 6.38/1.19 % (20343)Instructions burned: 259 (million)
% 6.38/1.19 % (20343)------------------------------
% 6.38/1.19 % (20343)------------------------------
% 6.38/1.20 % (20362)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on Vampire---4 for (2991ds/832Mi)
% 6.38/1.20 % (20362)Refutation not found, incomplete strategy
% 6.38/1.20 % (20362)------------------------------
% 6.38/1.20 % (20362)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.38/1.20 % (20362)Termination reason: Refutation not found, incomplete strategy
% 6.38/1.20
% 6.38/1.20
% 6.38/1.20 % (20362)Memory used [KB]: 5500
% 6.38/1.20 % (20362)Time elapsed: 0.003 s
% 6.38/1.20 % (20362)Instructions burned: 3 (million)
% 6.38/1.20 % (20362)------------------------------
% 6.38/1.20 % (20362)------------------------------
% 6.38/1.20 % (20363)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on Vampire---4 for (2991ds/668Mi)
% 6.38/1.21 % (20364)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 Vampire---4 for (2991ds/40Mi)
% 6.38/1.22 % (20364)Instruction limit reached!
% 6.38/1.22 % (20364)------------------------------
% 6.38/1.22 % (20364)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.38/1.22 % (20364)Termination reason: Unknown
% 6.38/1.22 % (20364)Termination phase: Saturation
% 6.38/1.22
% 6.38/1.22 % (20364)Memory used [KB]: 5628
% 6.38/1.22 % (20364)Time elapsed: 0.010 s
% 6.38/1.22 % (20364)Instructions burned: 44 (million)
% 6.38/1.22 % (20364)------------------------------
% 6.38/1.22 % (20364)------------------------------
% 6.38/1.22 % (20365)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on Vampire---4 for (2991ds/294Mi)
% 6.38/1.23 % (20361)Instruction limit reached!
% 6.38/1.23 % (20361)------------------------------
% 6.38/1.23 % (20361)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.38/1.23 % (20361)Termination reason: Unknown
% 6.38/1.23 % (20361)Termination phase: Saturation
% 6.38/1.23
% 6.38/1.23 % (20361)Memory used [KB]: 6140
% 6.38/1.23 % (20361)Time elapsed: 0.070 s
% 6.38/1.23 % (20361)Instructions burned: 253 (million)
% 6.38/1.23 % (20361)------------------------------
% 6.38/1.23 % (20361)------------------------------
% 6.76/1.23 % (20366)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on Vampire---4 for (2991ds/187Mi)
% 6.76/1.25 % (20360)Instruction limit reached!
% 6.76/1.25 % (20360)------------------------------
% 6.76/1.25 % (20360)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.76/1.25 % (20360)Termination reason: Unknown
% 6.76/1.25 % (20360)Termination phase: Saturation
% 6.76/1.25
% 6.76/1.25 % (20360)Memory used [KB]: 6908
% 6.76/1.25 % (20360)Time elapsed: 0.098 s
% 6.76/1.25 % (20360)Instructions burned: 374 (million)
% 6.76/1.25 % (20360)------------------------------
% 6.76/1.25 % (20360)------------------------------
% 6.93/1.26 % (20367)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on Vampire---4 for (2991ds/371Mi)
% 6.93/1.26 % (20367)Refutation not found, incomplete strategy
% 6.93/1.26 % (20367)------------------------------
% 6.93/1.26 % (20367)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.93/1.26 % (20367)Termination reason: Refutation not found, incomplete strategy
% 6.93/1.26
% 6.93/1.26
% 6.93/1.26 % (20367)Memory used [KB]: 5628
% 6.93/1.26 % (20367)Time elapsed: 0.007 s
% 6.93/1.26 % (20367)Instructions burned: 23 (million)
% 6.93/1.26 % (20367)------------------------------
% 6.93/1.26 % (20367)------------------------------
% 6.93/1.27 % (20368)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on Vampire---4 for (2991ds/1827Mi)
% 6.93/1.28 % (20366)Instruction limit reached!
% 6.93/1.28 % (20366)------------------------------
% 6.93/1.28 % (20366)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.93/1.28 % (20366)Termination reason: Unknown
% 6.93/1.28 % (20366)Termination phase: Saturation
% 6.93/1.28
% 6.93/1.28 % (20366)Memory used [KB]: 6012
% 6.93/1.28 % (20366)Time elapsed: 0.048 s
% 6.93/1.28 % (20366)Instructions burned: 189 (million)
% 6.93/1.28 % (20366)------------------------------
% 6.93/1.28 % (20366)------------------------------
% 6.93/1.29 % (20369)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on Vampire---4 for (2990ds/70Mi)
% 6.93/1.29 % (20365)Instruction limit reached!
% 6.93/1.29 % (20365)------------------------------
% 6.93/1.29 % (20365)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.93/1.29 % (20365)Termination reason: Unknown
% 6.93/1.29 % (20365)Termination phase: Saturation
% 6.93/1.29
% 6.93/1.30 % (20365)Memory used [KB]: 5756
% 6.93/1.30 % (20365)Time elapsed: 0.072 s
% 6.93/1.30 % (20365)Instructions burned: 297 (million)
% 6.93/1.30 % (20365)------------------------------
% 6.93/1.30 % (20365)------------------------------
% 6.93/1.30 % (20370)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 Vampire---4 for (2990ds/316Mi)
% 6.93/1.30 % (20369)Instruction limit reached!
% 6.93/1.30 % (20369)------------------------------
% 6.93/1.30 % (20369)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.93/1.30 % (20369)Termination reason: Unknown
% 6.93/1.30 % (20369)Termination phase: Saturation
% 6.93/1.30
% 6.93/1.30 % (20369)Memory used [KB]: 1151
% 6.93/1.30 % (20369)Time elapsed: 0.017 s
% 6.93/1.30 % (20369)Instructions burned: 71 (million)
% 6.93/1.30 % (20369)------------------------------
% 6.93/1.30 % (20369)------------------------------
% 6.93/1.31 % (20371)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on Vampire---4 for (2990ds/932Mi)
% 7.27/1.35 % (20363)Instruction limit reached!
% 7.27/1.35 % (20363)------------------------------
% 7.27/1.35 % (20363)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.27/1.35 % (20363)Termination reason: Unknown
% 7.27/1.35 % (20363)Termination phase: Saturation
% 7.27/1.35
% 7.27/1.35 % (20363)Memory used [KB]: 10490
% 7.27/1.35 % (20363)Time elapsed: 0.151 s
% 7.27/1.35 % (20363)Instructions burned: 670 (million)
% 7.27/1.35 % (20363)------------------------------
% 7.27/1.35 % (20363)------------------------------
% 7.56/1.36 % (20372)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 Vampire---4 for (2990ds/4714Mi)
% 7.56/1.38 % (20370)Instruction limit reached!
% 7.56/1.38 % (20370)------------------------------
% 7.56/1.38 % (20370)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.56/1.38 % (20370)Termination reason: Unknown
% 7.56/1.38 % (20370)Termination phase: Saturation
% 7.56/1.38
% 7.56/1.38 % (20370)Memory used [KB]: 6012
% 7.56/1.38 % (20370)Time elapsed: 0.081 s
% 7.56/1.38 % (20370)Instructions burned: 316 (million)
% 7.56/1.38 % (20370)------------------------------
% 7.56/1.38 % (20370)------------------------------
% 7.56/1.39 % (20359)Instruction limit reached!
% 7.56/1.39 % (20359)------------------------------
% 7.56/1.39 % (20359)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.56/1.39 % (20359)Termination reason: Unknown
% 7.56/1.39 % (20359)Termination phase: Saturation
% 7.56/1.39
% 7.56/1.39 % (20359)Memory used [KB]: 6268
% 7.56/1.39 % (20359)Time elapsed: 0.238 s
% 7.56/1.39 % (20359)Instructions burned: 995 (million)
% 7.56/1.39 % (20359)------------------------------
% 7.56/1.39 % (20359)------------------------------
% 7.56/1.39 % (20373)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on Vampire---4 for (2989ds/8250Mi)
% 7.56/1.40 % (20374)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 Vampire---4 for (2989ds/770Mi)
% 7.56/1.40 % (20374)Refutation not found, incomplete strategy
% 7.56/1.40 % (20374)------------------------------
% 7.56/1.40 % (20374)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.56/1.40 % (20374)Termination reason: Refutation not found, incomplete strategy
% 7.56/1.40
% 7.56/1.40
% 7.56/1.40 % (20374)Memory used [KB]: 5500
% 7.56/1.40 % (20374)Time elapsed: 0.002 s
% 7.56/1.40 % (20374)Instructions burned: 3 (million)
% 7.56/1.40 % (20374)------------------------------
% 7.56/1.40 % (20374)------------------------------
% 7.56/1.40 % (20275)Instruction limit reached!
% 7.56/1.40 % (20275)------------------------------
% 7.56/1.40 % (20275)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.56/1.40 % (20275)Termination reason: Unknown
% 7.56/1.40 % (20275)Termination phase: Saturation
% 7.56/1.40
% 7.56/1.40 % (20275)Memory used [KB]: 10874
% 7.56/1.40 % (20275)Time elapsed: 0.437 s
% 7.56/1.40 % (20275)Instructions burned: 1541 (million)
% 7.56/1.40 % (20275)------------------------------
% 7.56/1.40 % (20275)------------------------------
% 7.56/1.41 % (20375)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on Vampire---4 for (2989ds/794Mi)
% 7.56/1.41 % (20376)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on Vampire---4 for (2989ds/464Mi)
% 7.56/1.42 % (20375)Refutation not found, incomplete strategy
% 7.56/1.42 % (20375)------------------------------
% 7.56/1.42 % (20375)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.56/1.42 % (20375)Termination reason: Refutation not found, incomplete strategy
% 7.56/1.42
% 7.56/1.42
% 7.56/1.42 % (20375)Memory used [KB]: 1151
% 7.56/1.42 % (20375)Time elapsed: 0.013 s
% 7.56/1.42 % (20375)Instructions burned: 57 (million)
% 7.56/1.42 % (20375)------------------------------
% 7.56/1.42 % (20375)------------------------------
% 7.56/1.43 % (20377)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 Vampire---4 for (2989ds/1376Mi)
% 8.21/1.53 % (20376)Instruction limit reached!
% 8.21/1.53 % (20376)------------------------------
% 8.21/1.53 % (20376)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.21/1.53 % (20376)Termination reason: Unknown
% 8.21/1.53 % (20376)Termination phase: Saturation
% 8.21/1.53
% 8.21/1.53 % (20376)Memory used [KB]: 6012
% 8.21/1.53 % (20376)Time elapsed: 0.119 s
% 8.21/1.53 % (20376)Instructions burned: 465 (million)
% 8.21/1.53 % (20376)------------------------------
% 8.21/1.53 % (20376)------------------------------
% 8.45/1.54 % (20378)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on Vampire---4 for (2988ds/906Mi)
% 8.48/1.58 % (20371)Instruction limit reached!
% 8.48/1.58 % (20371)------------------------------
% 8.48/1.58 % (20371)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.48/1.58 % (20371)Termination reason: Unknown
% 8.48/1.58 % (20371)Termination phase: Saturation
% 8.48/1.58
% 8.48/1.58 % (20371)Memory used [KB]: 7164
% 8.48/1.58 % (20371)Time elapsed: 0.266 s
% 8.48/1.58 % (20371)Instructions burned: 934 (million)
% 8.48/1.58 % (20371)------------------------------
% 8.48/1.58 % (20371)------------------------------
% 8.48/1.58 % (20379)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on Vampire---4 for (2988ds/434Mi)
% 8.48/1.59 % (20379)Refutation not found, incomplete strategy
% 8.48/1.59 % (20379)------------------------------
% 8.48/1.59 % (20379)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.48/1.59 % (20379)Termination reason: Refutation not found, incomplete strategy
% 8.48/1.59
% 8.48/1.59
% 8.48/1.59 % (20379)Memory used [KB]: 5500
% 8.48/1.59 % (20379)Time elapsed: 0.002 s
% 8.48/1.59 % (20379)Instructions burned: 3 (million)
% 8.48/1.59 % (20379)------------------------------
% 8.48/1.59 % (20379)------------------------------
% 8.48/1.59 % (20380)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 Vampire---4 for (2988ds/865Mi)
% 11.28/1.80 % (20378)Instruction limit reached!
% 11.28/1.80 % (20378)------------------------------
% 11.28/1.80 % (20378)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.28/1.80 % (20378)Termination reason: Unknown
% 11.28/1.80 % (20378)Termination phase: Saturation
% 11.28/1.80
% 11.28/1.80 % (20378)Memory used [KB]: 8827
% 11.28/1.80 % (20378)Time elapsed: 0.256 s
% 11.28/1.80 % (20378)Instructions burned: 909 (million)
% 11.28/1.80 % (20378)------------------------------
% 11.28/1.80 % (20378)------------------------------
% 11.28/1.81 % (20377)Instruction limit reached!
% 11.28/1.81 % (20377)------------------------------
% 11.28/1.81 % (20377)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.28/1.81 % (20377)Termination reason: Unknown
% 11.28/1.81 % (20377)Termination phase: Saturation
% 11.28/1.81
% 11.28/1.81 % (20377)Memory used [KB]: 8315
% 11.28/1.81 % (20377)Time elapsed: 0.383 s
% 11.28/1.81 % (20377)Instructions burned: 1378 (million)
% 11.28/1.81 % (20377)------------------------------
% 11.28/1.81 % (20377)------------------------------
% 11.28/1.81 % (20381)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 Vampire---4 for (2985ds/593Mi)
% 11.28/1.82 % (20382)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on Vampire---4 for (2985ds/443Mi)
% 11.63/1.82 % (20368)Instruction limit reached!
% 11.63/1.82 % (20368)------------------------------
% 11.63/1.82 % (20368)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.63/1.82 % (20368)Termination reason: Unknown
% 11.63/1.82 % (20368)Termination phase: Saturation
% 11.63/1.82
% 11.63/1.82 % (20368)Memory used [KB]: 7931
% 11.63/1.82 % (20368)Time elapsed: 0.554 s
% 11.63/1.82 % (20368)Instructions burned: 1829 (million)
% 11.63/1.82 % (20368)------------------------------
% 11.63/1.82 % (20368)------------------------------
% 11.63/1.83 % (20383)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on Vampire---4 for (2985ds/594Mi)
% 11.63/1.84 % (20383)Refutation not found, incomplete strategy
% 11.63/1.84 % (20383)------------------------------
% 11.63/1.84 % (20383)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.63/1.84 % (20383)Termination reason: Refutation not found, incomplete strategy
% 11.63/1.84
% 11.63/1.84
% 11.63/1.84 % (20383)Memory used [KB]: 5628
% 11.63/1.84 % (20383)Time elapsed: 0.007 s
% 11.63/1.84 % (20383)Instructions burned: 23 (million)
% 11.63/1.84 % (20383)------------------------------
% 11.63/1.84 % (20383)------------------------------
% 11.75/1.85 % (20384)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 Vampire---4 for (2985ds/327Mi)
% 11.75/1.85 % (20380)Instruction limit reached!
% 11.75/1.85 % (20380)------------------------------
% 11.75/1.85 % (20380)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.75/1.85 % (20380)Termination reason: Unknown
% 11.75/1.85 % (20380)Termination phase: Saturation
% 11.75/1.85
% 11.75/1.85 % (20380)Memory used [KB]: 6396
% 11.75/1.85 % (20380)Time elapsed: 0.261 s
% 11.75/1.85 % (20380)Instructions burned: 867 (million)
% 11.75/1.85 % (20380)------------------------------
% 11.75/1.85 % (20380)------------------------------
% 11.75/1.86 % (20385)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on Vampire---4 for (2985ds/5411Mi)
% 11.75/1.86 % (20385)Refutation not found, incomplete strategy
% 11.75/1.86 % (20385)------------------------------
% 11.75/1.86 % (20385)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.75/1.86 % (20385)Termination reason: Refutation not found, incomplete strategy
% 11.75/1.86
% 11.75/1.86
% 11.75/1.86 % (20385)Memory used [KB]: 5500
% 11.75/1.86 % (20385)Time elapsed: 0.002 s
% 11.75/1.86 % (20385)Instructions burned: 2 (million)
% 11.75/1.86 % (20385)------------------------------
% 11.75/1.86 % (20385)------------------------------
% 11.75/1.87 % (20386)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on Vampire---4 for (2985ds/1762Mi)
% 12.06/1.93 % (20382)Instruction limit reached!
% 12.06/1.93 % (20382)------------------------------
% 12.06/1.93 % (20382)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 12.06/1.93 % (20382)Termination reason: Unknown
% 12.06/1.93 % (20382)Termination phase: Saturation
% 12.06/1.93
% 12.06/1.93 % (20382)Memory used [KB]: 6908
% 12.06/1.93 % (20382)Time elapsed: 0.119 s
% 12.06/1.93 % (20382)Instructions burned: 446 (million)
% 12.06/1.93 % (20382)------------------------------
% 12.06/1.93 % (20382)------------------------------
% 12.06/1.94 % (20387)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on Vampire---4 for (2984ds/96Mi)
% 12.06/1.94 % (20384)Instruction limit reached!
% 12.06/1.94 % (20384)------------------------------
% 12.06/1.94 % (20384)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 12.06/1.94 % (20384)Termination reason: Unknown
% 12.06/1.94 % (20384)Termination phase: Saturation
% 12.06/1.94
% 12.06/1.94 % (20384)Memory used [KB]: 7036
% 12.06/1.94 % (20384)Time elapsed: 0.100 s
% 12.06/1.94 % (20384)Instructions burned: 327 (million)
% 12.06/1.94 % (20384)------------------------------
% 12.06/1.94 % (20384)------------------------------
% 12.06/1.95 % (20388)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on Vampire---4 for (2984ds/503Mi)
% 12.06/1.95 % (20388)Refutation not found, incomplete strategy
% 12.06/1.95 % (20388)------------------------------
% 12.06/1.95 % (20388)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 12.06/1.95 % (20388)Termination reason: Refutation not found, incomplete strategy
% 12.06/1.95
% 12.06/1.95
% 12.06/1.95 % (20388)Memory used [KB]: 5500
% 12.06/1.95 % (20388)Time elapsed: 0.002 s
% 12.06/1.95 % (20388)Instructions burned: 3 (million)
% 12.06/1.95 % (20388)------------------------------
% 12.06/1.95 % (20388)------------------------------
% 12.06/1.96 % (20389)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on Vampire---4 for (2984ds/90Mi)
% 12.06/1.97 % (20387)Instruction limit reached!
% 12.06/1.97 % (20387)------------------------------
% 12.06/1.97 % (20387)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 12.06/1.97 % (20387)Termination reason: Unknown
% 12.06/1.97 % (20387)Termination phase: Saturation
% 12.06/1.97
% 12.06/1.97 % (20387)Memory used [KB]: 5884
% 12.06/1.97 % (20387)Time elapsed: 0.026 s
% 12.06/1.97 % (20387)Instructions burned: 97 (million)
% 12.06/1.97 % (20387)------------------------------
% 12.06/1.97 % (20387)------------------------------
% 12.56/1.97 % (20390)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on Vampire---4 for (2984ds/593Mi)
% 12.56/1.98 % (20381)Instruction limit reached!
% 12.56/1.98 % (20381)------------------------------
% 12.56/1.98 % (20381)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 12.56/1.98 % (20381)Termination reason: Unknown
% 12.56/1.98 % (20381)Termination phase: Saturation
% 12.56/1.98
% 12.56/1.98 % (20381)Memory used [KB]: 6780
% 12.56/1.98 % (20381)Time elapsed: 0.168 s
% 12.56/1.98 % (20381)Instructions burned: 595 (million)
% 12.56/1.98 % (20381)------------------------------
% 12.56/1.98 % (20381)------------------------------
% 12.56/1.99 % (20391)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 Vampire---4 for (2984ds/1512Mi)
% 12.56/1.99 % (20391)Refutation not found, incomplete strategy
% 12.56/1.99 % (20391)------------------------------
% 12.56/1.99 % (20391)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 12.56/1.99 % (20391)Termination reason: Refutation not found, incomplete strategy
% 12.56/1.99
% 12.56/1.99
% 12.56/1.99 % (20391)Memory used [KB]: 5500
% 12.56/1.99 % (20391)Time elapsed: 0.003 s
% 12.56/1.99 % (20391)Instructions burned: 6 (million)
% 12.56/1.99 % (20391)------------------------------
% 12.56/1.99 % (20391)------------------------------
% 12.56/1.99 % (20389)Instruction limit reached!
% 12.56/1.99 % (20389)------------------------------
% 12.56/1.99 % (20389)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 12.56/1.99 % (20389)Termination reason: Unknown
% 12.56/1.99 % (20389)Termination phase: Saturation
% 12.56/1.99
% 12.56/1.99 % (20389)Memory used [KB]: 6012
% 12.56/1.99 % (20389)Time elapsed: 0.032 s
% 12.56/1.99 % (20389)Instructions burned: 91 (million)
% 12.56/1.99 % (20389)------------------------------
% 12.56/1.99 % (20389)------------------------------
% 12.56/2.00 % (20392)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on Vampire---4 for (2984ds/569Mi)
% 12.56/2.00 % (20393)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on Vampire---4 for (2983ds/501Mi)
% 12.56/2.01 % (20393)Refutation not found, incomplete strategy
% 12.56/2.01 % (20393)------------------------------
% 12.56/2.01 % (20393)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 12.56/2.01 % (20393)Termination reason: Refutation not found, incomplete strategy
% 12.56/2.01
% 12.56/2.01
% 12.56/2.01 % (20393)Memory used [KB]: 5628
% 12.56/2.01 % (20393)Time elapsed: 0.033 s
% 12.56/2.01 % (20393)Instructions burned: 53 (million)
% 12.56/2.01 % (20393)------------------------------
% 12.56/2.01 % (20393)------------------------------
% 12.56/2.02 % (20394)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on Vampire---4 for (2983ds/562Mi)
% 13.42/2.13 % (20392)Instruction limit reached!
% 13.42/2.13 % (20392)------------------------------
% 13.42/2.13 % (20392)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 13.42/2.13 % (20392)Termination reason: Unknown
% 13.42/2.13 % (20392)Termination phase: Saturation
% 13.42/2.13
% 13.42/2.13 % (20392)Memory used [KB]: 5884
% 13.42/2.13 % (20392)Time elapsed: 0.134 s
% 13.42/2.13 % (20392)Instructions burned: 570 (million)
% 13.42/2.13 % (20392)------------------------------
% 13.42/2.13 % (20392)------------------------------
% 13.42/2.13 % (20390)Instruction limit reached!
% 13.42/2.13 % (20390)------------------------------
% 13.42/2.13 % (20390)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 13.42/2.13 % (20390)Termination reason: Unknown
% 13.42/2.13 % (20390)Termination phase: Saturation
% 13.42/2.13
% 13.42/2.13 % (20390)Memory used [KB]: 7803
% 13.42/2.13 % (20390)Time elapsed: 0.161 s
% 13.42/2.13 % (20390)Instructions burned: 595 (million)
% 13.42/2.13 % (20390)------------------------------
% 13.42/2.13 % (20390)------------------------------
% 13.42/2.14 % (20395)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on Vampire---4 for (2982ds/406Mi)
% 13.42/2.14 % (20396)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on Vampire---4 for (2982ds/582Mi)
% 14.26/2.18 % (20394)Instruction limit reached!
% 14.26/2.18 % (20394)------------------------------
% 14.26/2.18 % (20394)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 14.26/2.18 % (20394)Termination reason: Unknown
% 14.26/2.18 % (20394)Termination phase: Saturation
% 14.26/2.18
% 14.26/2.18 % (20394)Memory used [KB]: 6780
% 14.26/2.18 % (20394)Time elapsed: 0.163 s
% 14.26/2.18 % (20394)Instructions burned: 564 (million)
% 14.26/2.18 % (20394)------------------------------
% 14.26/2.18 % (20394)------------------------------
% 14.26/2.19 % (20397)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 Vampire---4 for (2981ds/456Mi)
% 14.26/2.22 % (20293)Instruction limit reached!
% 14.26/2.22 % (20293)------------------------------
% 14.26/2.22 % (20293)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 14.26/2.22 % (20293)Termination reason: Unknown
% 14.26/2.22 % (20293)Termination phase: Saturation
% 14.26/2.22
% 14.26/2.22 % (20293)Memory used [KB]: 23155
% 14.26/2.22 % (20293)Time elapsed: 1.213 s
% 14.26/2.22 % (20293)Instructions burned: 4353 (million)
% 14.26/2.22 % (20293)------------------------------
% 14.26/2.22 % (20293)------------------------------
% 14.85/2.23 % (20398)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on Vampire---4 for (2981ds/393Mi)
% 14.85/2.28 % (20395)Instruction limit reached!
% 14.85/2.28 % (20395)------------------------------
% 14.85/2.28 % (20395)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 14.85/2.28 % (20395)Termination reason: Unknown
% 14.85/2.28 % (20395)Termination phase: Saturation
% 14.85/2.28
% 14.85/2.28 % (20395)Memory used [KB]: 7291
% 14.85/2.28 % (20395)Time elapsed: 0.157 s
% 14.85/2.28 % (20395)Instructions burned: 406 (million)
% 14.85/2.28 % (20395)------------------------------
% 14.85/2.28 % (20395)------------------------------
% 15.16/2.29 % (20399)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 Vampire---4 for (2980ds/1335Mi)
% 15.16/2.30 % (20396)Instruction limit reached!
% 15.16/2.30 % (20396)------------------------------
% 15.16/2.30 % (20396)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.16/2.30 % (20396)Termination reason: Unknown
% 15.16/2.30 % (20396)Termination phase: Saturation
% 15.16/2.30
% 15.16/2.30 % (20396)Memory used [KB]: 7675
% 15.16/2.30 % (20396)Time elapsed: 0.157 s
% 15.16/2.30 % (20396)Instructions burned: 582 (million)
% 15.16/2.30 % (20396)------------------------------
% 15.16/2.30 % (20396)------------------------------
% 15.16/2.30 % (20399)Refutation not found, incomplete strategy
% 15.16/2.30 % (20399)------------------------------
% 15.16/2.30 % (20399)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.16/2.30 % (20399)Termination reason: Refutation not found, incomplete strategy
% 15.16/2.30
% 15.16/2.30
% 15.16/2.30 % (20399)Memory used [KB]: 5628
% 15.16/2.30 % (20399)Time elapsed: 0.015 s
% 15.16/2.30 % (20399)Instructions burned: 65 (million)
% 15.16/2.30 % (20399)------------------------------
% 15.16/2.30 % (20399)------------------------------
% 15.16/2.30 % (20400)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 Vampire---4 for (2980ds/3373Mi)
% 15.16/2.31 % (20401)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 Vampire---4 for (2980ds/474Mi)
% 15.16/2.31 % (20397)Instruction limit reached!
% 15.16/2.31 % (20397)------------------------------
% 15.16/2.31 % (20397)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.16/2.31 % (20397)Termination reason: Unknown
% 15.16/2.31 % (20397)Termination phase: Saturation
% 15.16/2.31
% 15.16/2.31 % (20397)Memory used [KB]: 7036
% 15.16/2.31 % (20397)Time elapsed: 0.122 s
% 15.16/2.31 % (20397)Instructions burned: 457 (million)
% 15.16/2.31 % (20397)------------------------------
% 15.16/2.31 % (20397)------------------------------
% 15.16/2.32 % (20402)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on Vampire---4 for (2980ds/157Mi)
% 15.16/2.33 % (20386)Instruction limit reached!
% 15.16/2.33 % (20386)------------------------------
% 15.16/2.33 % (20386)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.16/2.33 % (20386)Termination reason: Unknown
% 15.16/2.33 % (20386)Termination phase: Saturation
% 15.16/2.33
% 15.16/2.33 % (20386)Memory used [KB]: 6140
% 15.16/2.33 % (20386)Time elapsed: 0.459 s
% 15.16/2.33 % (20386)Instructions burned: 1763 (million)
% 15.16/2.33 % (20386)------------------------------
% 15.16/2.33 % (20386)------------------------------
% 15.16/2.34 % (20403)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on Vampire---4 for (2980ds/590Mi)
% 15.60/2.35 % (20398)Instruction limit reached!
% 15.60/2.35 % (20398)------------------------------
% 15.60/2.35 % (20398)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.60/2.35 % (20398)Termination reason: Unknown
% 15.60/2.35 % (20398)Termination phase: Saturation
% 15.60/2.35
% 15.60/2.35 % (20398)Memory used [KB]: 6780
% 15.60/2.35 % (20398)Time elapsed: 0.129 s
% 15.60/2.35 % (20398)Instructions burned: 395 (million)
% 15.60/2.35 % (20398)------------------------------
% 15.60/2.35 % (20398)------------------------------
% 15.60/2.36 % (20402)Instruction limit reached!
% 15.60/2.36 % (20402)------------------------------
% 15.60/2.36 % (20402)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.60/2.36 % (20402)Termination reason: Unknown
% 15.60/2.36 % (20402)Termination phase: Saturation
% 15.60/2.36
% 15.60/2.36 % (20402)Memory used [KB]: 5884
% 15.60/2.36 % (20402)Time elapsed: 0.040 s
% 15.60/2.36 % (20402)Instructions burned: 159 (million)
% 15.60/2.36 % (20402)------------------------------
% 15.60/2.36 % (20402)------------------------------
% 15.60/2.36 % (20404)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on Vampire---4 for (2980ds/104Mi)
% 15.60/2.36 % (20405)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on Vampire---4 for (2980ds/414Mi)
% 15.83/2.39 % (20404)Instruction limit reached!
% 15.83/2.39 % (20404)------------------------------
% 15.83/2.39 % (20404)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.83/2.39 % (20404)Termination reason: Unknown
% 15.83/2.39 % (20404)Termination phase: Saturation
% 15.83/2.39
% 15.83/2.39 % (20404)Memory used [KB]: 5756
% 15.83/2.39 % (20404)Time elapsed: 0.025 s
% 15.83/2.39 % (20404)Instructions burned: 107 (million)
% 15.83/2.39 % (20404)------------------------------
% 15.83/2.39 % (20404)------------------------------
% 15.83/2.39 % (20406)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on Vampire---4 for (2979ds/715Mi)
% 16.09/2.45 % (20401)Instruction limit reached!
% 16.09/2.45 % (20401)------------------------------
% 16.09/2.45 % (20401)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.09/2.45 % (20401)Termination reason: Unknown
% 16.09/2.45 % (20401)Termination phase: Saturation
% 16.09/2.45
% 16.09/2.45 % (20401)Memory used [KB]: 6780
% 16.09/2.45 % (20401)Time elapsed: 0.141 s
% 16.09/2.45 % (20401)Instructions burned: 476 (million)
% 16.09/2.45 % (20401)------------------------------
% 16.09/2.45 % (20401)------------------------------
% 16.09/2.46 % (20407)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on Vampire---4 for (2979ds/961Mi)
% 16.09/2.48 % (20405)Instruction limit reached!
% 16.09/2.48 % (20405)------------------------------
% 16.09/2.48 % (20405)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.09/2.48 % (20405)Termination reason: Unknown
% 16.09/2.48 % (20405)Termination phase: Saturation
% 16.09/2.48
% 16.09/2.48 % (20405)Memory used [KB]: 6396
% 16.09/2.48 % (20405)Time elapsed: 0.118 s
% 16.09/2.48 % (20405)Instructions burned: 417 (million)
% 16.09/2.48 % (20405)------------------------------
% 16.09/2.48 % (20405)------------------------------
% 16.09/2.49 % (20408)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 Vampire---4 for (2978ds/1213Mi)
% 16.09/2.50 % (20403)Instruction limit reached!
% 16.09/2.50 % (20403)------------------------------
% 16.09/2.50 % (20403)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.09/2.50 % (20403)Termination reason: Unknown
% 16.09/2.50 % (20403)Termination phase: Saturation
% 16.09/2.50
% 16.09/2.50 % (20403)Memory used [KB]: 7419
% 16.09/2.50 % (20403)Time elapsed: 0.164 s
% 16.09/2.50 % (20403)Instructions burned: 591 (million)
% 16.09/2.50 % (20403)------------------------------
% 16.09/2.50 % (20403)------------------------------
% 16.09/2.51 % (20409)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on Vampire---4 for (2978ds/1979Mi)
% 16.79/2.57 % (20285)Instruction limit reached!
% 16.79/2.57 % (20285)------------------------------
% 16.79/2.57 % (20285)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.79/2.57 % (20285)Termination reason: Unknown
% 16.79/2.57 % (20285)Termination phase: Saturation
% 16.79/2.57
% 16.79/2.57 % (20285)Memory used [KB]: 18549
% 16.79/2.57 % (20285)Time elapsed: 1.587 s
% 16.79/2.57 % (20285)Instructions burned: 5206 (million)
% 16.79/2.57 % (20285)------------------------------
% 16.79/2.57 % (20285)------------------------------
% 16.79/2.58 % (20410)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on Vampire---4 for (2978ds/481Mi)
% 16.94/2.59 % (20406)Instruction limit reached!
% 16.94/2.59 % (20406)------------------------------
% 16.94/2.59 % (20406)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.94/2.59 % (20406)Termination reason: Unknown
% 16.94/2.59 % (20406)Termination phase: Saturation
% 16.94/2.59
% 16.94/2.59 % (20406)Memory used [KB]: 3965
% 16.94/2.59 % (20406)Time elapsed: 0.195 s
% 16.94/2.59 % (20406)Instructions burned: 716 (million)
% 16.94/2.59 % (20406)------------------------------
% 16.94/2.59 % (20406)------------------------------
% 16.94/2.60 % (20411)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on Vampire---4 for (2977ds/783Mi)
% 16.94/2.63 % (20372)Instruction limit reached!
% 16.94/2.63 % (20372)------------------------------
% 16.94/2.63 % (20372)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.94/2.63 % (20372)Termination reason: Unknown
% 16.94/2.63 % (20372)Termination phase: Saturation
% 16.94/2.63
% 16.94/2.63 % (20372)Memory used [KB]: 11769
% 16.94/2.63 % (20372)Time elapsed: 1.274 s
% 16.94/2.63 % (20372)Instructions burned: 4714 (million)
% 16.94/2.63 % (20372)------------------------------
% 16.94/2.63 % (20372)------------------------------
% 16.94/2.64 % (20412)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on Vampire---4 for (2977ds/432Mi)
% 16.94/2.64 % (20412)Refutation not found, incomplete strategy
% 16.94/2.64 % (20412)------------------------------
% 16.94/2.64 % (20412)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.94/2.64 % (20412)Termination reason: Refutation not found, incomplete strategy
% 16.94/2.64
% 16.94/2.64
% 16.94/2.64 % (20412)Memory used [KB]: 5500
% 16.94/2.64 % (20412)Time elapsed: 0.003 s
% 16.94/2.64 % (20412)Instructions burned: 2 (million)
% 16.94/2.64 % (20412)------------------------------
% 16.94/2.64 % (20412)------------------------------
% 17.29/2.65 % (20413)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on Vampire---4 for (2977ds/1670Mi)
% 17.31/2.70 % (20410)Instruction limit reached!
% 17.31/2.70 % (20410)------------------------------
% 17.31/2.70 % (20410)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 17.31/2.70 % (20410)Termination reason: Unknown
% 17.31/2.70 % (20410)Termination phase: Saturation
% 17.31/2.70
% 17.31/2.70 % (20410)Memory used [KB]: 6140
% 17.31/2.70 % (20410)Time elapsed: 0.127 s
% 17.31/2.70 % (20410)Instructions burned: 484 (million)
% 17.31/2.70 % (20410)------------------------------
% 17.31/2.70 % (20410)------------------------------
% 17.31/2.71 % (20414)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on Vampire---4 for (2976ds/90Mi)
% 18.82/2.73 % (20407)Instruction limit reached!
% 18.82/2.73 % (20407)------------------------------
% 18.82/2.73 % (20407)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 18.82/2.73 % (20407)Termination reason: Unknown
% 18.82/2.73 % (20407)Termination phase: Saturation
% 18.82/2.73
% 18.82/2.73 % (20407)Memory used [KB]: 8827
% 18.82/2.73 % (20407)Time elapsed: 0.269 s
% 18.82/2.73 % (20407)Instructions burned: 961 (million)
% 18.82/2.73 % (20407)------------------------------
% 18.82/2.73 % (20407)------------------------------
% 18.82/2.73 % (20414)Instruction limit reached!
% 18.82/2.73 % (20414)------------------------------
% 18.82/2.73 % (20414)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 18.82/2.73 % (20414)Termination reason: Unknown
% 18.82/2.73 % (20414)Termination phase: Saturation
% 18.82/2.73
% 18.82/2.73 % (20414)Memory used [KB]: 5756
% 18.82/2.73 % (20414)Time elapsed: 0.021 s
% 18.82/2.73 % (20414)Instructions burned: 90 (million)
% 18.82/2.73 % (20414)------------------------------
% 18.82/2.73 % (20414)------------------------------
% 18.82/2.74 % (20415)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 Vampire---4 for (2976ds/346Mi)
% 18.82/2.74 % (20416)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on Vampire---4 for (2976ds/401Mi)
% 19.04/2.82 % (20415)Instruction limit reached!
% 19.04/2.82 % (20415)------------------------------
% 19.04/2.82 % (20415)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 19.04/2.82 % (20415)Termination reason: Unknown
% 19.04/2.82 % (20415)Termination phase: Saturation
% 19.04/2.82
% 19.04/2.82 % (20415)Memory used [KB]: 6012
% 19.04/2.82 % (20415)Time elapsed: 0.088 s
% 19.04/2.82 % (20415)Instructions burned: 346 (million)
% 19.04/2.82 % (20415)------------------------------
% 19.04/2.82 % (20415)------------------------------
% 19.04/2.83 % (20417)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on Vampire---4 for (2975ds/6454Mi)
% 19.66/2.84 % (20411)Instruction limit reached!
% 19.66/2.84 % (20411)------------------------------
% 19.66/2.84 % (20411)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 19.66/2.84 % (20411)Termination reason: Unknown
% 19.66/2.84 % (20411)Termination phase: Saturation
% 19.66/2.84
% 19.66/2.84 % (20411)Memory used [KB]: 8571
% 19.66/2.84 % (20411)Time elapsed: 0.240 s
% 19.66/2.84 % (20411)Instructions burned: 783 (million)
% 19.66/2.84 % (20411)------------------------------
% 19.66/2.84 % (20411)------------------------------
% 19.66/2.85 % (20418)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on Vampire---4 for (2975ds/283Mi)
% 19.66/2.85 % (20416)Instruction limit reached!
% 19.66/2.85 % (20416)------------------------------
% 19.66/2.85 % (20416)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 19.66/2.85 % (20416)Termination reason: Unknown
% 19.66/2.85 % (20416)Termination phase: Saturation
% 19.66/2.85
% 19.66/2.85 % (20416)Memory used [KB]: 6268
% 19.66/2.85 % (20416)Time elapsed: 0.115 s
% 19.66/2.85 % (20416)Instructions burned: 401 (million)
% 19.66/2.85 % (20416)------------------------------
% 19.66/2.85 % (20416)------------------------------
% 19.66/2.86 % (20419)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 Vampire---4 for (2975ds/865Mi)
% 19.66/2.86 % (20408)Instruction limit reached!
% 19.66/2.86 % (20408)------------------------------
% 19.66/2.86 % (20408)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 19.66/2.86 % (20408)Termination reason: Unknown
% 19.66/2.86 % (20408)Termination phase: Saturation
% 19.66/2.86
% 19.66/2.86 % (20408)Memory used [KB]: 7675
% 19.66/2.86 % (20408)Time elapsed: 0.374 s
% 19.66/2.86 % (20408)Instructions burned: 1215 (million)
% 19.66/2.86 % (20408)------------------------------
% 19.66/2.86 % (20408)------------------------------
% 19.66/2.87 % (20420)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 Vampire---4 for (2975ds/4528Mi)
% 19.66/2.87 % (20420)Refutation not found, incomplete strategy
% 19.66/2.87 % (20420)------------------------------
% 19.66/2.87 % (20420)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 19.66/2.87 % (20420)Termination reason: Refutation not found, incomplete strategy
% 19.66/2.87
% 19.66/2.87
% 19.66/2.87 % (20420)Memory used [KB]: 1023
% 19.66/2.87 % (20420)Time elapsed: 0.003 s
% 19.66/2.87 % (20420)Instructions burned: 2 (million)
% 19.66/2.87 % (20420)------------------------------
% 19.66/2.87 % (20420)------------------------------
% 19.66/2.88 % (20421)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 Vampire---4 for (2975ds/1001Mi)
% 19.98/2.92 % (20418)Instruction limit reached!
% 19.98/2.92 % (20418)------------------------------
% 19.98/2.92 % (20418)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 19.98/2.92 % (20418)Termination reason: Unknown
% 19.98/2.92 % (20418)Termination phase: Saturation
% 19.98/2.92
% 19.98/2.92 % (20418)Memory used [KB]: 6652
% 19.98/2.92 % (20418)Time elapsed: 0.074 s
% 19.98/2.92 % (20418)Instructions burned: 283 (million)
% 19.98/2.92 % (20418)------------------------------
% 19.98/2.92 % (20418)------------------------------
% 19.98/2.93 % (20422)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on Vampire---4 for (2974ds/102Mi)
% 20.30/2.95 % (20422)Instruction limit reached!
% 20.30/2.95 % (20422)------------------------------
% 20.30/2.95 % (20422)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.30/2.95 % (20422)Termination reason: Unknown
% 20.30/2.95 % (20422)Termination phase: Saturation
% 20.30/2.95
% 20.30/2.95 % (20422)Memory used [KB]: 5628
% 20.30/2.95 % (20422)Time elapsed: 0.023 s
% 20.30/2.95 % (20422)Instructions burned: 104 (million)
% 20.30/2.95 % (20422)------------------------------
% 20.30/2.95 % (20422)------------------------------
% 20.38/2.96 % (20423)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on Vampire---4 for (2974ds/952Mi)
% 20.61/3.03 % (20413)Instruction limit reached!
% 20.61/3.03 % (20413)------------------------------
% 20.61/3.03 % (20413)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.61/3.03 % (20413)Termination reason: Unknown
% 20.61/3.03 % (20413)Termination phase: Saturation
% 20.61/3.03
% 20.61/3.03 % (20413)Memory used [KB]: 6652
% 20.61/3.03 % (20413)Time elapsed: 0.376 s
% 20.61/3.03 % (20413)Instructions burned: 1671 (million)
% 20.61/3.03 % (20413)------------------------------
% 20.61/3.03 % (20413)------------------------------
% 20.61/3.03 % (20424)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 Vampire---4 for (2973ds/578Mi)
% 20.61/3.05 % (20409)Instruction limit reached!
% 20.61/3.05 % (20409)------------------------------
% 20.61/3.05 % (20409)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.61/3.05 % (20409)Termination reason: Unknown
% 20.61/3.05 % (20409)Termination phase: Saturation
% 20.61/3.05
% 20.61/3.05 % (20409)Memory used [KB]: 13176
% 20.61/3.05 % (20409)Time elapsed: 0.542 s
% 20.61/3.05 % (20409)Instructions burned: 1982 (million)
% 20.61/3.05 % (20409)------------------------------
% 20.61/3.05 % (20409)------------------------------
% 20.77/3.06 % (20425)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 Vampire---4 for (2973ds/643Mi)
% 20.77/3.12 % (20419)Instruction limit reached!
% 20.77/3.12 % (20419)------------------------------
% 20.77/3.12 % (20419)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.77/3.12 % (20419)Termination reason: Unknown
% 20.77/3.12 % (20419)Termination phase: Saturation
% 20.77/3.12
% 20.77/3.12 % (20419)Memory used [KB]: 6652
% 20.77/3.12 % (20419)Time elapsed: 0.258 s
% 20.77/3.12 % (20419)Instructions burned: 866 (million)
% 20.77/3.12 % (20419)------------------------------
% 20.77/3.12 % (20419)------------------------------
% 20.77/3.12 % (20426)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on Vampire---4 for (2972ds/865Mi)
% 20.77/3.14 % (20426)Refutation not found, incomplete strategy
% 20.77/3.14 % (20426)------------------------------
% 20.77/3.14 % (20426)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.77/3.14 % (20426)Termination reason: Refutation not found, incomplete strategy
% 20.77/3.14
% 20.77/3.14
% 20.77/3.14 % (20426)Memory used [KB]: 5628
% 20.77/3.14 % (20426)Time elapsed: 0.012 s
% 20.77/3.14 % (20426)Instructions burned: 53 (million)
% 20.77/3.14 % (20426)------------------------------
% 20.77/3.14 % (20426)------------------------------
% 21.22/3.14 % (20427)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on Vampire---4 for (2972ds/1174Mi)
% 21.22/3.15 % (20400)Instruction limit reached!
% 21.22/3.15 % (20400)------------------------------
% 21.22/3.15 % (20400)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 21.22/3.15 % (20400)Termination reason: Unknown
% 21.22/3.15 % (20400)Termination phase: Saturation
% 21.22/3.15
% 21.22/3.15 % (20400)Memory used [KB]: 13560
% 21.22/3.15 % (20400)Time elapsed: 0.847 s
% 21.22/3.15 % (20400)Instructions burned: 3373 (million)
% 21.22/3.15 % (20400)------------------------------
% 21.22/3.15 % (20400)------------------------------
% 21.22/3.15 % (20421)Instruction limit reached!
% 21.22/3.15 % (20421)------------------------------
% 21.22/3.15 % (20421)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 21.22/3.15 % (20421)Termination reason: Unknown
% 21.22/3.15 % (20421)Termination phase: Saturation
% 21.22/3.15
% 21.22/3.15 % (20421)Memory used [KB]: 9210
% 21.22/3.15 % (20421)Time elapsed: 0.277 s
% 21.22/3.15 % (20421)Instructions burned: 1003 (million)
% 21.22/3.15 % (20421)------------------------------
% 21.22/3.15 % (20421)------------------------------
% 21.22/3.16 % (20428)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 Vampire---4 for (2972ds/644Mi)
% 21.22/3.16 % (20429)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on Vampire---4 for (2972ds/1201Mi)
% 21.22/3.18 % (20428)Refutation not found, incomplete strategy
% 21.22/3.18 % (20428)------------------------------
% 21.22/3.18 % (20428)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 21.22/3.18 % (20428)Termination reason: Refutation not found, incomplete strategy
% 21.22/3.18
% 21.22/3.18
% 21.22/3.18 % (20428)Memory used [KB]: 5756
% 21.22/3.18 % (20428)Time elapsed: 0.020 s
% 21.22/3.18 % (20428)Instructions burned: 83 (million)
% 21.22/3.18 % (20428)------------------------------
% 21.22/3.18 % (20428)------------------------------
% 21.60/3.19 % (20430)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 Vampire---4 for (2972ds/1046Mi)
% 21.60/3.20 % (20425)Instruction limit reached!
% 21.60/3.20 % (20425)------------------------------
% 21.60/3.20 % (20425)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 21.60/3.20 % (20425)Termination reason: Unknown
% 21.60/3.20 % (20425)Termination phase: Saturation
% 21.60/3.20
% 21.60/3.20 % (20425)Memory used [KB]: 5884
% 21.60/3.20 % (20425)Time elapsed: 0.148 s
% 21.60/3.20 % (20425)Instructions burned: 646 (million)
% 21.60/3.20 % (20425)------------------------------
% 21.60/3.20 % (20425)------------------------------
% 21.60/3.21 % (20431)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 Vampire---4 for (2971ds/222Mi)
% 21.60/3.22 % (20423)Instruction limit reached!
% 21.60/3.22 % (20423)------------------------------
% 21.60/3.22 % (20423)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 21.60/3.22 % (20423)Termination reason: Unknown
% 21.60/3.22 % (20423)Termination phase: Saturation
% 21.60/3.22
% 21.60/3.22 % (20423)Memory used [KB]: 9338
% 21.60/3.22 % (20423)Time elapsed: 0.260 s
% 21.60/3.22 % (20423)Instructions burned: 954 (million)
% 21.60/3.22 % (20423)------------------------------
% 21.60/3.22 % (20423)------------------------------
% 21.60/3.22 % (20432)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 Vampire---4 for (2971ds/68Mi)
% 21.60/3.23 % (20424)Instruction limit reached!
% 21.60/3.23 % (20424)------------------------------
% 21.60/3.23 % (20424)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 21.60/3.23 % (20424)Termination reason: Unknown
% 21.60/3.23 % (20424)Termination phase: Saturation
% 21.60/3.23
% 21.60/3.23 % (20424)Memory used [KB]: 7675
% 21.60/3.23 % (20424)Time elapsed: 0.194 s
% 21.60/3.23 % (20424)Instructions burned: 578 (million)
% 21.60/3.23 % (20424)------------------------------
% 21.60/3.23 % (20424)------------------------------
% 21.60/3.23 % (20433)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 Vampire---4 for (2971ds/454Mi)
% 22.28/3.24 % (20432)Instruction limit reached!
% 22.28/3.24 % (20432)------------------------------
% 22.28/3.24 % (20432)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 22.28/3.24 % (20432)Termination reason: Unknown
% 22.28/3.24 % (20432)Termination phase: Saturation
% 22.28/3.24
% 22.28/3.24 % (20432)Memory used [KB]: 5628
% 22.28/3.24 % (20432)Time elapsed: 0.015 s
% 22.28/3.24 % (20432)Instructions burned: 68 (million)
% 22.28/3.24 % (20432)------------------------------
% 22.28/3.24 % (20432)------------------------------
% 22.28/3.25 % (20434)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 Vampire---4 for (2971ds/360Mi)
% 23.14/3.27 % (20431)Instruction limit reached!
% 23.14/3.27 % (20431)------------------------------
% 23.14/3.27 % (20431)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 23.14/3.27 % (20431)Termination reason: Unknown
% 23.14/3.27 % (20431)Termination phase: Saturation
% 23.14/3.27
% 23.14/3.27 % (20431)Memory used [KB]: 5884
% 23.14/3.27 % (20431)Time elapsed: 0.058 s
% 23.14/3.27 % (20431)Instructions burned: 222 (million)
% 23.14/3.27 % (20431)------------------------------
% 23.14/3.27 % (20431)------------------------------
% 23.14/3.28 % (20435)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on Vampire---4 for (2971ds/157Mi)
% 23.14/3.31 % (20435)Instruction limit reached!
% 23.14/3.31 % (20435)------------------------------
% 23.14/3.31 % (20435)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 23.14/3.31 % (20435)Termination reason: Unknown
% 23.14/3.31 % (20435)Termination phase: Saturation
% 23.14/3.31
% 23.14/3.31 % (20435)Memory used [KB]: 5884
% 23.14/3.31 % (20435)Time elapsed: 0.041 s
% 23.14/3.31 % (20435)Instructions burned: 159 (million)
% 23.14/3.31 % (20435)------------------------------
% 23.14/3.31 % (20435)------------------------------
% 23.62/3.32 % (20436)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 Vampire---4 for (2970ds/5061Mi)
% 23.62/3.34 % (20433)Instruction limit reached!
% 23.62/3.34 % (20433)------------------------------
% 23.62/3.34 % (20433)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 23.62/3.34 % (20433)Termination reason: Unknown
% 23.62/3.34 % (20433)Termination phase: Saturation
% 23.62/3.34
% 23.62/3.34 % (20433)Memory used [KB]: 10362
% 23.62/3.34 % (20433)Time elapsed: 0.103 s
% 23.62/3.34 % (20433)Instructions burned: 456 (million)
% 23.62/3.34 % (20433)------------------------------
% 23.62/3.34 % (20433)------------------------------
% 23.62/3.34 % (20437)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on Vampire---4 for (2970ds/2401Mi)
% 23.62/3.35 % (20434)Instruction limit reached!
% 23.62/3.35 % (20434)------------------------------
% 23.62/3.35 % (20434)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 23.62/3.35 % (20434)Termination reason: Unknown
% 23.62/3.35 % (20434)Termination phase: Saturation
% 23.62/3.35
% 23.62/3.35 % (20434)Memory used [KB]: 6268
% 23.62/3.35 % (20434)Time elapsed: 0.097 s
% 23.62/3.35 % (20434)Instructions burned: 360 (million)
% 23.62/3.35 % (20434)------------------------------
% 23.62/3.35 % (20434)------------------------------
% 23.62/3.36 % (20438)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on Vampire---4 for (2970ds/5798Mi)
% 24.38/3.47 % (20427)Instruction limit reached!
% 24.38/3.47 % (20427)------------------------------
% 24.38/3.47 % (20427)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.38/3.47 % (20427)Termination reason: Unknown
% 24.38/3.47 % (20427)Termination phase: Saturation
% 24.38/3.47
% 24.38/3.47 % (20427)Memory used [KB]: 9722
% 24.38/3.47 % (20427)Time elapsed: 0.328 s
% 24.38/3.47 % (20427)Instructions burned: 1175 (million)
% 24.38/3.47 % (20427)------------------------------
% 24.38/3.47 % (20427)------------------------------
% 24.38/3.48 % (20439)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 Vampire---4 for (2969ds/346Mi)
% 24.38/3.49 % (20430)Instruction limit reached!
% 24.38/3.49 % (20430)------------------------------
% 24.38/3.49 % (20430)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.38/3.49 % (20430)Termination reason: Unknown
% 24.38/3.49 % (20430)Termination phase: Saturation
% 24.38/3.49
% 24.38/3.49 % (20430)Memory used [KB]: 6908
% 24.38/3.49 % (20430)Time elapsed: 0.303 s
% 24.38/3.49 % (20430)Instructions burned: 1047 (million)
% 24.38/3.49 % (20430)------------------------------
% 24.38/3.49 % (20430)------------------------------
% 24.38/3.50 % (20440)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 Vampire---4 for (2968ds/1321Mi)
% 24.38/3.50 % (20440)Refutation not found, incomplete strategy
% 24.38/3.50 % (20440)------------------------------
% 24.38/3.50 % (20440)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.38/3.50 % (20440)Termination reason: Refutation not found, incomplete strategy
% 24.38/3.50
% 24.38/3.50
% 24.38/3.50 % (20440)Memory used [KB]: 1023
% 24.38/3.50 % (20440)Time elapsed: 0.003 s
% 24.38/3.50 % (20440)Instructions burned: 5 (million)
% 24.38/3.50 % (20440)------------------------------
% 24.38/3.50 % (20440)------------------------------
% 24.38/3.51 % (20441)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on Vampire---4 for (2968ds/1312Mi)
% 24.61/3.54 % (20429)Instruction limit reached!
% 24.61/3.54 % (20429)------------------------------
% 24.61/3.54 % (20429)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.61/3.54 % (20429)Termination reason: Unknown
% 24.61/3.54 % (20429)Termination phase: Saturation
% 24.61/3.54
% 24.61/3.54 % (20429)Memory used [KB]: 7675
% 24.61/3.54 % (20429)Time elapsed: 0.378 s
% 24.61/3.54 % (20429)Instructions burned: 1202 (million)
% 24.61/3.54 % (20429)------------------------------
% 24.61/3.54 % (20429)------------------------------
% 24.61/3.55 % (20442)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 Vampire---4 for (2968ds/672Mi)
% 24.61/3.55 % (20442)Refutation not found, incomplete strategy
% 24.61/3.55 % (20442)------------------------------
% 24.61/3.55 % (20442)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.61/3.55 % (20442)Termination reason: Refutation not found, incomplete strategy
% 24.61/3.55
% 24.61/3.55
% 24.61/3.55 % (20442)Memory used [KB]: 5500
% 24.61/3.55 % (20442)Time elapsed: 0.003 s
% 24.61/3.55 % (20442)Instructions burned: 5 (million)
% 24.61/3.55 % (20442)------------------------------
% 24.61/3.55 % (20442)------------------------------
% 24.71/3.56 % (20443)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 Vampire---4 for (2968ds/1897Mi)
% 24.71/3.56 % (20443)Refutation not found, incomplete strategy
% 24.71/3.56 % (20443)------------------------------
% 24.71/3.56 % (20443)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.71/3.56 % (20443)Termination reason: Refutation not found, incomplete strategy
% 24.71/3.56
% 24.71/3.56
% 24.71/3.56 % (20443)Memory used [KB]: 5500
% 24.71/3.56 % (20443)Time elapsed: 0.002 s
% 24.71/3.56 % (20443)Instructions burned: 3 (million)
% 24.71/3.56 % (20443)------------------------------
% 24.71/3.56 % (20443)------------------------------
% 24.71/3.57 % (20439)Instruction limit reached!
% 24.71/3.57 % (20439)------------------------------
% 24.71/3.57 % (20439)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.71/3.57 % (20439)Termination reason: Unknown
% 24.71/3.57 % (20439)Termination phase: Saturation
% 24.71/3.57
% 24.71/3.57 % (20439)Memory used [KB]: 6012
% 24.71/3.57 % (20439)Time elapsed: 0.088 s
% 24.71/3.57 % (20439)Instructions burned: 347 (million)
% 24.71/3.57 % (20439)------------------------------
% 24.71/3.57 % (20439)------------------------------
% 24.71/3.57 % (20444)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 Vampire---4 for (2968ds/1202Mi)
% 24.71/3.57 % (20445)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 Vampire---4 for (2968ds/1493Mi)
% 24.71/3.57 % (20445)Refutation not found, incomplete strategy
% 24.71/3.57 % (20445)------------------------------
% 24.71/3.57 % (20445)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.71/3.57 % (20445)Termination reason: Refutation not found, incomplete strategy
% 24.71/3.57
% 24.71/3.57
% 24.71/3.57 % (20445)Memory used [KB]: 5500
% 24.71/3.57 % (20445)Time elapsed: 0.003 s
% 24.71/3.57 % (20445)Instructions burned: 3 (million)
% 24.71/3.57 % (20445)------------------------------
% 24.71/3.57 % (20445)------------------------------
% 24.71/3.58 % (20446)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 Vampire---4 for (2968ds/7679Mi)
% 27.70/3.84 % (20441)Instruction limit reached!
% 27.70/3.84 % (20441)------------------------------
% 27.70/3.84 % (20441)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 27.70/3.84 % (20441)Termination reason: Unknown
% 27.70/3.84 % (20441)Termination phase: Saturation
% 27.70/3.84
% 27.70/3.84 % (20441)Memory used [KB]: 6396
% 27.70/3.84 % (20441)Time elapsed: 0.340 s
% 27.70/3.84 % (20441)Instructions burned: 1315 (million)
% 27.70/3.84 % (20441)------------------------------
% 27.70/3.84 % (20441)------------------------------
% 27.70/3.85 % (20447)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 Vampire---4 for (2965ds/340Mi)
% 27.70/3.86 % (20447)Refutation not found, incomplete strategy
% 27.70/3.86 % (20447)------------------------------
% 27.70/3.86 % (20447)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 27.70/3.86 % (20447)Termination reason: Refutation not found, incomplete strategy
% 27.70/3.86
% 27.70/3.86
% 27.70/3.86 % (20447)Memory used [KB]: 5628
% 27.70/3.86 % (20447)Time elapsed: 0.014 s
% 27.70/3.86 % (20447)Instructions burned: 56 (million)
% 27.70/3.86 % (20447)------------------------------
% 27.70/3.86 % (20447)------------------------------
% 27.91/3.87 % (20448)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 Vampire---4 for (2965ds/3672Mi)
% 27.91/3.88 % (20448)Refutation not found, incomplete strategy
% 27.91/3.88 % (20448)------------------------------
% 27.91/3.88 % (20448)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 27.91/3.88 % (20448)Termination reason: Refutation not found, incomplete strategy
% 27.91/3.88
% 27.91/3.88
% 27.91/3.88 % (20448)Memory used [KB]: 5756
% 27.91/3.88 % (20448)Time elapsed: 0.009 s
% 27.91/3.88 % (20448)Instructions burned: 33 (million)
% 27.91/3.88 % (20448)------------------------------
% 27.91/3.88 % (20448)------------------------------
% 27.91/3.89 % (20449)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 Vampire---4 for (2965ds/1535Mi)
% 27.91/3.91 % (20373)Instruction limit reached!
% 27.91/3.91 % (20373)------------------------------
% 27.91/3.91 % (20373)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 27.91/3.91 % (20373)Termination reason: Unknown
% 27.91/3.91 % (20373)Termination phase: Saturation
% 27.91/3.91
% 27.91/3.91 % (20373)Memory used [KB]: 11897
% 27.91/3.91 % (20373)Time elapsed: 2.530 s
% 27.91/3.91 % (20373)Instructions burned: 8252 (million)
% 27.91/3.91 % (20373)------------------------------
% 27.91/3.91 % (20373)------------------------------
% 27.91/3.92 % (20450)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 Vampire---4 for (2964ds/4637Mi)
% 28.41/3.94 % (20444)Instruction limit reached!
% 28.41/3.94 % (20444)------------------------------
% 28.41/3.94 % (20444)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 28.41/3.94 % (20444)Termination reason: Unknown
% 28.41/3.94 % (20444)Termination phase: Saturation
% 28.41/3.94
% 28.41/3.94 % (20444)Memory used [KB]: 3326
% 28.41/3.94 % (20444)Time elapsed: 0.379 s
% 28.41/3.94 % (20444)Instructions burned: 1203 (million)
% 28.41/3.94 % (20444)------------------------------
% 28.41/3.94 % (20444)------------------------------
% 28.41/3.95 % (20451)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on Vampire---4 for (2964ds/3174Mi)
% 28.61/4.01 % (20437)Instruction limit reached!
% 28.61/4.01 % (20437)------------------------------
% 28.61/4.01 % (20437)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 28.61/4.02 % (20437)Termination reason: Unknown
% 28.61/4.02 % (20437)Termination phase: Saturation
% 28.61/4.02
% 28.61/4.02 % (20437)Memory used [KB]: 9594
% 28.61/4.02 % (20437)Time elapsed: 0.673 s
% 28.61/4.02 % (20437)Instructions burned: 2401 (million)
% 28.61/4.02 % (20437)------------------------------
% 28.61/4.02 % (20437)------------------------------
% 28.61/4.02 % (20452)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on Vampire---4 for (2963ds/307Mi)
% 29.04/4.11 % (20452)Instruction limit reached!
% 29.04/4.11 % (20452)------------------------------
% 29.04/4.11 % (20452)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 29.04/4.11 % (20452)Termination reason: Unknown
% 29.04/4.11 % (20452)Termination phase: Saturation
% 29.04/4.11
% 29.04/4.11 % (20452)Memory used [KB]: 6140
% 29.04/4.11 % (20452)Time elapsed: 0.085 s
% 29.04/4.11 % (20452)Instructions burned: 308 (million)
% 29.04/4.11 % (20452)------------------------------
% 29.04/4.11 % (20452)------------------------------
% 29.04/4.12 % (20453)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 Vampire---4 for (2962ds/3619Mi)
% 29.04/4.12 % (20453)Refutation not found, incomplete strategy
% 29.04/4.12 % (20453)------------------------------
% 29.04/4.12 % (20453)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 29.04/4.12 % (20453)Termination reason: Refutation not found, incomplete strategy
% 29.04/4.12
% 29.04/4.12
% 29.04/4.12 % (20453)Memory used [KB]: 5500
% 29.04/4.12 % (20453)Time elapsed: 0.003 s
% 29.04/4.12 % (20453)Instructions burned: 5 (million)
% 29.04/4.12 % (20453)------------------------------
% 29.04/4.12 % (20453)------------------------------
% 29.04/4.12 % (20454)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on Vampire---4 for (2962ds/2325Mi)
% 29.83/4.26 % (20449)Instruction limit reached!
% 29.83/4.26 % (20449)------------------------------
% 29.83/4.26 % (20449)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 29.83/4.26 % (20449)Termination reason: Unknown
% 29.83/4.26 % (20449)Termination phase: Saturation
% 29.83/4.26
% 29.83/4.26 % (20449)Memory used [KB]: 7291
% 29.83/4.26 % (20449)Time elapsed: 0.369 s
% 29.83/4.26 % (20449)Instructions burned: 1537 (million)
% 29.83/4.26 % (20449)------------------------------
% 29.83/4.26 % (20449)------------------------------
% 30.32/4.26 % (20455)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 Vampire---4 for (2961ds/2341Mi)
% 30.32/4.27 % (20455)Refutation not found, incomplete strategy
% 30.32/4.27 % (20455)------------------------------
% 30.32/4.27 % (20455)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 30.32/4.27 % (20455)Termination reason: Refutation not found, incomplete strategy
% 30.32/4.27
% 30.32/4.27
% 30.32/4.27 % (20455)Memory used [KB]: 5628
% 30.32/4.27 % (20455)Time elapsed: 0.009 s
% 30.32/4.27 % (20455)Instructions burned: 31 (million)
% 30.32/4.27 % (20455)------------------------------
% 30.32/4.27 % (20455)------------------------------
% 30.32/4.28 % (20456)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 Vampire---4 for (2961ds/7257Mi)
% 30.32/4.28 % (20456)Refutation not found, incomplete strategy
% 30.32/4.28 % (20456)------------------------------
% 30.32/4.28 % (20456)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 30.32/4.28 % (20456)Termination reason: Refutation not found, incomplete strategy
% 30.32/4.28
% 30.32/4.28
% 30.32/4.28 % (20456)Memory used [KB]: 5500
% 30.32/4.28 % (20456)Time elapsed: 0.003 s
% 30.32/4.28 % (20456)Instructions burned: 5 (million)
% 30.32/4.28 % (20456)------------------------------
% 30.32/4.28 % (20456)------------------------------
% 30.32/4.29 % (20457)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 Vampire---4 for (2961ds/3710Mi)
% 33.93/4.63 % (20417)Instruction limit reached!
% 33.93/4.63 % (20417)------------------------------
% 33.93/4.63 % (20417)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 33.93/4.63 % (20417)Termination reason: Unknown
% 33.93/4.63 % (20417)Termination phase: Saturation
% 33.93/4.63
% 33.93/4.63 % (20417)Memory used [KB]: 34157
% 33.93/4.63 % (20417)Time elapsed: 1.796 s
% 33.93/4.63 % (20417)Instructions burned: 6454 (million)
% 33.93/4.63 % (20417)------------------------------
% 33.93/4.63 % (20417)------------------------------
% 33.93/4.64 % (20458)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 Vampire---4 for (2957ds/326Mi)
% 33.93/4.64 % (20458)Refutation not found, incomplete strategy
% 33.93/4.64 % (20458)------------------------------
% 33.93/4.64 % (20458)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 33.93/4.64 % (20458)Termination reason: Refutation not found, incomplete strategy
% 33.93/4.64
% 33.93/4.64
% 33.93/4.64 % (20458)Memory used [KB]: 5500
% 33.93/4.64 % (20458)Time elapsed: 0.003 s
% 33.93/4.64 % (20458)Instructions burned: 4 (million)
% 33.93/4.64 % (20458)------------------------------
% 33.93/4.64 % (20458)------------------------------
% 33.93/4.65 % (20459)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 Vampire---4 for (2957ds/1100Mi)
% 35.49/4.84 % (20454)Instruction limit reached!
% 35.49/4.84 % (20454)------------------------------
% 35.49/4.84 % (20454)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 35.49/4.84 % (20454)Termination reason: Unknown
% 35.49/4.84 % (20454)Termination phase: Saturation
% 35.49/4.84
% 35.49/4.84 % (20454)Memory used [KB]: 8827
% 35.49/4.84 % (20454)Time elapsed: 0.719 s
% 35.49/4.84 % (20454)Instructions burned: 2327 (million)
% 35.49/4.84 % (20454)------------------------------
% 35.49/4.84 % (20454)------------------------------
% 35.49/4.85 % (20436)Instruction limit reached!
% 35.49/4.85 % (20436)------------------------------
% 35.49/4.85 % (20436)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 35.49/4.85 % (20436)Termination reason: Unknown
% 35.49/4.85 % (20436)Termination phase: Saturation
% 35.49/4.85
% 35.49/4.85 % (20436)Memory used [KB]: 10106
% 35.49/4.85 % (20436)Time elapsed: 1.522 s
% 35.49/4.85 % (20436)Instructions burned: 5062 (million)
% 35.49/4.85 % (20436)------------------------------
% 35.49/4.85 % (20436)------------------------------
% 35.49/4.85 % (20460)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on Vampire---4 for (2955ds/406Mi)
% 35.62/4.85 % (20461)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 Vampire---4 for (2955ds/1871Mi)
% 35.62/4.87 % (20459)Instruction limit reached!
% 35.62/4.87 % (20459)------------------------------
% 35.62/4.87 % (20459)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 35.62/4.87 % (20459)Termination reason: Unknown
% 35.62/4.87 % (20459)Termination phase: Saturation
% 35.62/4.87
% 35.62/4.87 % (20459)Memory used [KB]: 6012
% 35.62/4.87 % (20459)Time elapsed: 0.220 s
% 35.62/4.87 % (20459)Instructions burned: 1103 (million)
% 35.62/4.87 % (20459)------------------------------
% 35.62/4.87 % (20459)------------------------------
% 35.62/4.87 % (20462)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 Vampire---4 for (2955ds/1194Mi)
% 35.62/4.91 % (20451)Instruction limit reached!
% 35.62/4.91 % (20451)------------------------------
% 35.62/4.91 % (20451)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 35.62/4.91 % (20451)Termination reason: Unknown
% 35.62/4.92 % (20451)Termination phase: Saturation
% 35.62/4.92
% 35.62/4.92 % (20451)Memory used [KB]: 9083
% 35.62/4.92 % (20451)Time elapsed: 0.964 s
% 35.62/4.92 % (20451)Instructions burned: 3176 (million)
% 35.62/4.92 % (20451)------------------------------
% 35.62/4.92 % (20451)------------------------------
% 35.62/4.92 % (20463)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 Vampire---4 for (2954ds/474Mi)
% 36.74/4.98 % (20460)Instruction limit reached!
% 36.74/4.98 % (20460)------------------------------
% 36.74/4.98 % (20460)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 36.74/4.98 % (20460)Termination reason: Unknown
% 36.74/4.98 % (20460)Termination phase: Saturation
% 36.74/4.98
% 36.74/4.98 % (20460)Memory used [KB]: 7036
% 36.74/4.98 % (20460)Time elapsed: 0.155 s
% 36.74/4.98 % (20460)Instructions burned: 408 (million)
% 36.74/4.98 % (20460)------------------------------
% 36.74/4.98 % (20460)------------------------------
% 36.74/4.99 % (20464)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 Vampire---4 for (2954ds/3115Mi)
% 36.74/5.01 % (20438)Instruction limit reached!
% 36.74/5.01 % (20438)------------------------------
% 36.74/5.01 % (20438)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 36.74/5.01 % (20438)Termination reason: Unknown
% 36.74/5.01 % (20438)Termination phase: Saturation
% 36.74/5.01
% 36.74/5.01 % (20438)Memory used [KB]: 21748
% 36.74/5.01 % (20438)Time elapsed: 1.649 s
% 36.74/5.01 % (20438)Instructions burned: 5801 (million)
% 36.74/5.01 % (20438)------------------------------
% 36.74/5.01 % (20438)------------------------------
% 36.74/5.02 % (20465)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on Vampire---4 for (2953ds/831Mi)
% 37.30/5.06 % (20463)Instruction limit reached!
% 37.30/5.06 % (20463)------------------------------
% 37.30/5.06 % (20463)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 37.30/5.06 % (20463)Termination reason: Unknown
% 37.30/5.06 % (20463)Termination phase: Saturation
% 37.30/5.06
% 37.30/5.06 % (20463)Memory used [KB]: 6780
% 37.30/5.06 % (20463)Time elapsed: 0.159 s
% 37.30/5.06 % (20463)Instructions burned: 475 (million)
% 37.30/5.06 % (20463)------------------------------
% 37.30/5.06 % (20463)------------------------------
% 37.30/5.07 % (20466)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 Vampire---4 for (2953ds/1188Mi)
% 37.47/5.10 % (20457)First to succeed.
% 37.78/5.16 % (20457)Refutation found. Thanks to Tanya!
% 37.78/5.16 % SZS status Theorem for Vampire---4
% 37.78/5.16 % SZS output start Proof for Vampire---4
% 37.78/5.16 thf(func_def_0, type, irel: $i > $i > $o).
% 37.78/5.16 thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 37.78/5.16 thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 37.78/5.16 thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 37.78/5.16 thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 37.78/5.16 thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 37.78/5.16 thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 37.78/5.16 thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 37.78/5.16 thf(func_def_9, type, itrue: $i > $o).
% 37.78/5.16 thf(func_def_10, type, ifalse: $i > $o).
% 37.78/5.16 thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 37.78/5.16 thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 37.78/5.16 thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 37.78/5.16 thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 37.78/5.16 thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 37.78/5.16 thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 37.78/5.16 thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 37.78/5.16 thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 37.78/5.16 thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 37.78/5.16 thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 37.78/5.16 thf(func_def_21, type, a1: $i > $o).
% 37.78/5.16 thf(func_def_22, type, a2: $i > $o).
% 37.78/5.16 thf(func_def_23, type, a3: $i > $o).
% 37.78/5.16 thf(func_def_24, type, a4: $i > $o).
% 37.78/5.16 thf(func_def_38, type, ph1: !>[X0: $tType]:(X0)).
% 37.78/5.16 thf(f9866,plain,(
% 37.78/5.16 $false),
% 37.78/5.16 inference(avatar_sat_refutation,[],[f117,f192,f278,f299,f557,f681,f773,f1063,f1345,f1351,f1401,f1479,f1735,f1743,f1866,f2198,f2770,f2854,f2868,f3184,f3274,f3279,f3284,f3351,f3360,f3541,f3647,f3661,f3667,f4555,f4874,f4885,f6057,f6062,f6154,f6314,f6559,f6570,f6682,f6691,f7120,f7124,f7147,f7225,f7289,f7439,f7938,f8080,f8092,f8116,f8131,f8359,f8366,f8976,f8985,f9004,f9174,f9232,f9237,f9823,f9847])).
% 37.78/5.16 thf(f9847,plain,(
% 37.78/5.16 ~spl0_2 | ~spl0_9 | spl0_10 | ~spl0_103),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f9846])).
% 37.78/5.16 thf(f9846,plain,(
% 37.78/5.16 $false | (~spl0_2 | ~spl0_9 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f9845])).
% 37.78/5.16 thf(f9845,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_2 | ~spl0_9 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f9844])).
% 37.78/5.16 thf(f9844,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => $true) = $false) | (~spl0_2 | ~spl0_9 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(forward_demodulation,[],[f9843,f294])).
% 37.78/5.16 thf(f294,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | ~spl0_9),
% 37.78/5.16 inference(avatar_component_clause,[],[f292])).
% 37.78/5.16 thf(f292,plain,(
% 37.78/5.16 spl0_9 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])).
% 37.78/5.16 thf(f9843,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) = $false) | (~spl0_2 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f9842])).
% 37.78/5.16 thf(f9842,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) = $false) | (~spl0_2 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f9841])).
% 37.78/5.16 thf(f9841,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) = $false) | (~spl0_2 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f9840])).
% 37.78/5.16 thf(f9840,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & $true)) = $false) | (~spl0_2 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f9839])).
% 37.78/5.16 thf(f9839,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | $true))) = $false) | (~spl0_2 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(forward_demodulation,[],[f7629,f8162])).
% 37.78/5.16 thf(f8162,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) | spl0_10),
% 37.78/5.16 inference(not_proxy_clausification,[],[f297])).
% 37.78/5.16 thf(f297,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) != $true) | spl0_10),
% 37.78/5.16 inference(avatar_component_clause,[],[f296])).
% 37.78/5.16 thf(f296,plain,(
% 37.78/5.16 spl0_10 <=> ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) = $true)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_10])])).
% 37.78/5.16 thf(f7629,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))))) = $false) | (~spl0_2 | ~spl0_103)),
% 37.78/5.16 inference(beta_eta_normalization,[],[f7628])).
% 37.78/5.16 thf(f7628,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))) @ sK3) = $false) | (~spl0_2 | ~spl0_103)),
% 37.78/5.16 inference(sigma_clausification,[],[f7621])).
% 37.78/5.16 thf(f7621,plain,(
% 37.78/5.16 ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) | (~spl0_2 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7620])).
% 37.78/5.16 thf(f7620,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) = $false) | (~spl0_2 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7619])).
% 37.78/5.16 thf(f7619,plain,(
% 37.78/5.16 (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) = $false) | (~spl0_2 | ~spl0_103)),
% 37.78/5.16 inference(forward_demodulation,[],[f116,f7224])).
% 37.78/5.16 thf(f7224,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | ~spl0_103),
% 37.78/5.16 inference(avatar_component_clause,[],[f7222])).
% 37.78/5.16 thf(f7222,plain,(
% 37.78/5.16 spl0_103 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_103])])).
% 37.78/5.16 thf(f116,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) = $false) | ~spl0_2),
% 37.78/5.16 inference(avatar_component_clause,[],[f114])).
% 37.78/5.16 thf(f114,plain,(
% 37.78/5.16 spl0_2 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 37.78/5.16 thf(f9823,plain,(
% 37.78/5.16 ~spl0_8 | ~spl0_19 | ~spl0_29 | ~spl0_53),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f9822])).
% 37.78/5.16 thf(f9822,plain,(
% 37.78/5.16 $false | (~spl0_8 | ~spl0_19 | ~spl0_29 | ~spl0_53)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f9821])).
% 37.78/5.16 thf(f9821,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_8 | ~spl0_19 | ~spl0_29 | ~spl0_53)),
% 37.78/5.16 inference(boolean_simplification,[],[f9820])).
% 37.78/5.16 thf(f9820,plain,(
% 37.78/5.16 ($true = ($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))))) | (~spl0_8 | ~spl0_19 | ~spl0_29 | ~spl0_53)),
% 37.78/5.16 inference(forward_demodulation,[],[f9790,f1058])).
% 37.78/5.16 thf(f1058,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) = $false) | ~spl0_29),
% 37.78/5.16 inference(avatar_component_clause,[],[f1056])).
% 37.78/5.16 thf(f1056,plain,(
% 37.78/5.16 spl0_29 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_29])])).
% 37.78/5.16 thf(f9790,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))))) | (~spl0_8 | ~spl0_19 | ~spl0_29 | ~spl0_53)),
% 37.78/5.16 inference(boolean_simplification,[],[f9758])).
% 37.78/5.16 thf(f9758,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0)))))))) | (~spl0_8 | ~spl0_19 | ~spl0_29 | ~spl0_53)),
% 37.78/5.16 inference(superposition,[],[f9736,f9308])).
% 37.78/5.16 thf(f9308,plain,(
% 37.78/5.16 ($true = (irel @ sK4 @ sK10)) | (~spl0_8 | ~spl0_19 | ~spl0_29)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f9307])).
% 37.78/5.16 thf(f9307,plain,(
% 37.78/5.16 ((~ (irel @ sK4 @ sK10)) = $false) | (~spl0_8 | ~spl0_19 | ~spl0_29)),
% 37.78/5.16 inference(boolean_simplification,[],[f9306])).
% 37.78/5.16 thf(f9306,plain,(
% 37.78/5.16 (((irel @ sK4 @ sK10) => $false) = $false) | (~spl0_8 | ~spl0_19 | ~spl0_29)),
% 37.78/5.16 inference(boolean_simplification,[],[f9305])).
% 37.78/5.16 thf(f9305,plain,(
% 37.78/5.16 (((irel @ sK4 @ sK10) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) & $false)) = $false) | (~spl0_8 | ~spl0_19 | ~spl0_29)),
% 37.78/5.16 inference(forward_demodulation,[],[f9304,f1058])).
% 37.78/5.16 thf(f9304,plain,(
% 37.78/5.16 (((irel @ sK4 @ sK10) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))))) = $false) | (~spl0_8 | ~spl0_19)),
% 37.78/5.16 inference(beta_eta_normalization,[],[f9303])).
% 37.78/5.16 thf(f9303,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ sK10) = $false) | (~spl0_8 | ~spl0_19)),
% 37.78/5.16 inference(sigma_clausification,[],[f9242])).
% 37.78/5.16 thf(f9242,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))) = $false) | (~spl0_8 | ~spl0_19)),
% 37.78/5.16 inference(boolean_simplification,[],[f9241])).
% 37.78/5.16 thf(f9241,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $false) | (~spl0_8 | ~spl0_19)),
% 37.78/5.16 inference(boolean_simplification,[],[f9240])).
% 37.78/5.16 thf(f9240,plain,(
% 37.78/5.16 (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $false) | (~spl0_8 | ~spl0_19)),
% 37.78/5.16 inference(backward_demodulation,[],[f277,f676])).
% 37.78/5.16 thf(f676,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | ~spl0_19),
% 37.78/5.16 inference(avatar_component_clause,[],[f674])).
% 37.78/5.16 thf(f674,plain,(
% 37.78/5.16 spl0_19 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0)))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_19])])).
% 37.78/5.16 thf(f277,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $false) | ~spl0_8),
% 37.78/5.16 inference(avatar_component_clause,[],[f275])).
% 37.78/5.16 thf(f275,plain,(
% 37.78/5.16 spl0_8 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])).
% 37.78/5.16 thf(f9736,plain,(
% 37.78/5.16 ( ! [X1 : $i] : ((((irel @ sK4 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))))) = $true)) ) | ~spl0_53),
% 37.78/5.16 inference(beta_eta_normalization,[],[f9725])).
% 37.78/5.16 thf(f9725,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ X1))) ) | ~spl0_53),
% 37.78/5.16 inference(pi_clausification,[],[f2610])).
% 37.78/5.16 thf(f2610,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))) = $true) | ~spl0_53),
% 37.78/5.16 inference(avatar_component_clause,[],[f2608])).
% 37.78/5.16 thf(f2608,plain,(
% 37.78/5.16 spl0_53 <=> ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))) = $true)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_53])])).
% 37.78/5.16 thf(f9237,plain,(
% 37.78/5.16 spl0_19 | ~spl0_2 | ~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20 | ~spl0_53 | ~spl0_103),
% 37.78/5.16 inference(avatar_split_clause,[],[f9236,f7222,f2608,f678,f296,f275,f185,f114,f674])).
% 37.78/5.16 thf(f185,plain,(
% 37.78/5.16 spl0_5 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 37.78/5.16 thf(f678,plain,(
% 37.78/5.16 spl0_20 <=> ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_20])])).
% 37.78/5.16 thf(f9236,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (~spl0_2 | ~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20 | ~spl0_53 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f9235])).
% 37.78/5.16 thf(f9235,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) = $true) | (~spl0_2 | ~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20 | ~spl0_53 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f9234])).
% 37.78/5.16 thf(f9234,plain,(
% 37.78/5.16 ($true = ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0)))))) | (~spl0_2 | ~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20 | ~spl0_53 | ~spl0_103)),
% 37.78/5.16 inference(backward_demodulation,[],[f9207,f2610])).
% 37.78/5.16 thf(f9207,plain,(
% 37.78/5.16 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0)))))) | (~spl0_2 | ~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20 | ~spl0_103)),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f9199])).
% 37.78/5.16 thf(f9199,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl0_2 | ~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f9191])).
% 37.78/5.16 thf(f9191,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl0_2 | ~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20 | ~spl0_103)),
% 37.78/5.16 inference(superposition,[],[f8276,f9182])).
% 37.78/5.16 thf(f9182,plain,(
% 37.78/5.16 ($true = (irel @ sK3 @ sK4)) | (~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f9181])).
% 37.78/5.16 thf(f9181,plain,(
% 37.78/5.16 ((~ (irel @ sK3 @ sK4)) = $false) | (~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20)),
% 37.78/5.16 inference(boolean_simplification,[],[f9180])).
% 37.78/5.16 thf(f9180,plain,(
% 37.78/5.16 ($false = ((irel @ sK3 @ sK4) => $false)) | (~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20)),
% 37.78/5.16 inference(backward_demodulation,[],[f9177,f277])).
% 37.78/5.16 thf(f9177,plain,(
% 37.78/5.16 ($false = ((irel @ sK3 @ sK4) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | (~spl0_5 | spl0_10 | ~spl0_20)),
% 37.78/5.16 inference(boolean_simplification,[],[f9176])).
% 37.78/5.16 thf(f9176,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & $true)) = $false) | (~spl0_5 | spl0_10 | ~spl0_20)),
% 37.78/5.16 inference(boolean_simplification,[],[f9175])).
% 37.78/5.16 thf(f9175,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))))) = $false) | (~spl0_5 | spl0_10 | ~spl0_20)),
% 37.78/5.16 inference(backward_demodulation,[],[f8249,f680])).
% 37.78/5.16 thf(f680,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | ~spl0_20),
% 37.78/5.16 inference(avatar_component_clause,[],[f678])).
% 37.78/5.16 thf(f8249,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))))) = $false) | (~spl0_5 | spl0_10)),
% 37.78/5.16 inference(beta_eta_normalization,[],[f8248])).
% 37.78/5.16 thf(f8248,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))) @ sK4) = $false) | (~spl0_5 | spl0_10)),
% 37.78/5.16 inference(sigma_clausification,[],[f8169])).
% 37.78/5.16 thf(f8169,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))) = $false) | (~spl0_5 | spl0_10)),
% 37.78/5.16 inference(boolean_simplification,[],[f8168])).
% 37.78/5.16 thf(f8168,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) = $false) | (~spl0_5 | spl0_10)),
% 37.78/5.16 inference(boolean_simplification,[],[f8165])).
% 37.78/5.16 thf(f8165,plain,(
% 37.78/5.16 (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) = $false) | (~spl0_5 | spl0_10)),
% 37.78/5.16 inference(backward_demodulation,[],[f187,f8162])).
% 37.78/5.16 thf(f187,plain,(
% 37.78/5.16 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) | ~spl0_5),
% 37.78/5.16 inference(avatar_component_clause,[],[f185])).
% 37.78/5.16 thf(f8276,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((irel @ sK3 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))))) ) | (~spl0_2 | ~spl0_5 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(beta_eta_normalization,[],[f8273])).
% 37.78/5.16 thf(f8273,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))) @ X1))) ) | (~spl0_2 | ~spl0_5 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(pi_clausification,[],[f8173])).
% 37.78/5.16 thf(f8173,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))) = $true) | (~spl0_2 | ~spl0_5 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8172])).
% 37.78/5.16 thf(f8172,plain,(
% 37.78/5.16 ($true = ($true & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) | (~spl0_2 | ~spl0_5 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8171])).
% 37.78/5.16 thf(f8171,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $true) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) | (~spl0_2 | ~spl0_5 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8170])).
% 37.78/5.16 thf(f8170,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $true) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | (~spl0_2 | ~spl0_5 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8163])).
% 37.78/5.16 thf(f8163,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $true) & ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | (~spl0_2 | ~spl0_5 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(backward_demodulation,[],[f8158,f8162])).
% 37.78/5.16 thf(f8158,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | (~spl0_2 | ~spl0_5 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8152])).
% 37.78/5.16 thf(f8152,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))))) | (~spl0_2 | ~spl0_5 | ~spl0_103)),
% 37.78/5.16 inference(superposition,[],[f7298,f8149])).
% 37.78/5.16 thf(f8149,plain,(
% 37.78/5.16 ($true = (irel @ sK2 @ sK3)) | (~spl0_2 | ~spl0_5 | ~spl0_103)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f8134])).
% 37.78/5.16 thf(f8134,plain,(
% 37.78/5.16 ((~ (irel @ sK2 @ sK3)) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8133])).
% 37.78/5.16 thf(f8133,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => $false) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8132])).
% 37.78/5.16 thf(f8132,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => ($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))))) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_103)),
% 37.78/5.16 inference(backward_demodulation,[],[f7629,f187])).
% 37.78/5.16 thf(f7298,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((irel @ sK2 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a4 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))))) ) | ~spl0_103),
% 37.78/5.16 inference(beta_eta_normalization,[],[f7297])).
% 37.78/5.16 thf(f7297,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))) @ X1))) ) | ~spl0_103),
% 37.78/5.16 inference(pi_clausification,[],[f7224])).
% 37.78/5.16 thf(f9232,plain,(
% 37.78/5.16 ~spl0_2 | ~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20 | spl0_53 | ~spl0_103),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f9231])).
% 37.78/5.16 thf(f9231,plain,(
% 37.78/5.16 $false | (~spl0_2 | ~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20 | spl0_53 | ~spl0_103)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f9230])).
% 37.78/5.16 thf(f9230,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_2 | ~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20 | spl0_53 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f9229])).
% 37.78/5.16 thf(f9229,plain,(
% 37.78/5.16 (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20 | spl0_53 | ~spl0_103)),
% 37.78/5.16 inference(backward_demodulation,[],[f277,f9227])).
% 37.78/5.16 thf(f9227,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) = $true) | (~spl0_2 | ~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20 | spl0_53 | ~spl0_103)),
% 37.78/5.16 inference(subsumption_resolution,[],[f9222,f2609])).
% 37.78/5.16 thf(f2609,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))) != $true) | spl0_53),
% 37.78/5.16 inference(avatar_component_clause,[],[f2608])).
% 37.78/5.16 thf(f9222,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) = $true) | (~spl0_2 | ~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20 | ~spl0_103)),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f9211])).
% 37.78/5.16 thf(f9211,plain,(
% 37.78/5.16 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | (~spl0_2 | ~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f9210])).
% 37.78/5.16 thf(f9210,plain,(
% 37.78/5.16 ($true = ($true & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl0_2 | ~spl0_5 | ~spl0_8 | spl0_10 | ~spl0_20 | ~spl0_103)),
% 37.78/5.16 inference(backward_demodulation,[],[f9199,f9207])).
% 37.78/5.16 thf(f9174,plain,(
% 37.78/5.16 ~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | spl0_19 | spl0_27 | ~spl0_103),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f9173])).
% 37.78/5.16 thf(f9173,plain,(
% 37.78/5.16 $false | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | spl0_19 | spl0_27 | ~spl0_103)),
% 37.78/5.16 inference(subsumption_resolution,[],[f9172,f906])).
% 37.78/5.16 thf(f906,plain,(
% 37.78/5.16 ($true != (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | spl0_27),
% 37.78/5.16 inference(avatar_component_clause,[],[f905])).
% 37.78/5.16 thf(f905,plain,(
% 37.78/5.16 spl0_27 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_27])])).
% 37.78/5.16 thf(f9172,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | spl0_19 | ~spl0_103)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f9140])).
% 37.78/5.16 thf(f9140,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | spl0_19 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f9139])).
% 37.78/5.16 thf(f9139,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $false) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | spl0_19 | ~spl0_103)),
% 37.78/5.16 inference(backward_demodulation,[],[f273,f9128])).
% 37.78/5.16 thf(f9128,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0)))) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | spl0_19 | ~spl0_103)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f9073])).
% 37.78/5.16 thf(f9073,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) = $true) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | spl0_19 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f9071])).
% 37.78/5.16 thf(f9071,plain,(
% 37.78/5.16 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | $false)) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | spl0_19 | ~spl0_103)),
% 37.78/5.16 inference(backward_demodulation,[],[f9033,f9064])).
% 37.78/5.16 thf(f9064,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | spl0_19 | ~spl0_103)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f9049])).
% 37.78/5.16 thf(f9049,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | spl0_19 | ~spl0_103)),
% 37.78/5.16 inference(subsumption_resolution,[],[f9044,f675])).
% 37.78/5.16 thf(f675,plain,(
% 37.78/5.16 ($true != (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | spl0_19),
% 37.78/5.16 inference(avatar_component_clause,[],[f674])).
% 37.78/5.16 thf(f9044,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f9038])).
% 37.78/5.16 thf(f9038,plain,(
% 37.78/5.16 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0)))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f9037])).
% 37.78/5.16 thf(f9037,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) & $true) = $true) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(backward_demodulation,[],[f9029,f9033])).
% 37.78/5.16 thf(f9029,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f9021])).
% 37.78/5.16 thf(f9021,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(superposition,[],[f8276,f9012])).
% 37.78/5.16 thf(f9012,plain,(
% 37.78/5.16 ($true = (irel @ sK3 @ sK4)) | (~spl0_5 | ~spl0_7 | spl0_10)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f9007])).
% 37.78/5.16 thf(f9007,plain,(
% 37.78/5.16 ((~ (irel @ sK3 @ sK4)) = $false) | (~spl0_5 | ~spl0_7 | spl0_10)),
% 37.78/5.16 inference(boolean_simplification,[],[f9006])).
% 37.78/5.16 thf(f9006,plain,(
% 37.78/5.16 ($false = ((irel @ sK3 @ sK4) => $false)) | (~spl0_5 | ~spl0_7 | spl0_10)),
% 37.78/5.16 inference(boolean_simplification,[],[f9005])).
% 37.78/5.16 thf(f9005,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & $false)) = $false) | (~spl0_5 | ~spl0_7 | spl0_10)),
% 37.78/5.16 inference(forward_demodulation,[],[f8249,f273])).
% 37.78/5.16 thf(f9033,plain,(
% 37.78/5.16 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f9029])).
% 37.78/5.16 thf(f273,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) = $false) | ~spl0_7),
% 37.78/5.16 inference(avatar_component_clause,[],[f271])).
% 37.78/5.16 thf(f271,plain,(
% 37.78/5.16 spl0_7 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])).
% 37.78/5.16 thf(f9004,plain,(
% 37.78/5.16 ~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_84 | ~spl0_103),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f9003])).
% 37.78/5.16 thf(f9003,plain,(
% 37.78/5.16 $false | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_84 | ~spl0_103)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f9002])).
% 37.78/5.16 thf(f9002,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_84 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f9001])).
% 37.78/5.16 thf(f9001,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) & $false)) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_84 | ~spl0_103)),
% 37.78/5.16 inference(forward_demodulation,[],[f8999,f4869])).
% 37.78/5.16 thf(f4869,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) = $false) | ~spl0_84),
% 37.78/5.16 inference(avatar_component_clause,[],[f4867])).
% 37.78/5.16 thf(f4867,plain,(
% 37.78/5.16 spl0_84 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_84])])).
% 37.78/5.16 thf(f8999,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_84 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8993])).
% 37.78/5.16 thf(f8993,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0)))))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_84 | ~spl0_103)),
% 37.78/5.16 inference(superposition,[],[f8863,f8990])).
% 37.78/5.16 thf(f8990,plain,(
% 37.78/5.16 ((irel @ sK4 @ sK26) = $true) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_84 | ~spl0_103)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f8989])).
% 37.78/5.16 thf(f8989,plain,(
% 37.78/5.16 ((~ (irel @ sK4 @ sK26)) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_84 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8988])).
% 37.78/5.16 thf(f8988,plain,(
% 37.78/5.16 (((irel @ sK4 @ sK26) => $false) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_84 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8987])).
% 37.78/5.16 thf(f8987,plain,(
% 37.78/5.16 ($false = ((irel @ sK4 @ sK26) => ($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0)))))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_84 | ~spl0_103)),
% 37.78/5.16 inference(backward_demodulation,[],[f8440,f4869])).
% 37.78/5.16 thf(f8440,plain,(
% 37.78/5.16 (((irel @ sK4 @ sK26) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_103)),
% 37.78/5.16 inference(beta_eta_normalization,[],[f8438])).
% 37.78/5.16 thf(f8438,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ sK26) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_103)),
% 37.78/5.16 inference(sigma_clausification,[],[f8422])).
% 37.78/5.16 thf(f8422,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_103)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f8413])).
% 37.78/5.16 thf(f8413,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8412])).
% 37.78/5.16 thf(f8412,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) = $true) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8411])).
% 37.78/5.16 thf(f8411,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) & $true)) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8410])).
% 37.78/5.16 thf(f8410,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8409])).
% 37.78/5.16 thf(f8409,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) & ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_103)),
% 37.78/5.16 inference(forward_demodulation,[],[f8404,f8372])).
% 37.78/5.16 thf(f8372,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0)))) = $false) | (~spl0_7 | ~spl0_27)),
% 37.78/5.16 inference(boolean_simplification,[],[f8371])).
% 37.78/5.16 thf(f8371,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) = $false) | (~spl0_7 | ~spl0_27)),
% 37.78/5.16 inference(boolean_simplification,[],[f8370])).
% 37.78/5.16 thf(f8370,plain,(
% 37.78/5.16 ($false = ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0)))))) | (~spl0_7 | ~spl0_27)),
% 37.78/5.16 inference(forward_demodulation,[],[f273,f907])).
% 37.78/5.16 thf(f907,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | ~spl0_27),
% 37.78/5.16 inference(avatar_component_clause,[],[f905])).
% 37.78/5.16 thf(f8404,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8399])).
% 37.78/5.16 thf(f8399,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_103)),
% 37.78/5.16 inference(superposition,[],[f8276,f8395])).
% 37.78/5.16 thf(f8395,plain,(
% 37.78/5.16 ($true = (irel @ sK3 @ sK4)) | (~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f8384])).
% 37.78/5.16 thf(f8384,plain,(
% 37.78/5.16 ((~ (irel @ sK3 @ sK4)) = $false) | (~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27)),
% 37.78/5.16 inference(boolean_simplification,[],[f8383])).
% 37.78/5.16 thf(f8383,plain,(
% 37.78/5.16 ($false = ((irel @ sK3 @ sK4) => $false)) | (~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27)),
% 37.78/5.16 inference(boolean_simplification,[],[f8382])).
% 37.78/5.16 thf(f8382,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => (~ $true)) = $false) | (~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27)),
% 37.78/5.16 inference(forward_demodulation,[],[f8381,f907])).
% 37.78/5.16 thf(f8381,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) = $false) | (~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27)),
% 37.78/5.16 inference(boolean_simplification,[],[f8380])).
% 37.78/5.16 thf(f8380,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => ($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) = $false) | (~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27)),
% 37.78/5.16 inference(boolean_simplification,[],[f8379])).
% 37.78/5.16 thf(f8379,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) = $false) | (~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27)),
% 37.78/5.16 inference(boolean_simplification,[],[f8378])).
% 37.78/5.16 thf(f8378,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) = $false) | (~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27)),
% 37.78/5.16 inference(boolean_simplification,[],[f8377])).
% 37.78/5.16 thf(f8377,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $false))) = $false) | (~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27)),
% 37.78/5.16 inference(forward_demodulation,[],[f8249,f8372])).
% 37.78/5.16 thf(f8863,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((irel @ sK4 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))))))) ) | ~spl0_27),
% 37.78/5.16 inference(beta_eta_normalization,[],[f8862])).
% 37.78/5.16 thf(f8862,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ X1))) ) | ~spl0_27),
% 37.78/5.16 inference(pi_clausification,[],[f907])).
% 37.78/5.16 thf(f8985,plain,(
% 37.78/5.16 ~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_53 | ~spl0_103),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f8984])).
% 37.78/5.16 thf(f8984,plain,(
% 37.78/5.16 $false | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_53 | ~spl0_103)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f8983])).
% 37.78/5.16 thf(f8983,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_53 | ~spl0_103)),
% 37.78/5.16 inference(forward_demodulation,[],[f2610,f8422])).
% 37.78/5.16 thf(f8976,plain,(
% 37.78/5.16 ~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_85 | ~spl0_103),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f8975])).
% 37.78/5.16 thf(f8975,plain,(
% 37.78/5.16 $false | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_85 | ~spl0_103)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f8974])).
% 37.78/5.16 thf(f8974,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_85 | ~spl0_103)),
% 37.78/5.16 inference(forward_demodulation,[],[f8973,f8817])).
% 37.78/5.16 thf(f8817,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) = $false) | ~spl0_85),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f4873])).
% 37.78/5.16 thf(f4873,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) = $false) | ~spl0_85),
% 37.78/5.16 inference(avatar_component_clause,[],[f4871])).
% 37.78/5.16 thf(f4871,plain,(
% 37.78/5.16 spl0_85 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_85])])).
% 37.78/5.16 thf(f8973,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0)))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_85 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8972])).
% 37.78/5.16 thf(f8972,plain,(
% 37.78/5.16 ($true = ($true => (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_85 | ~spl0_103)),
% 37.78/5.16 inference(forward_demodulation,[],[f8903,f8464])).
% 37.78/5.16 thf(f8464,plain,(
% 37.78/5.16 ((irel @ sK4 @ sK26) = $true) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_85 | ~spl0_103)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f8451])).
% 37.78/5.16 thf(f8451,plain,(
% 37.78/5.16 ((~ (irel @ sK4 @ sK26)) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_85 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8450])).
% 37.78/5.16 thf(f8450,plain,(
% 37.78/5.16 (((irel @ sK4 @ sK26) => $false) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_85 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8449])).
% 37.78/5.16 thf(f8449,plain,(
% 37.78/5.16 (((irel @ sK4 @ sK26) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) & $false)) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_7 | spl0_10 | ~spl0_27 | ~spl0_85 | ~spl0_103)),
% 37.78/5.16 inference(forward_demodulation,[],[f8440,f4873])).
% 37.78/5.16 thf(f8903,plain,(
% 37.78/5.16 ($true = ((irel @ sK4 @ sK26) => (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) | (~spl0_27 | ~spl0_85)),
% 37.78/5.16 inference(boolean_simplification,[],[f8902])).
% 37.78/5.16 thf(f8902,plain,(
% 37.78/5.16 ($true = ((irel @ sK4 @ sK26) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | $false))) | (~spl0_27 | ~spl0_85)),
% 37.78/5.16 inference(boolean_simplification,[],[f8901])).
% 37.78/5.16 thf(f8901,plain,(
% 37.78/5.16 ($true = ((irel @ sK4 @ sK26) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | $false) & $true))) | (~spl0_27 | ~spl0_85)),
% 37.78/5.16 inference(boolean_simplification,[],[f8900])).
% 37.78/5.16 thf(f8900,plain,(
% 37.78/5.16 (((irel @ sK4 @ sK26) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | $false) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl0_27 | ~spl0_85)),
% 37.78/5.16 inference(boolean_simplification,[],[f8877])).
% 37.78/5.16 thf(f8877,plain,(
% 37.78/5.16 (((irel @ sK4 @ sK26) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | $false) & ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))))) = $true) | (~spl0_27 | ~spl0_85)),
% 37.78/5.16 inference(superposition,[],[f8863,f8822])).
% 37.78/5.16 thf(f8822,plain,(
% 37.78/5.16 ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | ~spl0_85),
% 37.78/5.16 inference(boolean_simplification,[],[f8821])).
% 37.78/5.16 thf(f8821,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) = $false) | ~spl0_85),
% 37.78/5.16 inference(backward_demodulation,[],[f4873,f8817])).
% 37.78/5.16 thf(f8366,plain,(
% 37.78/5.16 ~spl0_5 | spl0_10 | ~spl0_19 | ~spl0_27),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f8365])).
% 37.78/5.16 thf(f8365,plain,(
% 37.78/5.16 $false | (~spl0_5 | spl0_10 | ~spl0_19 | ~spl0_27)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f8364])).
% 37.78/5.16 thf(f8364,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_5 | spl0_10 | ~spl0_19 | ~spl0_27)),
% 37.78/5.16 inference(boolean_simplification,[],[f8362])).
% 37.78/5.16 thf(f8362,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => $true) = $false) | (~spl0_5 | spl0_10 | ~spl0_19 | ~spl0_27)),
% 37.78/5.16 inference(backward_demodulation,[],[f8258,f907])).
% 37.78/5.16 thf(f8258,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $false) | (~spl0_5 | spl0_10 | ~spl0_19)),
% 37.78/5.16 inference(boolean_simplification,[],[f8257])).
% 37.78/5.16 thf(f8257,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) = $false) | (~spl0_5 | spl0_10 | ~spl0_19)),
% 37.78/5.16 inference(boolean_simplification,[],[f8256])).
% 37.78/5.16 thf(f8256,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) = $false) | (~spl0_5 | spl0_10 | ~spl0_19)),
% 37.78/5.16 inference(boolean_simplification,[],[f8255])).
% 37.78/5.16 thf(f8255,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & $true)) = $false) | (~spl0_5 | spl0_10 | ~spl0_19)),
% 37.78/5.16 inference(boolean_simplification,[],[f8254])).
% 37.78/5.16 thf(f8254,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $true))) = $false) | (~spl0_5 | spl0_10 | ~spl0_19)),
% 37.78/5.16 inference(forward_demodulation,[],[f8249,f676])).
% 37.78/5.16 thf(f8359,plain,(
% 37.78/5.16 ~spl0_7 | ~spl0_19),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f8358])).
% 37.78/5.16 thf(f8358,plain,(
% 37.78/5.16 $false | (~spl0_7 | ~spl0_19)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f8357])).
% 37.78/5.16 thf(f8357,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_7 | ~spl0_19)),
% 37.78/5.16 inference(boolean_simplification,[],[f8356])).
% 37.78/5.16 thf(f8356,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $true) = $false) | (~spl0_7 | ~spl0_19)),
% 37.78/5.16 inference(forward_demodulation,[],[f273,f676])).
% 37.78/5.16 thf(f8131,plain,(
% 37.78/5.16 ~spl0_8 | ~spl0_19 | spl0_20),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f8130])).
% 37.78/5.16 thf(f8130,plain,(
% 37.78/5.16 $false | (~spl0_8 | ~spl0_19 | spl0_20)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f8129])).
% 37.78/5.16 thf(f8129,plain,(
% 37.78/5.16 ($true != $true) | (~spl0_8 | ~spl0_19 | spl0_20)),
% 37.78/5.16 inference(boolean_simplification,[],[f8128])).
% 37.78/5.16 thf(f8128,plain,(
% 37.78/5.16 ($true != (~ $false)) | (~spl0_8 | ~spl0_19 | spl0_20)),
% 37.78/5.16 inference(forward_demodulation,[],[f679,f8097])).
% 37.78/5.16 thf(f8097,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))) = $false) | (~spl0_8 | ~spl0_19)),
% 37.78/5.16 inference(boolean_simplification,[],[f8096])).
% 37.78/5.16 thf(f8096,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $false) | (~spl0_8 | ~spl0_19)),
% 37.78/5.16 inference(boolean_simplification,[],[f8095])).
% 37.78/5.16 thf(f8095,plain,(
% 37.78/5.16 (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $false) | (~spl0_8 | ~spl0_19)),
% 37.78/5.16 inference(forward_demodulation,[],[f277,f676])).
% 37.78/5.16 thf(f679,plain,(
% 37.78/5.16 ($true != (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | spl0_20),
% 37.78/5.16 inference(avatar_component_clause,[],[f678])).
% 37.78/5.16 thf(f8116,plain,(
% 37.78/5.16 ~spl0_5 | ~spl0_10),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f8115])).
% 37.78/5.16 thf(f8115,plain,(
% 37.78/5.16 $false | (~spl0_5 | ~spl0_10)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f8114])).
% 37.78/5.16 thf(f8114,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_5 | ~spl0_10)),
% 37.78/5.16 inference(boolean_simplification,[],[f8113])).
% 37.78/5.16 thf(f8113,plain,(
% 37.78/5.16 (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) = $false) | (~spl0_5 | ~spl0_10)),
% 37.78/5.16 inference(boolean_simplification,[],[f8112])).
% 37.78/5.16 thf(f8112,plain,(
% 37.78/5.16 (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) = $false) | (~spl0_5 | ~spl0_10)),
% 37.78/5.16 inference(forward_demodulation,[],[f187,f452])).
% 37.78/5.16 thf(f452,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0)))) = $false) | ~spl0_10),
% 37.78/5.16 inference(not_proxy_clausification,[],[f298])).
% 37.78/5.16 thf(f298,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) = $true) | ~spl0_10),
% 37.78/5.16 inference(avatar_component_clause,[],[f296])).
% 37.78/5.16 thf(f8092,plain,(
% 37.78/5.16 ~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | spl0_39 | ~spl0_51 | ~spl0_103),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f8091])).
% 37.78/5.16 thf(f8091,plain,(
% 37.78/5.16 $false | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | spl0_39 | ~spl0_51 | ~spl0_103)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f8090])).
% 37.78/5.16 thf(f8090,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | spl0_39 | ~spl0_51 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f8089])).
% 37.78/5.16 thf(f8089,plain,(
% 37.78/5.16 ($true = (~ $true)) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | spl0_39 | ~spl0_51 | ~spl0_103)),
% 37.78/5.16 inference(backward_demodulation,[],[f7946,f2468])).
% 37.78/5.16 thf(f2468,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | ~spl0_51),
% 37.78/5.16 inference(avatar_component_clause,[],[f2466])).
% 37.78/5.16 thf(f2466,plain,(
% 37.78/5.16 spl0_51 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_51])])).
% 37.78/5.16 thf(f7946,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | spl0_39 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7945])).
% 37.78/5.16 thf(f7945,plain,(
% 37.78/5.16 ($true = ($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | spl0_39 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7944])).
% 37.78/5.16 thf(f7944,plain,(
% 37.78/5.16 ($true = (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | spl0_39 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7943])).
% 37.78/5.16 thf(f7943,plain,(
% 37.78/5.16 ($true = (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | spl0_39 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7941])).
% 37.78/5.16 thf(f7941,plain,(
% 37.78/5.16 ((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $false)) = $true) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | spl0_39 | ~spl0_103)),
% 37.78/5.16 inference(backward_demodulation,[],[f7719,f7940])).
% 37.78/5.16 thf(f7940,plain,(
% 37.78/5.16 ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | (~spl0_22 | spl0_39)),
% 37.78/5.16 inference(boolean_simplification,[],[f7939])).
% 37.78/5.16 thf(f7939,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) = $false) | (~spl0_22 | spl0_39)),
% 37.78/5.16 inference(boolean_simplification,[],[f7933])).
% 37.78/5.16 thf(f7933,plain,(
% 37.78/5.16 (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) = $false) | (~spl0_22 | spl0_39)),
% 37.78/5.16 inference(backward_demodulation,[],[f768,f7931])).
% 37.78/5.16 thf(f7931,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))) = $true) | spl0_39),
% 37.78/5.16 inference(not_proxy_clausification,[],[f1365])).
% 37.78/5.16 thf(f1365,plain,(
% 37.78/5.16 ($true != (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | spl0_39),
% 37.78/5.16 inference(avatar_component_clause,[],[f1364])).
% 37.78/5.16 thf(f1364,plain,(
% 37.78/5.16 spl0_39 <=> ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_39])])).
% 37.78/5.16 thf(f768,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) = $false) | ~spl0_22),
% 37.78/5.16 inference(avatar_component_clause,[],[f766])).
% 37.78/5.16 thf(f766,plain,(
% 37.78/5.16 spl0_22 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_22])])).
% 37.78/5.16 thf(f7719,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7714])).
% 37.78/5.16 thf(f7714,plain,(
% 37.78/5.16 (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))))) = $true) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | ~spl0_103)),
% 37.78/5.16 inference(superposition,[],[f572,f7710])).
% 37.78/5.16 thf(f7710,plain,(
% 37.78/5.16 ($true = (irel @ sK3 @ sK8)) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | ~spl0_103)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f7705])).
% 37.78/5.16 thf(f7705,plain,(
% 37.78/5.16 ((~ (irel @ sK3 @ sK8)) = $false) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7704])).
% 37.78/5.16 thf(f7704,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK8) => $false) = $false) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7703])).
% 37.78/5.16 thf(f7703,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK8) => ($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) = $false) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | ~spl0_103)),
% 37.78/5.16 inference(forward_demodulation,[],[f7702,f768])).
% 37.78/5.16 thf(f7702,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK8) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) = $false) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(beta_eta_normalization,[],[f7696])).
% 37.78/5.16 thf(f7696,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))) @ sK8) = $false) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(sigma_clausification,[],[f7673])).
% 37.78/5.16 thf(f7673,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))) = $false) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f7654])).
% 37.78/5.16 thf(f7654,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7652])).
% 37.78/5.16 thf(f7652,plain,(
% 37.78/5.16 ($true = ($true => (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(backward_demodulation,[],[f7330,f7650])).
% 37.78/5.16 thf(f7650,plain,(
% 37.78/5.16 ($true = (irel @ sK2 @ sK3)) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f7637])).
% 37.78/5.16 thf(f7637,plain,(
% 37.78/5.16 ((~ (irel @ sK2 @ sK3)) = $false) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7636])).
% 37.78/5.16 thf(f7636,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => $false) = $false) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7635])).
% 37.78/5.16 thf(f7635,plain,(
% 37.78/5.16 ($false = ((irel @ sK2 @ sK3) => (~ $true))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(forward_demodulation,[],[f7634,f294])).
% 37.78/5.16 thf(f7634,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) = $false) | (~spl0_2 | ~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7633])).
% 37.78/5.16 thf(f7633,plain,(
% 37.78/5.16 ($false = ((irel @ sK2 @ sK3) => ($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))))) | (~spl0_2 | ~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7632])).
% 37.78/5.16 thf(f7632,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))))) = $false) | (~spl0_2 | ~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7631])).
% 37.78/5.16 thf(f7631,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))))) = $false) | (~spl0_2 | ~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7630])).
% 37.78/5.16 thf(f7630,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | $false))) = $false) | (~spl0_2 | ~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(forward_demodulation,[],[f7629,f452])).
% 37.78/5.16 thf(f7330,plain,(
% 37.78/5.16 ($true = ((irel @ sK2 @ sK3) => (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | (~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7329])).
% 37.78/5.16 thf(f7329,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $false)) = $true) | (~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7328])).
% 37.78/5.16 thf(f7328,plain,(
% 37.78/5.16 ($true = ((irel @ sK2 @ sK3) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $false) & $true))) | (~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7327])).
% 37.78/5.16 thf(f7327,plain,(
% 37.78/5.16 ($true = ((irel @ sK2 @ sK3) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $false) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))))) | (~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(boolean_simplification,[],[f7315])).
% 37.78/5.16 thf(f7315,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $false) & ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) = $true) | (~spl0_10 | ~spl0_103)),
% 37.78/5.16 inference(superposition,[],[f7298,f452])).
% 37.78/5.16 thf(f572,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((irel @ sK3 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0))))))))) ) | ~spl0_9),
% 37.78/5.16 inference(beta_eta_normalization,[],[f571])).
% 37.78/5.16 thf(f571,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))) @ X1))) ) | ~spl0_9),
% 37.78/5.16 inference(pi_clausification,[],[f294])).
% 37.78/5.16 thf(f8080,plain,(
% 37.78/5.16 ~spl0_37 | spl0_39 | spl0_51),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f8079])).
% 37.78/5.16 thf(f8079,plain,(
% 37.78/5.16 $false | (~spl0_37 | spl0_39 | spl0_51)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f8078])).
% 37.78/5.16 thf(f8078,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_37 | spl0_39 | spl0_51)),
% 37.78/5.16 inference(boolean_simplification,[],[f8077])).
% 37.78/5.16 thf(f8077,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))) & $false) = $true) | (~spl0_37 | spl0_39 | spl0_51)),
% 37.78/5.16 inference(forward_demodulation,[],[f8026,f1344])).
% 37.78/5.16 thf(f1344,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) = $false) | ~spl0_37),
% 37.78/5.16 inference(avatar_component_clause,[],[f1342])).
% 37.78/5.16 thf(f1342,plain,(
% 37.78/5.16 spl0_37 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_37])])).
% 37.78/5.16 thf(f8026,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))))) | (spl0_39 | spl0_51)),
% 37.78/5.16 inference(boolean_simplification,[],[f8009])).
% 37.78/5.16 thf(f8009,plain,(
% 37.78/5.16 (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))))) = $true) | (spl0_39 | spl0_51)),
% 37.78/5.16 inference(superposition,[],[f7991,f2571])).
% 37.78/5.16 thf(f2571,plain,(
% 37.78/5.16 ($true = (irel @ sK8 @ sK11)) | spl0_51),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f2566])).
% 37.78/5.16 thf(f2566,plain,(
% 37.78/5.16 ($false = ((irel @ sK8 @ sK11) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0)))))))) | spl0_51),
% 37.78/5.16 inference(beta_eta_normalization,[],[f2565])).
% 37.78/5.16 thf(f2565,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ sK11) = $false) | spl0_51),
% 37.78/5.16 inference(sigma_clausification,[],[f2467])).
% 37.78/5.16 thf(f2467,plain,(
% 37.78/5.16 ($true != (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | spl0_51),
% 37.78/5.16 inference(avatar_component_clause,[],[f2466])).
% 37.78/5.16 thf(f7991,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((irel @ sK8 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))))))) ) | spl0_39),
% 37.78/5.16 inference(beta_eta_normalization,[],[f7990])).
% 37.78/5.16 thf(f7990,plain,(
% 37.78/5.16 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ X1) = $true)) ) | spl0_39),
% 37.78/5.16 inference(pi_clausification,[],[f7931])).
% 37.78/5.16 thf(f7938,plain,(
% 37.78/5.16 ~spl0_23 | spl0_39),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f7937])).
% 37.78/5.16 thf(f7937,plain,(
% 37.78/5.16 $false | (~spl0_23 | spl0_39)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f7936])).
% 37.78/5.16 thf(f7936,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_23 | spl0_39)),
% 37.78/5.16 inference(boolean_simplification,[],[f7932])).
% 37.78/5.16 thf(f7932,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | $true) = $false) | (~spl0_23 | spl0_39)),
% 37.78/5.16 inference(backward_demodulation,[],[f772,f7931])).
% 37.78/5.16 thf(f772,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) = $false) | ~spl0_23),
% 37.78/5.16 inference(avatar_component_clause,[],[f770])).
% 37.78/5.16 thf(f770,plain,(
% 37.78/5.16 spl0_23 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_23])])).
% 37.78/5.16 thf(f7439,plain,(
% 37.78/5.16 ~spl0_57 | spl0_67),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f7438])).
% 37.78/5.16 thf(f7438,plain,(
% 37.78/5.16 $false | (~spl0_57 | spl0_67)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f7437])).
% 37.78/5.16 thf(f7437,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_57 | spl0_67)),
% 37.78/5.16 inference(boolean_simplification,[],[f7433])).
% 37.78/5.16 thf(f7433,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $true) = $false) | (~spl0_57 | spl0_67)),
% 37.78/5.16 inference(backward_demodulation,[],[f2769,f7432])).
% 37.78/5.16 thf(f7432,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | spl0_67),
% 37.78/5.16 inference(not_proxy_clausification,[],[f3452])).
% 37.78/5.16 thf(f3452,plain,(
% 37.78/5.16 ($true != (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0)))))) | spl0_67),
% 37.78/5.16 inference(avatar_component_clause,[],[f3451])).
% 37.78/5.16 thf(f3451,plain,(
% 37.78/5.16 spl0_67 <=> ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_67])])).
% 37.78/5.16 thf(f2769,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) = $false) | ~spl0_57),
% 37.78/5.16 inference(avatar_component_clause,[],[f2767])).
% 37.78/5.16 thf(f2767,plain,(
% 37.78/5.16 spl0_57 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_57])])).
% 37.78/5.16 thf(f7289,plain,(
% 37.78/5.16 spl0_103 | ~spl0_2 | ~spl0_102),
% 37.78/5.16 inference(avatar_split_clause,[],[f7288,f7218,f114,f7222])).
% 37.78/5.16 thf(f7218,plain,(
% 37.78/5.16 spl0_102 <=> ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_102])])).
% 37.78/5.16 thf(f7288,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | (~spl0_2 | ~spl0_102)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f7238])).
% 37.78/5.16 thf(f7238,plain,(
% 37.78/5.16 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))))))))) | (~spl0_2 | ~spl0_102)),
% 37.78/5.16 inference(boolean_simplification,[],[f7236])).
% 37.78/5.16 thf(f7236,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | $false) = $false) | (~spl0_2 | ~spl0_102)),
% 37.78/5.16 inference(backward_demodulation,[],[f116,f7234])).
% 37.78/5.16 thf(f7234,plain,(
% 37.78/5.16 ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) | ~spl0_102),
% 37.78/5.16 inference(not_proxy_clausification,[],[f7220])).
% 37.78/5.16 thf(f7220,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))))))))) | ~spl0_102),
% 37.78/5.16 inference(avatar_component_clause,[],[f7218])).
% 37.78/5.16 thf(f7225,plain,(
% 37.78/5.16 spl0_102 | spl0_103 | spl0_1),
% 37.78/5.16 inference(avatar_split_clause,[],[f7216,f110,f7222,f7218])).
% 37.78/5.16 thf(f110,plain,(
% 37.78/5.16 spl0_1 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 37.78/5.16 thf(f7216,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))))))))) | spl0_1),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f111])).
% 37.78/5.16 thf(f111,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) != $false) | spl0_1),
% 37.78/5.16 inference(avatar_component_clause,[],[f110])).
% 37.78/5.16 thf(f7147,plain,(
% 37.78/5.16 ~spl0_22 | ~spl0_39),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f7146])).
% 37.78/5.16 thf(f7146,plain,(
% 37.78/5.16 $false | (~spl0_22 | ~spl0_39)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f7145])).
% 37.78/5.16 thf(f7145,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_22 | ~spl0_39)),
% 37.78/5.16 inference(boolean_simplification,[],[f7144])).
% 37.78/5.16 thf(f7144,plain,(
% 37.78/5.16 (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) = $false) | (~spl0_22 | ~spl0_39)),
% 37.78/5.16 inference(boolean_simplification,[],[f7143])).
% 37.78/5.16 thf(f7143,plain,(
% 37.78/5.16 (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) = $false) | (~spl0_22 | ~spl0_39)),
% 37.78/5.16 inference(forward_demodulation,[],[f768,f1373])).
% 37.78/5.16 thf(f1373,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))) = $false) | ~spl0_39),
% 37.78/5.16 inference(not_proxy_clausification,[],[f1366])).
% 37.78/5.16 thf(f1366,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | ~spl0_39),
% 37.78/5.16 inference(avatar_component_clause,[],[f1364])).
% 37.78/5.16 thf(f7124,plain,(
% 37.78/5.16 ~spl0_48 | ~spl0_94),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f7123])).
% 37.78/5.16 thf(f7123,plain,(
% 37.78/5.16 $false | (~spl0_48 | ~spl0_94)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f7122])).
% 37.78/5.16 thf(f7122,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_48 | ~spl0_94)),
% 37.78/5.16 inference(boolean_simplification,[],[f7121])).
% 37.78/5.16 thf(f7121,plain,(
% 37.78/5.16 (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) = $false) | (~spl0_48 | ~spl0_94)),
% 37.78/5.16 inference(forward_demodulation,[],[f2193,f6104])).
% 37.78/5.16 thf(f6104,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | ~spl0_94),
% 37.78/5.16 inference(avatar_component_clause,[],[f6102])).
% 37.78/5.16 thf(f6102,plain,(
% 37.78/5.16 spl0_94 <=> ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_94])])).
% 37.78/5.16 thf(f2193,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) = $false) | ~spl0_48),
% 37.78/5.16 inference(avatar_component_clause,[],[f2191])).
% 37.78/5.16 thf(f2191,plain,(
% 37.78/5.16 spl0_48 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_48])])).
% 37.78/5.16 thf(f7120,plain,(
% 37.78/5.16 ~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_92 | ~spl0_99),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f7119])).
% 37.78/5.16 thf(f7119,plain,(
% 37.78/5.16 $false | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_92 | ~spl0_99)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f7118])).
% 37.78/5.16 thf(f7118,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_92 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f7117])).
% 37.78/5.16 thf(f7117,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) & $false)) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_92 | ~spl0_99)),
% 37.78/5.16 inference(forward_demodulation,[],[f7114,f6052])).
% 37.78/5.16 thf(f6052,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) = $false) | ~spl0_92),
% 37.78/5.16 inference(avatar_component_clause,[],[f6050])).
% 37.78/5.16 thf(f6050,plain,(
% 37.78/5.16 spl0_92 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_92])])).
% 37.78/5.16 thf(f7114,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))))) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_92 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f7109])).
% 37.78/5.16 thf(f7109,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0)))))))) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_92 | ~spl0_99)),
% 37.78/5.16 inference(superposition,[],[f6916,f7106])).
% 37.78/5.16 thf(f7106,plain,(
% 37.78/5.16 ($true = (irel @ sK17 @ sK27)) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_92 | ~spl0_99)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f7091])).
% 37.78/5.16 thf(f7091,plain,(
% 37.78/5.16 ((~ (irel @ sK17 @ sK27)) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_92 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f7090])).
% 37.78/5.16 thf(f7090,plain,(
% 37.78/5.16 (((irel @ sK17 @ sK27) => $false) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_92 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f7089])).
% 37.78/5.16 thf(f7089,plain,(
% 37.78/5.16 (((irel @ sK17 @ sK27) => ($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_92 | ~spl0_99)),
% 37.78/5.16 inference(forward_demodulation,[],[f7080,f6052])).
% 37.78/5.16 thf(f7080,plain,(
% 37.78/5.16 (((irel @ sK17 @ sK27) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(beta_eta_normalization,[],[f7073])).
% 37.78/5.16 thf(f7073,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ sK27) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(sigma_clausification,[],[f7054])).
% 37.78/5.16 thf(f7054,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f6730])).
% 37.78/5.16 thf(f6730,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) = $true) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f6729])).
% 37.78/5.16 thf(f6729,plain,(
% 37.78/5.16 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false)) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f6728])).
% 37.78/5.16 thf(f6728,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) & $true)) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f6727])).
% 37.78/5.16 thf(f6727,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f6726])).
% 37.78/5.16 thf(f6726,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) & ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(forward_demodulation,[],[f6725,f6688])).
% 37.78/5.16 thf(f6688,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0)))) = $false) | (~spl0_48 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f6687])).
% 37.78/5.16 thf(f6687,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) = $false) | (~spl0_48 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f6684])).
% 37.78/5.16 thf(f6684,plain,(
% 37.78/5.16 (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) = $false) | (~spl0_48 | ~spl0_99)),
% 37.78/5.16 inference(backward_demodulation,[],[f2193,f6581])).
% 37.78/5.16 thf(f6581,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | ~spl0_99),
% 37.78/5.16 inference(avatar_component_clause,[],[f6579])).
% 37.78/5.16 thf(f6579,plain,(
% 37.78/5.16 spl0_99 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_99])])).
% 37.78/5.16 thf(f6725,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f6718])).
% 37.78/5.16 thf(f6718,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(superposition,[],[f3705,f6715])).
% 37.78/5.16 thf(f6715,plain,(
% 37.78/5.16 ((irel @ sK15 @ sK17) = $true) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f6705])).
% 37.78/5.16 thf(f6705,plain,(
% 37.78/5.16 ((~ (irel @ sK15 @ sK17)) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f6704])).
% 37.78/5.16 thf(f6704,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => $false) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f6703])).
% 37.78/5.16 thf(f6703,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => (~ $true)) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(forward_demodulation,[],[f6702,f6581])).
% 37.78/5.16 thf(f6702,plain,(
% 37.78/5.16 ($false = ((irel @ sK15 @ sK17) => (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f6701])).
% 37.78/5.16 thf(f6701,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => ($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f6700])).
% 37.78/5.16 thf(f6700,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f6699])).
% 37.78/5.16 thf(f6699,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f6698])).
% 37.78/5.16 thf(f6698,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $false))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_99)),
% 37.78/5.16 inference(forward_demodulation,[],[f3952,f6688])).
% 37.78/5.16 thf(f3952,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_59)),
% 37.78/5.16 inference(beta_eta_normalization,[],[f3945])).
% 37.78/5.16 thf(f3945,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))) @ sK17) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_59)),
% 37.78/5.16 inference(sigma_clausification,[],[f3928])).
% 37.78/5.16 thf(f3928,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_59)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f3677])).
% 37.78/5.16 thf(f3677,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) | (~spl0_1 | ~spl0_45 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f3676])).
% 37.78/5.16 thf(f3676,plain,(
% 37.78/5.16 ($true = ($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))))) | (~spl0_1 | ~spl0_45 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f3675])).
% 37.78/5.16 thf(f3675,plain,(
% 37.78/5.16 ($true = (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))))) | (~spl0_1 | ~spl0_45 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f3674])).
% 37.78/5.16 thf(f3674,plain,(
% 37.78/5.16 ((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) = $true) | (~spl0_1 | ~spl0_45 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f3673])).
% 37.78/5.16 thf(f3673,plain,(
% 37.78/5.16 ($true = (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | $false))) | (~spl0_1 | ~spl0_45 | ~spl0_59)),
% 37.78/5.16 inference(backward_demodulation,[],[f1855,f3672])).
% 37.78/5.16 thf(f3672,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0)))) = $false) | (~spl0_45 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f3671])).
% 37.78/5.16 thf(f3671,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) = $false) | (~spl0_45 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f3670])).
% 37.78/5.16 thf(f3670,plain,(
% 37.78/5.16 (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) = $false) | (~spl0_45 | ~spl0_59)),
% 37.78/5.16 inference(backward_demodulation,[],[f1865,f2795])).
% 37.78/5.16 thf(f2795,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | ~spl0_59),
% 37.78/5.16 inference(avatar_component_clause,[],[f2793])).
% 37.78/5.16 thf(f2793,plain,(
% 37.78/5.16 spl0_59 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_59])])).
% 37.78/5.16 thf(f1865,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) = $false) | ~spl0_45),
% 37.78/5.16 inference(avatar_component_clause,[],[f1863])).
% 37.78/5.16 thf(f1863,plain,(
% 37.78/5.16 spl0_45 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_45])])).
% 37.78/5.16 thf(f1855,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))))) | ~spl0_1),
% 37.78/5.16 inference(boolean_simplification,[],[f1847])).
% 37.78/5.16 thf(f1847,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0)))))))) | ~spl0_1),
% 37.78/5.16 inference(superposition,[],[f1785,f1844])).
% 37.78/5.16 thf(f1844,plain,(
% 37.78/5.16 ((irel @ sK2 @ sK15) = $true) | ~spl0_1),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f1828])).
% 37.78/5.16 thf(f1828,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK15) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) = $false) | ~spl0_1),
% 37.78/5.16 inference(beta_eta_normalization,[],[f1827])).
% 37.78/5.16 thf(f1827,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))) @ sK15) = $false) | ~spl0_1),
% 37.78/5.16 inference(sigma_clausification,[],[f1753])).
% 37.78/5.16 thf(f1753,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))))))) = $false) | ~spl0_1),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f112])).
% 37.78/5.16 thf(f112,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) = $false) | ~spl0_1),
% 37.78/5.16 inference(avatar_component_clause,[],[f110])).
% 37.78/5.16 thf(f1785,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((irel @ sK2 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a4 @ Y0))))))))) ) | ~spl0_1),
% 37.78/5.16 inference(beta_eta_normalization,[],[f1784])).
% 37.78/5.16 thf(f1784,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))) @ X1))) ) | ~spl0_1),
% 37.78/5.16 inference(pi_clausification,[],[f1771])).
% 37.78/5.16 thf(f1771,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) | ~spl0_1),
% 37.78/5.16 inference(not_proxy_clausification,[],[f1757])).
% 37.78/5.16 thf(f1757,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) = $false) | ~spl0_1),
% 37.78/5.16 inference(boolean_simplification,[],[f1756])).
% 37.78/5.16 thf(f1756,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) | $false) = $false) | ~spl0_1),
% 37.78/5.16 inference(backward_demodulation,[],[f112,f1753])).
% 37.78/5.16 thf(f3705,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((irel @ sK15 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))))) ) | ~spl0_59),
% 37.78/5.16 inference(beta_eta_normalization,[],[f3704])).
% 37.78/5.16 thf(f3704,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))) @ X1))) ) | ~spl0_59),
% 37.78/5.16 inference(pi_clausification,[],[f2795])).
% 37.78/5.16 thf(f6916,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((irel @ sK17 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))))))) ) | ~spl0_99),
% 37.78/5.16 inference(beta_eta_normalization,[],[f6913])).
% 37.78/5.16 thf(f6913,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ X1))) ) | ~spl0_99),
% 37.78/5.16 inference(pi_clausification,[],[f6581])).
% 37.78/5.16 thf(f6691,plain,(
% 37.78/5.16 ~spl0_49 | ~spl0_99),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f6690])).
% 37.78/5.16 thf(f6690,plain,(
% 37.78/5.16 $false | (~spl0_49 | ~spl0_99)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f6689])).
% 37.78/5.16 thf(f6689,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_49 | ~spl0_99)),
% 37.78/5.16 inference(boolean_simplification,[],[f6683])).
% 37.78/5.16 thf(f6683,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) | $true) = $false) | (~spl0_49 | ~spl0_99)),
% 37.78/5.16 inference(backward_demodulation,[],[f2197,f6581])).
% 37.78/5.16 thf(f2197,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $false) | ~spl0_49),
% 37.78/5.16 inference(avatar_component_clause,[],[f2195])).
% 37.78/5.16 thf(f2195,plain,(
% 37.78/5.16 spl0_49 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_49])])).
% 37.78/5.16 thf(f6682,plain,(
% 37.78/5.16 spl0_99 | spl0_94),
% 37.78/5.16 inference(avatar_split_clause,[],[f6681,f6102,f6579])).
% 37.78/5.16 thf(f6681,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | spl0_94),
% 37.78/5.16 inference(not_proxy_clausification,[],[f6103])).
% 37.78/5.16 thf(f6103,plain,(
% 37.78/5.16 ($true != (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | spl0_94),
% 37.78/5.16 inference(avatar_component_clause,[],[f6102])).
% 37.78/5.16 thf(f6570,plain,(
% 37.78/5.16 ~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95 | ~spl0_96),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f6569])).
% 37.78/5.16 thf(f6569,plain,(
% 37.78/5.16 $false | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95 | ~spl0_96)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f6568])).
% 37.78/5.16 thf(f6568,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95 | ~spl0_96)),
% 37.78/5.16 inference(boolean_simplification,[],[f6567])).
% 37.78/5.16 thf(f6567,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0))))) & $false)) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95 | ~spl0_96)),
% 37.78/5.16 inference(backward_demodulation,[],[f6522,f6309])).
% 37.78/5.16 thf(f6309,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) = $false) | ~spl0_96),
% 37.78/5.16 inference(avatar_component_clause,[],[f6307])).
% 37.78/5.16 thf(f6307,plain,(
% 37.78/5.16 spl0_96 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_96])])).
% 37.78/5.16 thf(f6522,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))))) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95)),
% 37.78/5.16 inference(boolean_simplification,[],[f6475])).
% 37.78/5.16 thf(f6475,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0)))))))) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95)),
% 37.78/5.16 inference(superposition,[],[f6450,f6258])).
% 37.78/5.16 thf(f6258,plain,(
% 37.78/5.16 ($true = (irel @ sK17 @ sK29)) | ~spl0_94),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f6242])).
% 37.78/5.16 thf(f6242,plain,(
% 37.78/5.16 (((irel @ sK17 @ sK29) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0))))))) = $false) | ~spl0_94),
% 37.78/5.16 inference(beta_eta_normalization,[],[f6231])).
% 37.78/5.16 thf(f6231,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ sK29) = $false) | ~spl0_94),
% 37.78/5.16 inference(sigma_clausification,[],[f6115])).
% 37.78/5.16 thf(f6115,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))) = $false) | ~spl0_94),
% 37.78/5.16 inference(not_proxy_clausification,[],[f6104])).
% 37.78/5.16 thf(f6450,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((irel @ sK17 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))))))) ) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95)),
% 37.78/5.16 inference(beta_eta_normalization,[],[f6444])).
% 37.78/5.16 thf(f6444,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ X1))) ) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95)),
% 37.78/5.16 inference(pi_clausification,[],[f6163])).
% 37.78/5.16 thf(f6163,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95)),
% 37.78/5.16 inference(boolean_simplification,[],[f6162])).
% 37.78/5.16 thf(f6162,plain,(
% 37.78/5.16 ($true = ($true & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95)),
% 37.78/5.16 inference(boolean_simplification,[],[f6159])).
% 37.78/5.16 thf(f6159,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $true) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95)),
% 37.78/5.16 inference(backward_demodulation,[],[f6129,f6108])).
% 37.78/5.16 thf(f6108,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) | ~spl0_95),
% 37.78/5.16 inference(avatar_component_clause,[],[f6106])).
% 37.78/5.16 thf(f6106,plain,(
% 37.78/5.16 spl0_95 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0)))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_95])])).
% 37.78/5.16 thf(f6129,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) = $true) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94)),
% 37.78/5.16 inference(boolean_simplification,[],[f6128])).
% 37.78/5.16 thf(f6128,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) = $true) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94)),
% 37.78/5.16 inference(backward_demodulation,[],[f6096,f6127])).
% 37.78/5.16 thf(f6127,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) = $false) | (~spl0_49 | ~spl0_94)),
% 37.78/5.16 inference(boolean_simplification,[],[f6125])).
% 37.78/5.16 thf(f6125,plain,(
% 37.78/5.16 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) | $false)) | (~spl0_49 | ~spl0_94)),
% 37.78/5.16 inference(backward_demodulation,[],[f2197,f6115])).
% 37.78/5.16 thf(f6096,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f6092])).
% 37.78/5.16 thf(f6092,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59)),
% 37.78/5.16 inference(superposition,[],[f3705,f6089])).
% 37.78/5.16 thf(f6089,plain,(
% 37.78/5.16 ((irel @ sK15 @ sK17) = $true) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f6082])).
% 37.78/5.16 thf(f6082,plain,(
% 37.78/5.16 ((~ (irel @ sK15 @ sK17)) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f6081])).
% 37.78/5.16 thf(f6081,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => $false) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f6080])).
% 37.78/5.16 thf(f6080,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => ($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59)),
% 37.78/5.16 inference(forward_demodulation,[],[f3952,f2197])).
% 37.78/5.16 thf(f6559,plain,(
% 37.78/5.16 ~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95 | ~spl0_97),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f6558])).
% 37.78/5.16 thf(f6558,plain,(
% 37.78/5.16 $false | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95 | ~spl0_97)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f6557])).
% 37.78/5.16 thf(f6557,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95 | ~spl0_97)),
% 37.78/5.16 inference(forward_demodulation,[],[f6556,f6330])).
% 37.78/5.16 thf(f6330,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) = $false) | ~spl0_97),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f6313])).
% 37.78/5.16 thf(f6313,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0))))) = $false) | ~spl0_97),
% 37.78/5.16 inference(avatar_component_clause,[],[f6311])).
% 37.78/5.16 thf(f6311,plain,(
% 37.78/5.16 spl0_97 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_97])])).
% 37.78/5.16 thf(f6556,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0)))))) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95 | ~spl0_97)),
% 37.78/5.16 inference(boolean_simplification,[],[f6555])).
% 37.78/5.16 thf(f6555,plain,(
% 37.78/5.16 ($true = ($true => (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))))) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95 | ~spl0_97)),
% 37.78/5.16 inference(forward_demodulation,[],[f6496,f6258])).
% 37.78/5.16 thf(f6496,plain,(
% 37.78/5.16 ($true = ((irel @ sK17 @ sK29) => (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))))) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95 | ~spl0_97)),
% 37.78/5.16 inference(boolean_simplification,[],[f6495])).
% 37.78/5.16 thf(f6495,plain,(
% 37.78/5.16 ($true = ((irel @ sK17 @ sK29) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) | $false))) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95 | ~spl0_97)),
% 37.78/5.16 inference(boolean_simplification,[],[f6494])).
% 37.78/5.16 thf(f6494,plain,(
% 37.78/5.16 ($true = ((irel @ sK17 @ sK29) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) | $false) & $true))) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95 | ~spl0_97)),
% 37.78/5.16 inference(boolean_simplification,[],[f6493])).
% 37.78/5.16 thf(f6493,plain,(
% 37.78/5.16 ($true = ((irel @ sK17 @ sK29) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) | $false) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0)))))))) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95 | ~spl0_97)),
% 37.78/5.16 inference(boolean_simplification,[],[f6467])).
% 37.78/5.16 thf(f6467,plain,(
% 37.78/5.16 (((irel @ sK17 @ sK29) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) | $false) & ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl0_1 | ~spl0_45 | ~spl0_49 | ~spl0_59 | ~spl0_94 | ~spl0_95 | ~spl0_97)),
% 37.78/5.16 inference(superposition,[],[f6450,f6356])).
% 37.78/5.16 thf(f6356,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0)))) = $false) | ~spl0_97),
% 37.78/5.16 inference(boolean_simplification,[],[f6355])).
% 37.78/5.16 thf(f6355,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0))))) = $false) | ~spl0_97),
% 37.78/5.16 inference(backward_demodulation,[],[f6313,f6330])).
% 37.78/5.16 thf(f6314,plain,(
% 37.78/5.16 spl0_96 | spl0_97 | ~spl0_94),
% 37.78/5.16 inference(avatar_split_clause,[],[f6297,f6102,f6311,f6307])).
% 37.78/5.16 thf(f6297,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) = $false) | ~spl0_94),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f6257])).
% 37.78/5.16 thf(f6257,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK29 @ Y0) => (a2 @ Y0)))))) = $false) | ~spl0_94),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f6242])).
% 37.78/5.16 thf(f6154,plain,(
% 37.78/5.16 spl0_95 | ~spl0_49 | ~spl0_94),
% 37.78/5.16 inference(avatar_split_clause,[],[f6142,f6102,f2195,f6106])).
% 37.78/5.16 thf(f6142,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) | (~spl0_49 | ~spl0_94)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f6127])).
% 37.78/5.16 thf(f6062,plain,(
% 37.78/5.16 ~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_93),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f6061])).
% 37.78/5.16 thf(f6061,plain,(
% 37.78/5.16 $false | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_93)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f6060])).
% 37.78/5.16 thf(f6060,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_93)),
% 37.78/5.16 inference(boolean_simplification,[],[f6058])).
% 37.78/5.16 thf(f6058,plain,(
% 37.78/5.16 (($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0)))))) = $true) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59 | ~spl0_93)),
% 37.78/5.16 inference(backward_demodulation,[],[f5316,f6056])).
% 37.78/5.16 thf(f6056,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) = $false) | ~spl0_93),
% 37.78/5.16 inference(avatar_component_clause,[],[f6054])).
% 37.78/5.16 thf(f6054,plain,(
% 37.78/5.16 spl0_93 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_93])])).
% 37.78/5.16 thf(f5316,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))))) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f5311])).
% 37.78/5.16 thf(f5311,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0)))))))) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(superposition,[],[f2398,f5306])).
% 37.78/5.16 thf(f5306,plain,(
% 37.78/5.16 ($true = (irel @ sK17 @ sK27)) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f5291])).
% 37.78/5.16 thf(f5291,plain,(
% 37.78/5.16 (((irel @ sK17 @ sK27) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(beta_eta_normalization,[],[f5289])).
% 37.78/5.16 thf(f5289,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ sK27) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(sigma_clausification,[],[f5264])).
% 37.78/5.16 thf(f5264,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f4018])).
% 37.78/5.16 thf(f4018,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) = $true) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f4017])).
% 37.78/5.16 thf(f4017,plain,(
% 37.78/5.16 ($true = ($true => (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(backward_demodulation,[],[f3730,f4015])).
% 37.78/5.16 thf(f4015,plain,(
% 37.78/5.16 ((irel @ sK15 @ sK17) = $true) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f3968])).
% 37.78/5.16 thf(f3968,plain,(
% 37.78/5.16 ((~ (irel @ sK15 @ sK17)) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f3967])).
% 37.78/5.16 thf(f3967,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => $false) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f3966])).
% 37.78/5.16 thf(f3966,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => (~ $true)) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(forward_demodulation,[],[f3965,f2375])).
% 37.78/5.16 thf(f2375,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | ~spl0_48),
% 37.78/5.16 inference(not_proxy_clausification,[],[f2205])).
% 37.78/5.16 thf(f2205,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $false) | ~spl0_48),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f2193])).
% 37.78/5.16 thf(f3965,plain,(
% 37.78/5.16 ($false = ((irel @ sK15 @ sK17) => (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f3964])).
% 37.78/5.16 thf(f3964,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => ($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f3963])).
% 37.78/5.16 thf(f3963,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f3962])).
% 37.78/5.16 thf(f3962,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f3961])).
% 37.78/5.16 thf(f3961,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $false))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(forward_demodulation,[],[f3952,f2210])).
% 37.78/5.16 thf(f2210,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0)))) = $false) | ~spl0_48),
% 37.78/5.16 inference(boolean_simplification,[],[f2209])).
% 37.78/5.16 thf(f2209,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) = $false) | ~spl0_48),
% 37.78/5.16 inference(backward_demodulation,[],[f2193,f2205])).
% 37.78/5.16 thf(f3730,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) = $true) | (~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f3729])).
% 37.78/5.16 thf(f3729,plain,(
% 37.78/5.16 ($true = ((irel @ sK15 @ sK17) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false))) | (~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f3728])).
% 37.78/5.16 thf(f3728,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) & $true)) = $true) | (~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f3727])).
% 37.78/5.16 thf(f3727,plain,(
% 37.78/5.16 ($true = ((irel @ sK15 @ sK17) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(boolean_simplification,[],[f3717])).
% 37.78/5.16 thf(f3717,plain,(
% 37.78/5.16 ($true = ((irel @ sK15 @ sK17) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) & ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(superposition,[],[f3705,f2210])).
% 37.78/5.16 thf(f2398,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((irel @ sK17 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))))))) ) | ~spl0_48),
% 37.78/5.16 inference(beta_eta_normalization,[],[f2396])).
% 37.78/5.16 thf(f2396,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ X1))) ) | ~spl0_48),
% 37.78/5.16 inference(pi_clausification,[],[f2375])).
% 37.78/5.16 thf(f6057,plain,(
% 37.78/5.16 spl0_92 | spl0_93 | ~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59),
% 37.78/5.16 inference(avatar_split_clause,[],[f6040,f2793,f2191,f1863,f110,f6054,f6050])).
% 37.78/5.16 thf(f6040,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) = $false) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f5305])).
% 37.78/5.16 thf(f5305,plain,(
% 37.78/5.16 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK27 @ Y0) => (a1 @ Y0))))))) | (~spl0_1 | ~spl0_45 | ~spl0_48 | ~spl0_59)),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f5291])).
% 37.78/5.16 thf(f4885,plain,(
% 37.78/5.16 ~spl0_20 | ~spl0_27),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f4884])).
% 37.78/5.16 thf(f4884,plain,(
% 37.78/5.16 $false | (~spl0_20 | ~spl0_27)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f4883])).
% 37.78/5.16 thf(f4883,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_20 | ~spl0_27)),
% 37.78/5.16 inference(boolean_simplification,[],[f4882])).
% 37.78/5.16 thf(f4882,plain,(
% 37.78/5.16 ($true = (~ $true)) | (~spl0_20 | ~spl0_27)),
% 37.78/5.16 inference(forward_demodulation,[],[f680,f907])).
% 37.78/5.16 thf(f4874,plain,(
% 37.78/5.16 spl0_84 | spl0_85 | spl0_53),
% 37.78/5.16 inference(avatar_split_clause,[],[f4863,f2608,f4871,f4867])).
% 37.78/5.16 thf(f4863,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) = $false) | spl0_53),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f4852])).
% 37.78/5.16 thf(f4852,plain,(
% 37.78/5.16 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))) | spl0_53),
% 37.78/5.16 inference(boolean_simplification,[],[f4851])).
% 37.78/5.16 thf(f4851,plain,(
% 37.78/5.16 (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))) = $false) | spl0_53),
% 37.78/5.16 inference(backward_demodulation,[],[f4845,f4850])).
% 37.78/5.16 thf(f4850,plain,(
% 37.78/5.16 ((irel @ sK4 @ sK26) = $true) | spl0_53),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f4845])).
% 37.78/5.16 thf(f4845,plain,(
% 37.78/5.16 (((irel @ sK4 @ sK26) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK26 @ Y0) => (a1 @ Y0))))))) = $false) | spl0_53),
% 37.78/5.16 inference(beta_eta_normalization,[],[f4844])).
% 37.78/5.16 thf(f4844,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ sK26) = $false) | spl0_53),
% 37.78/5.16 inference(sigma_clausification,[],[f2609])).
% 37.78/5.16 thf(f4555,plain,(
% 37.78/5.16 spl0_27 | ~spl0_30 | ~spl0_53),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f4554])).
% 37.78/5.16 thf(f4554,plain,(
% 37.78/5.16 $false | (spl0_27 | ~spl0_30 | ~spl0_53)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f4553])).
% 37.78/5.16 thf(f4553,plain,(
% 37.78/5.16 ($true = $false) | (spl0_27 | ~spl0_30 | ~spl0_53)),
% 37.78/5.16 inference(boolean_simplification,[],[f4552])).
% 37.78/5.16 thf(f4552,plain,(
% 37.78/5.16 ($true = (~ $true)) | (spl0_27 | ~spl0_30 | ~spl0_53)),
% 37.78/5.16 inference(forward_demodulation,[],[f4551,f1097])).
% 37.78/5.16 thf(f1097,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) | ~spl0_30),
% 37.78/5.16 inference(not_proxy_clausification,[],[f1078])).
% 37.78/5.16 thf(f1078,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) = $false) | ~spl0_30),
% 37.78/5.16 inference(boolean_simplification,[],[f1077])).
% 37.78/5.16 thf(f1077,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) | $false) = $false) | ~spl0_30),
% 37.78/5.16 inference(backward_demodulation,[],[f1062,f1069])).
% 37.78/5.16 thf(f1069,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0)))) = $false) | ~spl0_30),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f1062])).
% 37.78/5.16 thf(f1062,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) = $false) | ~spl0_30),
% 37.78/5.16 inference(avatar_component_clause,[],[f1060])).
% 37.78/5.16 thf(f1060,plain,(
% 37.78/5.16 spl0_30 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_30])])).
% 37.78/5.16 thf(f4551,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0)))))) | (spl0_27 | ~spl0_30 | ~spl0_53)),
% 37.78/5.16 inference(boolean_simplification,[],[f4550])).
% 37.78/5.16 thf(f4550,plain,(
% 37.78/5.16 ($true = ($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))))) | (spl0_27 | ~spl0_30 | ~spl0_53)),
% 37.78/5.16 inference(boolean_simplification,[],[f4549])).
% 37.78/5.16 thf(f4549,plain,(
% 37.78/5.16 ($true = (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))))) | (spl0_27 | ~spl0_30 | ~spl0_53)),
% 37.78/5.16 inference(boolean_simplification,[],[f4548])).
% 37.78/5.16 thf(f4548,plain,(
% 37.78/5.16 ($true = (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))))) | (spl0_27 | ~spl0_30 | ~spl0_53)),
% 37.78/5.16 inference(boolean_simplification,[],[f4547])).
% 37.78/5.16 thf(f4547,plain,(
% 37.78/5.16 ($true = (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) | $false))) | (spl0_27 | ~spl0_30 | ~spl0_53)),
% 37.78/5.16 inference(forward_demodulation,[],[f4489,f1069])).
% 37.78/5.16 thf(f4489,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))))) | (spl0_27 | ~spl0_53)),
% 37.78/5.16 inference(boolean_simplification,[],[f4480])).
% 37.78/5.16 thf(f4480,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0)))))))) | (spl0_27 | ~spl0_53)),
% 37.78/5.16 inference(superposition,[],[f4458,f982])).
% 37.78/5.16 thf(f982,plain,(
% 37.78/5.16 ($true = (irel @ sK4 @ sK10)) | spl0_27),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f977])).
% 37.78/5.16 thf(f977,plain,(
% 37.78/5.16 (((irel @ sK4 @ sK10) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))))) = $false) | spl0_27),
% 37.78/5.16 inference(beta_eta_normalization,[],[f976])).
% 37.78/5.16 thf(f976,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ sK10) = $false) | spl0_27),
% 37.78/5.16 inference(sigma_clausification,[],[f906])).
% 37.78/5.16 thf(f4458,plain,(
% 37.78/5.16 ( ! [X1 : $i] : ((((irel @ sK4 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))))) = $true)) ) | ~spl0_53),
% 37.78/5.16 inference(beta_eta_normalization,[],[f4456])).
% 37.78/5.16 thf(f4456,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ X1))) ) | ~spl0_53),
% 37.78/5.16 inference(pi_clausification,[],[f2610])).
% 37.78/5.16 thf(f3667,plain,(
% 37.78/5.16 spl0_61 | ~spl0_66 | ~spl0_69),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f3666])).
% 37.78/5.16 thf(f3666,plain,(
% 37.78/5.16 $false | (spl0_61 | ~spl0_66 | ~spl0_69)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f3665])).
% 37.78/5.16 thf(f3665,plain,(
% 37.78/5.16 ($true = $false) | (spl0_61 | ~spl0_66 | ~spl0_69)),
% 37.78/5.16 inference(boolean_simplification,[],[f3664])).
% 37.78/5.16 thf(f3664,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0))))) & $false) = $true) | (spl0_61 | ~spl0_66 | ~spl0_69)),
% 37.78/5.16 inference(forward_demodulation,[],[f3657,f3646])).
% 37.78/5.16 thf(f3646,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0))))) = $false) | ~spl0_69),
% 37.78/5.16 inference(avatar_component_clause,[],[f3644])).
% 37.78/5.16 thf(f3644,plain,(
% 37.78/5.16 spl0_69 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_69])])).
% 37.78/5.16 thf(f3657,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0)))))) = $true) | (spl0_61 | ~spl0_66)),
% 37.78/5.16 inference(boolean_simplification,[],[f3650])).
% 37.78/5.16 thf(f3650,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0)))))))) | (spl0_61 | ~spl0_66)),
% 37.78/5.16 inference(superposition,[],[f3551,f3617])).
% 37.78/5.16 thf(f3617,plain,(
% 37.78/5.16 ($true = (irel @ sK19 @ sK22)) | spl0_61),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f3610])).
% 37.78/5.16 thf(f3610,plain,(
% 37.78/5.16 (((irel @ sK19 @ sK22) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0))))))) = $false) | spl0_61),
% 37.78/5.16 inference(beta_eta_normalization,[],[f3609])).
% 37.78/5.16 thf(f3609,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ sK22) = $false) | spl0_61),
% 37.78/5.16 inference(sigma_clausification,[],[f3070])).
% 37.78/5.16 thf(f3070,plain,(
% 37.78/5.16 ($true != (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | spl0_61),
% 37.78/5.16 inference(avatar_component_clause,[],[f3069])).
% 37.78/5.16 thf(f3069,plain,(
% 37.78/5.16 spl0_61 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_61])])).
% 37.78/5.16 thf(f3551,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((irel @ sK19 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))))))) ) | ~spl0_66),
% 37.78/5.16 inference(beta_eta_normalization,[],[f3550])).
% 37.78/5.16 thf(f3550,plain,(
% 37.78/5.16 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ X1) = $true)) ) | ~spl0_66),
% 37.78/5.16 inference(pi_clausification,[],[f3449])).
% 37.78/5.16 thf(f3449,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | ~spl0_66),
% 37.78/5.16 inference(avatar_component_clause,[],[f3447])).
% 37.78/5.16 thf(f3447,plain,(
% 37.78/5.16 spl0_66 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_66])])).
% 37.78/5.16 thf(f3661,plain,(
% 37.78/5.16 spl0_61 | ~spl0_66 | ~spl0_68),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f3660])).
% 37.78/5.16 thf(f3660,plain,(
% 37.78/5.16 $false | (spl0_61 | ~spl0_66 | ~spl0_68)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f3659])).
% 37.78/5.16 thf(f3659,plain,(
% 37.78/5.16 ($true = $false) | (spl0_61 | ~spl0_66 | ~spl0_68)),
% 37.78/5.16 inference(boolean_simplification,[],[f3658])).
% 37.78/5.16 thf(f3658,plain,(
% 37.78/5.16 ($true = ($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0))))))) | (spl0_61 | ~spl0_66 | ~spl0_68)),
% 37.78/5.16 inference(forward_demodulation,[],[f3657,f3642])).
% 37.78/5.16 thf(f3642,plain,(
% 37.78/5.16 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0)))))) | ~spl0_68),
% 37.78/5.16 inference(avatar_component_clause,[],[f3640])).
% 37.78/5.16 thf(f3640,plain,(
% 37.78/5.16 spl0_68 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_68])])).
% 37.78/5.16 thf(f3647,plain,(
% 37.78/5.16 spl0_68 | spl0_69 | spl0_61),
% 37.78/5.16 inference(avatar_split_clause,[],[f3634,f3069,f3644,f3640])).
% 37.78/5.16 thf(f3634,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0))))) = $false) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0)))))) | spl0_61),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f3619])).
% 37.78/5.16 thf(f3619,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0)))))) = $false) | spl0_61),
% 37.78/5.16 inference(boolean_simplification,[],[f3618])).
% 37.78/5.16 thf(f3618,plain,(
% 37.78/5.16 (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK22 @ Y0) => (a2 @ Y0))))))) = $false) | spl0_61),
% 37.78/5.16 inference(backward_demodulation,[],[f3610,f3617])).
% 37.78/5.16 thf(f3541,plain,(
% 37.78/5.16 spl0_66 | ~spl0_57 | ~spl0_67),
% 37.78/5.16 inference(avatar_split_clause,[],[f3540,f3451,f2767,f3447])).
% 37.78/5.16 thf(f3540,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (~spl0_57 | ~spl0_67)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f3490])).
% 37.78/5.16 thf(f3490,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) = $false) | (~spl0_57 | ~spl0_67)),
% 37.78/5.16 inference(boolean_simplification,[],[f3487])).
% 37.78/5.16 thf(f3487,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false) = $false) | (~spl0_57 | ~spl0_67)),
% 37.78/5.16 inference(backward_demodulation,[],[f2769,f3474])).
% 37.78/5.16 thf(f3474,plain,(
% 37.78/5.16 ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | ~spl0_67),
% 37.78/5.16 inference(not_proxy_clausification,[],[f3453])).
% 37.78/5.16 thf(f3453,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0)))))) | ~spl0_67),
% 37.78/5.16 inference(avatar_component_clause,[],[f3451])).
% 37.78/5.16 thf(f3360,plain,(
% 37.78/5.16 ~spl0_45 | spl0_58),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f3359])).
% 37.78/5.16 thf(f3359,plain,(
% 37.78/5.16 $false | (~spl0_45 | spl0_58)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f3358])).
% 37.78/5.16 thf(f3358,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_45 | spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f3357])).
% 37.78/5.16 thf(f3357,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $true) = $false) | (~spl0_45 | spl0_58)),
% 37.78/5.16 inference(forward_demodulation,[],[f1865,f2883])).
% 37.78/5.16 thf(f2883,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) | spl0_58),
% 37.78/5.16 inference(not_proxy_clausification,[],[f2790])).
% 37.78/5.16 thf(f2790,plain,(
% 37.78/5.16 ($true != (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0)))))) | spl0_58),
% 37.78/5.16 inference(avatar_component_clause,[],[f2789])).
% 37.78/5.16 thf(f2789,plain,(
% 37.78/5.16 spl0_58 <=> ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_58])])).
% 37.78/5.16 thf(f3351,plain,(
% 37.78/5.16 ~spl0_1 | ~spl0_44 | ~spl0_57 | spl0_58 | ~spl0_61),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f3350])).
% 37.78/5.16 thf(f3350,plain,(
% 37.78/5.16 $false | (~spl0_1 | ~spl0_44 | ~spl0_57 | spl0_58 | ~spl0_61)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f3349])).
% 37.78/5.16 thf(f3349,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_1 | ~spl0_44 | ~spl0_57 | spl0_58 | ~spl0_61)),
% 37.78/5.16 inference(boolean_simplification,[],[f3348])).
% 37.78/5.16 thf(f3348,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $true) = $false) | (~spl0_1 | ~spl0_44 | ~spl0_57 | spl0_58 | ~spl0_61)),
% 37.78/5.16 inference(backward_demodulation,[],[f2769,f3346])).
% 37.78/5.16 thf(f3346,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | (~spl0_1 | ~spl0_44 | ~spl0_57 | spl0_58 | ~spl0_61)),
% 37.78/5.16 inference(boolean_simplification,[],[f3344])).
% 37.78/5.16 thf(f3344,plain,(
% 37.78/5.16 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0)))))) | (~spl0_1 | ~spl0_44 | ~spl0_57 | spl0_58 | ~spl0_61)),
% 37.78/5.16 inference(backward_demodulation,[],[f3199,f3339])).
% 37.78/5.16 thf(f3339,plain,(
% 37.78/5.16 ($true = (irel @ sK15 @ sK19)) | (~spl0_44 | ~spl0_57 | spl0_58)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f3289])).
% 37.78/5.16 thf(f3289,plain,(
% 37.78/5.16 ((~ (irel @ sK15 @ sK19)) = $false) | (~spl0_44 | ~spl0_57 | spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f3288])).
% 37.78/5.16 thf(f3288,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK19) => $false) = $false) | (~spl0_44 | ~spl0_57 | spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f3287])).
% 37.78/5.16 thf(f3287,plain,(
% 37.78/5.16 ($false = ((irel @ sK15 @ sK19) => ($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl0_44 | ~spl0_57 | spl0_58)),
% 37.78/5.16 inference(backward_demodulation,[],[f2935,f2769])).
% 37.78/5.16 thf(f2935,plain,(
% 37.78/5.16 ($false = ((irel @ sK15 @ sK19) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | (~spl0_44 | spl0_58)),
% 37.78/5.16 inference(beta_eta_normalization,[],[f2934])).
% 37.78/5.16 thf(f2934,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))) @ sK19) = $false) | (~spl0_44 | spl0_58)),
% 37.78/5.16 inference(sigma_clausification,[],[f2890])).
% 37.78/5.16 thf(f2890,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))) = $false) | (~spl0_44 | spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f2889])).
% 37.78/5.16 thf(f2889,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) = $false) | (~spl0_44 | spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f2887])).
% 37.78/5.16 thf(f2887,plain,(
% 37.78/5.16 (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) = $false) | (~spl0_44 | spl0_58)),
% 37.78/5.16 inference(backward_demodulation,[],[f1861,f2883])).
% 37.78/5.16 thf(f1861,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) = $false) | ~spl0_44),
% 37.78/5.16 inference(avatar_component_clause,[],[f1859])).
% 37.78/5.16 thf(f1859,plain,(
% 37.78/5.16 spl0_44 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_44])])).
% 37.78/5.16 thf(f3199,plain,(
% 37.78/5.16 ($true = ((irel @ sK15 @ sK19) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0)))))) | (~spl0_1 | spl0_58 | ~spl0_61)),
% 37.78/5.16 inference(boolean_simplification,[],[f3198])).
% 37.78/5.16 thf(f3198,plain,(
% 37.78/5.16 ($true = ((irel @ sK15 @ sK19) => ($true & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))))) | (~spl0_1 | spl0_58 | ~spl0_61)),
% 37.78/5.16 inference(boolean_simplification,[],[f3197])).
% 37.78/5.16 thf(f3197,plain,(
% 37.78/5.16 ($true = ((irel @ sK15 @ sK19) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | $true) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))))) | (~spl0_1 | spl0_58 | ~spl0_61)),
% 37.78/5.16 inference(boolean_simplification,[],[f3196])).
% 37.78/5.16 thf(f3196,plain,(
% 37.78/5.16 ($true = ((irel @ sK15 @ sK19) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | $true) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0)))))))) | (~spl0_1 | spl0_58 | ~spl0_61)),
% 37.78/5.16 inference(boolean_simplification,[],[f3194])).
% 37.78/5.16 thf(f3194,plain,(
% 37.78/5.16 ($true = ((irel @ sK15 @ sK19) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | $true) & ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0)))))))) | (~spl0_1 | spl0_58 | ~spl0_61)),
% 37.78/5.16 inference(superposition,[],[f3107,f3071])).
% 37.78/5.16 thf(f3071,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | ~spl0_61),
% 37.78/5.16 inference(avatar_component_clause,[],[f3069])).
% 37.78/5.16 thf(f3107,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((irel @ sK15 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a3 @ Y0))))))))) ) | (~spl0_1 | spl0_58)),
% 37.78/5.16 inference(beta_eta_normalization,[],[f3100])).
% 37.78/5.16 thf(f3100,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))) @ X1))) ) | (~spl0_1 | spl0_58)),
% 37.78/5.16 inference(pi_clausification,[],[f2894])).
% 37.78/5.16 thf(f2894,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (~spl0_1 | spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f2893])).
% 37.78/5.16 thf(f2893,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) = $true) | (~spl0_1 | spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f2892])).
% 37.78/5.16 thf(f2892,plain,(
% 37.78/5.16 ($true = ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) | (~spl0_1 | spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f2891])).
% 37.78/5.16 thf(f2891,plain,(
% 37.78/5.16 ($true = (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & $true)) | (~spl0_1 | spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f2885])).
% 37.78/5.16 thf(f2885,plain,(
% 37.78/5.16 ((((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | $true)) = $true) | (~spl0_1 | spl0_58)),
% 37.78/5.16 inference(backward_demodulation,[],[f1855,f2883])).
% 37.78/5.16 thf(f3284,plain,(
% 37.78/5.16 ~spl0_56 | ~spl0_61 | ~spl0_62),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f3283])).
% 37.78/5.16 thf(f3283,plain,(
% 37.78/5.16 $false | (~spl0_56 | ~spl0_61 | ~spl0_62)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f3282])).
% 37.78/5.16 thf(f3282,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_56 | ~spl0_61 | ~spl0_62)),
% 37.78/5.16 inference(boolean_simplification,[],[f3281])).
% 37.78/5.16 thf(f3281,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a1 @ Y0))))) & $false)) | (~spl0_56 | ~spl0_61 | ~spl0_62)),
% 37.78/5.16 inference(backward_demodulation,[],[f3243,f3269])).
% 37.78/5.16 thf(f3269,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a2 @ Y0))))) = $false) | ~spl0_62),
% 37.78/5.16 inference(avatar_component_clause,[],[f3267])).
% 37.78/5.16 thf(f3267,plain,(
% 37.78/5.16 spl0_62 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a2 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_62])])).
% 37.78/5.16 thf(f3243,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a2 @ Y0))))))) | (~spl0_56 | ~spl0_61)),
% 37.78/5.16 inference(boolean_simplification,[],[f3228])).
% 37.78/5.16 thf(f3228,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a2 @ Y0)))))))) | (~spl0_56 | ~spl0_61)),
% 37.78/5.16 inference(superposition,[],[f3195,f3050])).
% 37.78/5.16 thf(f3050,plain,(
% 37.78/5.16 ($true = (irel @ sK19 @ sK20)) | ~spl0_56),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f3038])).
% 37.78/5.16 thf(f3038,plain,(
% 37.78/5.16 (((irel @ sK19 @ sK20) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a1 @ Y0))))))) = $false) | ~spl0_56),
% 37.78/5.16 inference(beta_eta_normalization,[],[f3037])).
% 37.78/5.16 thf(f3037,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ sK20) = $false) | ~spl0_56),
% 37.78/5.16 inference(sigma_clausification,[],[f2967])).
% 37.78/5.16 thf(f2967,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))) = $false) | ~spl0_56),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f2765])).
% 37.78/5.16 thf(f2765,plain,(
% 37.78/5.16 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | ~spl0_56),
% 37.78/5.16 inference(avatar_component_clause,[],[f2763])).
% 37.78/5.16 thf(f2763,plain,(
% 37.78/5.16 spl0_56 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_56])])).
% 37.78/5.16 thf(f3195,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((irel @ sK19 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))))))) ) | ~spl0_61),
% 37.78/5.16 inference(beta_eta_normalization,[],[f3192])).
% 37.78/5.16 thf(f3192,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ X1))) ) | ~spl0_61),
% 37.78/5.16 inference(pi_clausification,[],[f3071])).
% 37.78/5.16 thf(f3279,plain,(
% 37.78/5.16 ~spl0_56 | ~spl0_61 | ~spl0_63),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f3278])).
% 37.78/5.16 thf(f3278,plain,(
% 37.78/5.16 $false | (~spl0_56 | ~spl0_61 | ~spl0_63)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f3277])).
% 37.78/5.16 thf(f3277,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_56 | ~spl0_61 | ~spl0_63)),
% 37.78/5.16 inference(boolean_simplification,[],[f3275])).
% 37.78/5.16 thf(f3275,plain,(
% 37.78/5.16 ($true = ($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a2 @ Y0))))))) | (~spl0_56 | ~spl0_61 | ~spl0_63)),
% 37.78/5.16 inference(backward_demodulation,[],[f3243,f3273])).
% 37.78/5.16 thf(f3273,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a1 @ Y0))))) = $false) | ~spl0_63),
% 37.78/5.16 inference(avatar_component_clause,[],[f3271])).
% 37.78/5.16 thf(f3271,plain,(
% 37.78/5.16 spl0_63 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a1 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_63])])).
% 37.78/5.16 thf(f3274,plain,(
% 37.78/5.16 spl0_62 | spl0_63 | ~spl0_56),
% 37.78/5.16 inference(avatar_split_clause,[],[f3265,f2763,f3271,f3267])).
% 37.78/5.16 thf(f3265,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a2 @ Y0))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a1 @ Y0))))) = $false) | ~spl0_56),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f3049])).
% 37.78/5.16 thf(f3049,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK20 @ Y0) => (a1 @ Y0)))))) = $false) | ~spl0_56),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f3038])).
% 37.78/5.16 thf(f3184,plain,(
% 37.78/5.16 spl0_61 | ~spl0_1 | ~spl0_44 | ~spl0_56 | spl0_58),
% 37.78/5.16 inference(avatar_split_clause,[],[f3183,f2789,f2763,f1859,f110,f3069])).
% 37.78/5.16 thf(f3183,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (~spl0_1 | ~spl0_44 | ~spl0_56 | spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f3182])).
% 37.78/5.16 thf(f3182,plain,(
% 37.78/5.16 ($true = ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | (~spl0_1 | ~spl0_44 | ~spl0_56 | spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f3181])).
% 37.78/5.16 thf(f3181,plain,(
% 37.78/5.16 ($true = ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | (~spl0_1 | ~spl0_44 | ~spl0_56 | spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f3180])).
% 37.78/5.16 thf(f3180,plain,(
% 37.78/5.16 ((((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & $true) = $true) | (~spl0_1 | ~spl0_44 | ~spl0_56 | spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f3179])).
% 37.78/5.16 thf(f3179,plain,(
% 37.78/5.16 ($true = (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $true))) | (~spl0_1 | ~spl0_44 | ~spl0_56 | spl0_58)),
% 37.78/5.16 inference(forward_demodulation,[],[f3153,f2974])).
% 37.78/5.16 thf(f2974,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | ~spl0_56),
% 37.78/5.16 inference(not_proxy_clausification,[],[f2970])).
% 37.78/5.16 thf(f2970,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) = $false) | ~spl0_56),
% 37.78/5.16 inference(boolean_simplification,[],[f2969])).
% 37.78/5.16 thf(f2969,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | $false) = $false) | ~spl0_56),
% 37.78/5.16 inference(backward_demodulation,[],[f2765,f2967])).
% 37.78/5.16 thf(f3153,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))))) | (~spl0_1 | ~spl0_44 | ~spl0_56 | spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f3135])).
% 37.78/5.16 thf(f3135,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0)))))))) | (~spl0_1 | ~spl0_44 | ~spl0_56 | spl0_58)),
% 37.78/5.16 inference(superposition,[],[f3107,f2939])).
% 37.78/5.16 thf(f2939,plain,(
% 37.78/5.16 ($true = (irel @ sK15 @ sK19)) | (~spl0_44 | ~spl0_56 | spl0_58)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f2938])).
% 37.78/5.16 thf(f2938,plain,(
% 37.78/5.16 ((~ (irel @ sK15 @ sK19)) = $false) | (~spl0_44 | ~spl0_56 | spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f2937])).
% 37.78/5.16 thf(f2937,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK19) => $false) = $false) | (~spl0_44 | ~spl0_56 | spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f2936])).
% 37.78/5.16 thf(f2936,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK19) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) & $false)) = $false) | (~spl0_44 | ~spl0_56 | spl0_58)),
% 37.78/5.16 inference(forward_demodulation,[],[f2935,f2765])).
% 37.78/5.16 thf(f2868,plain,(
% 37.78/5.16 ~spl0_1 | spl0_45 | ~spl0_58),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f2867])).
% 37.78/5.16 thf(f2867,plain,(
% 37.78/5.16 $false | (~spl0_1 | spl0_45 | ~spl0_58)),
% 37.78/5.16 inference(subsumption_resolution,[],[f2866,f2861])).
% 37.78/5.16 thf(f2861,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) != $false) | (spl0_45 | ~spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f2860])).
% 37.78/5.16 thf(f2860,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $false) != $false) | (spl0_45 | ~spl0_58)),
% 37.78/5.16 inference(forward_demodulation,[],[f1864,f2805])).
% 37.78/5.16 thf(f2805,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0)))) = $false) | ~spl0_58),
% 37.78/5.16 inference(not_proxy_clausification,[],[f2791])).
% 37.78/5.16 thf(f2791,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0)))))) | ~spl0_58),
% 37.78/5.16 inference(avatar_component_clause,[],[f2789])).
% 37.78/5.16 thf(f1864,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) != $false) | spl0_45),
% 37.78/5.16 inference(avatar_component_clause,[],[f1863])).
% 37.78/5.16 thf(f2866,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) = $false) | (~spl0_1 | ~spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f2865])).
% 37.78/5.16 thf(f2865,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $false) = $false) | (~spl0_1 | ~spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f2864])).
% 37.78/5.16 thf(f2864,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $false) & $true) = $false) | (~spl0_1 | ~spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f2863])).
% 37.78/5.16 thf(f2863,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $false) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) = $false) | (~spl0_1 | ~spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f2862])).
% 37.78/5.16 thf(f2862,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $false) & ((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) = $false) | (~spl0_1 | ~spl0_58)),
% 37.78/5.16 inference(forward_demodulation,[],[f1846,f2805])).
% 37.78/5.16 thf(f1846,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) = $false) | ~spl0_1),
% 37.78/5.16 inference(boolean_simplification,[],[f1845])).
% 37.78/5.16 thf(f1845,plain,(
% 37.78/5.16 (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) = $false) | ~spl0_1),
% 37.78/5.16 inference(backward_demodulation,[],[f1828,f1844])).
% 37.78/5.16 thf(f2854,plain,(
% 37.78/5.16 spl0_59 | ~spl0_45 | ~spl0_58),
% 37.78/5.16 inference(avatar_split_clause,[],[f2853,f2789,f1863,f2793])).
% 37.78/5.16 thf(f2853,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (~spl0_45 | ~spl0_58)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f2815])).
% 37.78/5.16 thf(f2815,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) = $false) | (~spl0_45 | ~spl0_58)),
% 37.78/5.16 inference(boolean_simplification,[],[f2814])).
% 37.78/5.16 thf(f2814,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $false) = $false) | (~spl0_45 | ~spl0_58)),
% 37.78/5.16 inference(backward_demodulation,[],[f1865,f2805])).
% 37.78/5.16 thf(f2770,plain,(
% 37.78/5.16 spl0_56 | spl0_57 | ~spl0_44),
% 37.78/5.16 inference(avatar_split_clause,[],[f2761,f1859,f2767,f2763])).
% 37.78/5.16 thf(f2761,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) = $false) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | ~spl0_44),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f2654])).
% 37.78/5.16 thf(f2654,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) = $false) | ~spl0_44),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f2643])).
% 37.78/5.16 thf(f2643,plain,(
% 37.78/5.16 ($false = ((irel @ sK15 @ sK19) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK19 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))) | ~spl0_44),
% 37.78/5.16 inference(beta_eta_normalization,[],[f2642])).
% 37.78/5.16 thf(f2642,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))) @ sK19) = $false) | ~spl0_44),
% 37.78/5.16 inference(sigma_clausification,[],[f2635])).
% 37.78/5.16 thf(f2635,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))) = $false) | ~spl0_44),
% 37.78/5.16 inference(boolean_simplification,[],[f2632])).
% 37.78/5.16 thf(f2632,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) = $false) | ~spl0_44),
% 37.78/5.16 inference(backward_demodulation,[],[f1861,f2631])).
% 37.78/5.16 thf(f2631,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) = $false) | ~spl0_44),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f1861])).
% 37.78/5.16 thf(f2198,plain,(
% 37.78/5.16 spl0_48 | spl0_49 | ~spl0_1 | ~spl0_45),
% 37.78/5.16 inference(avatar_split_clause,[],[f2187,f1863,f110,f2195,f2191])).
% 37.78/5.16 thf(f2187,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) = $false) | (~spl0_1 | ~spl0_45)),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f2178])).
% 37.78/5.16 thf(f2178,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0)))))) = $false) | (~spl0_1 | ~spl0_45)),
% 37.78/5.16 inference(boolean_simplification,[],[f2177])).
% 37.78/5.16 thf(f2177,plain,(
% 37.78/5.16 ($false = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0)))))))) | (~spl0_1 | ~spl0_45)),
% 37.78/5.16 inference(backward_demodulation,[],[f2154,f2176])).
% 37.78/5.16 thf(f2176,plain,(
% 37.78/5.16 ((irel @ sK15 @ sK17) = $true) | (~spl0_1 | ~spl0_45)),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f2154])).
% 37.78/5.16 thf(f2154,plain,(
% 37.78/5.16 (((irel @ sK15 @ sK17) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK17 @ Y0) => (a3 @ Y0))))))) = $false) | (~spl0_1 | ~spl0_45)),
% 37.78/5.16 inference(beta_eta_normalization,[],[f2143])).
% 37.78/5.16 thf(f2143,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))) @ sK17) = $false) | (~spl0_1 | ~spl0_45)),
% 37.78/5.16 inference(sigma_clausification,[],[f2126])).
% 37.78/5.16 thf(f2126,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))) = $false) | (~spl0_1 | ~spl0_45)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f1880])).
% 37.78/5.16 thf(f1880,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) | (~spl0_1 | ~spl0_45)),
% 37.78/5.16 inference(boolean_simplification,[],[f1879])).
% 37.78/5.16 thf(f1879,plain,(
% 37.78/5.16 ($true = ($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))))) | (~spl0_1 | ~spl0_45)),
% 37.78/5.16 inference(boolean_simplification,[],[f1878])).
% 37.78/5.16 thf(f1878,plain,(
% 37.78/5.16 ($true = (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))))) | (~spl0_1 | ~spl0_45)),
% 37.78/5.16 inference(boolean_simplification,[],[f1877])).
% 37.78/5.16 thf(f1877,plain,(
% 37.78/5.16 ((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) = $true) | (~spl0_1 | ~spl0_45)),
% 37.78/5.16 inference(boolean_simplification,[],[f1876])).
% 37.78/5.16 thf(f1876,plain,(
% 37.78/5.16 ($true = (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | $false))) | (~spl0_1 | ~spl0_45)),
% 37.78/5.16 inference(backward_demodulation,[],[f1855,f1875])).
% 37.78/5.16 thf(f1875,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0)))) = $false) | ~spl0_45),
% 37.78/5.16 inference(boolean_simplification,[],[f1874])).
% 37.78/5.16 thf(f1874,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) = $false) | ~spl0_45),
% 37.78/5.16 inference(backward_demodulation,[],[f1865,f1873])).
% 37.78/5.16 thf(f1873,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) = $false) | ~spl0_45),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f1865])).
% 37.78/5.16 thf(f1866,plain,(
% 37.78/5.16 spl0_44 | spl0_45 | ~spl0_1),
% 37.78/5.16 inference(avatar_split_clause,[],[f1857,f110,f1863,f1859])).
% 37.78/5.16 thf(f1857,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK15 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) = $false) | ~spl0_1),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f1846])).
% 37.78/5.16 thf(f1743,plain,(
% 37.78/5.16 ~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39 | ~spl0_41),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f1742])).
% 37.78/5.16 thf(f1742,plain,(
% 37.78/5.16 $false | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39 | ~spl0_41)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f1741])).
% 37.78/5.16 thf(f1741,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39 | ~spl0_41)),
% 37.78/5.16 inference(boolean_simplification,[],[f1740])).
% 37.78/5.16 thf(f1740,plain,(
% 37.78/5.16 ($true = ($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39 | ~spl0_41)),
% 37.78/5.16 inference(backward_demodulation,[],[f1713,f1478])).
% 37.78/5.16 thf(f1478,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))) = $false) | ~spl0_41),
% 37.78/5.16 inference(avatar_component_clause,[],[f1476])).
% 37.78/5.16 thf(f1476,plain,(
% 37.78/5.16 spl0_41 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_41])])).
% 37.78/5.16 thf(f1713,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39)),
% 37.78/5.16 inference(boolean_simplification,[],[f1689])).
% 37.78/5.16 thf(f1689,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0)))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39)),
% 37.78/5.16 inference(superposition,[],[f1671,f1457])).
% 37.78/5.16 thf(f1457,plain,(
% 37.78/5.16 ((irel @ sK8 @ sK13) = $true) | ~spl0_39),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f1449])).
% 37.78/5.16 thf(f1449,plain,(
% 37.78/5.16 (((irel @ sK8 @ sK13) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))))) = $false) | ~spl0_39),
% 37.78/5.16 inference(beta_eta_normalization,[],[f1448])).
% 37.78/5.16 thf(f1448,plain,(
% 37.78/5.16 ($false = ((^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ sK13)) | ~spl0_39),
% 37.78/5.16 inference(sigma_clausification,[],[f1373])).
% 37.78/5.16 thf(f1671,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((irel @ sK8 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))))))) ) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39)),
% 37.78/5.16 inference(beta_eta_normalization,[],[f1669])).
% 37.78/5.16 thf(f1669,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ X1))) ) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39)),
% 37.78/5.16 inference(pi_clausification,[],[f1406])).
% 37.78/5.16 thf(f1406,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39)),
% 37.78/5.16 inference(boolean_simplification,[],[f1405])).
% 37.78/5.16 thf(f1405,plain,(
% 37.78/5.16 ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))) & $true)) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39)),
% 37.78/5.16 inference(boolean_simplification,[],[f1402])).
% 37.78/5.16 thf(f1402,plain,(
% 37.78/5.16 (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $true)) = $true) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39)),
% 37.78/5.16 inference(backward_demodulation,[],[f1379,f1362])).
% 37.78/5.16 thf(f1362,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | ~spl0_38),
% 37.78/5.16 inference(avatar_component_clause,[],[f1360])).
% 37.78/5.16 thf(f1360,plain,(
% 37.78/5.16 spl0_38 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0)))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_38])])).
% 37.78/5.16 thf(f1379,plain,(
% 37.78/5.16 ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_39)),
% 37.78/5.16 inference(boolean_simplification,[],[f1378])).
% 37.78/5.16 thf(f1378,plain,(
% 37.78/5.16 ($true = (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_39)),
% 37.78/5.16 inference(backward_demodulation,[],[f763,f1377])).
% 37.78/5.16 thf(f1377,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) = $false) | (~spl0_23 | ~spl0_39)),
% 37.78/5.16 inference(boolean_simplification,[],[f1375])).
% 37.78/5.16 thf(f1375,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | $false) = $false) | (~spl0_23 | ~spl0_39)),
% 37.78/5.16 inference(backward_demodulation,[],[f772,f1373])).
% 37.78/5.16 thf(f763,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10)),
% 37.78/5.16 inference(boolean_simplification,[],[f752])).
% 37.78/5.16 thf(f752,plain,(
% 37.78/5.16 (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))))) = $true) | (~spl0_2 | ~spl0_9 | ~spl0_10)),
% 37.78/5.16 inference(superposition,[],[f572,f749])).
% 37.78/5.16 thf(f749,plain,(
% 37.78/5.16 ($true = (irel @ sK3 @ sK8)) | (~spl0_2 | ~spl0_10)),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f735])).
% 37.78/5.16 thf(f735,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK8) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) = $false) | (~spl0_2 | ~spl0_10)),
% 37.78/5.16 inference(beta_eta_normalization,[],[f733])).
% 37.78/5.16 thf(f733,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))) @ sK8) = $false) | (~spl0_2 | ~spl0_10)),
% 37.78/5.16 inference(sigma_clausification,[],[f718])).
% 37.78/5.16 thf(f718,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))) = $false) | (~spl0_2 | ~spl0_10)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f459])).
% 37.78/5.16 thf(f459,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))) | (~spl0_2 | ~spl0_10)),
% 37.78/5.16 inference(boolean_simplification,[],[f457])).
% 37.78/5.16 thf(f457,plain,(
% 37.78/5.16 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | $false)) | (~spl0_2 | ~spl0_10)),
% 37.78/5.16 inference(backward_demodulation,[],[f443,f452])).
% 37.78/5.16 thf(f443,plain,(
% 37.78/5.16 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0)))))) | (~spl0_2 | ~spl0_10)),
% 37.78/5.16 inference(boolean_simplification,[],[f442])).
% 37.78/5.16 thf(f442,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) & $true)) | (~spl0_2 | ~spl0_10)),
% 37.78/5.16 inference(boolean_simplification,[],[f441])).
% 37.78/5.16 thf(f441,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) & ($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | (~spl0_2 | ~spl0_10)),
% 37.78/5.16 inference(backward_demodulation,[],[f180,f298])).
% 37.78/5.16 thf(f180,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))) | ~spl0_2),
% 37.78/5.16 inference(boolean_simplification,[],[f175])).
% 37.78/5.16 thf(f175,plain,(
% 37.78/5.16 ($true = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))))))) | ~spl0_2),
% 37.78/5.16 inference(superposition,[],[f134,f172])).
% 37.78/5.16 thf(f172,plain,(
% 37.78/5.16 ($true = (irel @ sK2 @ sK3)) | ~spl0_2),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f154])).
% 37.78/5.16 thf(f154,plain,(
% 37.78/5.16 (((irel @ sK2 @ sK3) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))))) = $false) | ~spl0_2),
% 37.78/5.16 inference(beta_eta_normalization,[],[f153])).
% 37.78/5.16 thf(f153,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))) @ sK3) = $false) | ~spl0_2),
% 37.78/5.16 inference(sigma_clausification,[],[f122])).
% 37.78/5.16 thf(f122,plain,(
% 37.78/5.16 ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) | ~spl0_2),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f116])).
% 37.78/5.16 thf(f134,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((irel @ sK2 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a4 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))))))) ) | ~spl0_2),
% 37.78/5.16 inference(beta_eta_normalization,[],[f133])).
% 37.78/5.16 thf(f133,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))) @ X1))) ) | ~spl0_2),
% 37.78/5.16 inference(pi_clausification,[],[f128])).
% 37.78/5.16 thf(f128,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | ~spl0_2),
% 37.78/5.16 inference(not_proxy_clausification,[],[f125])).
% 37.78/5.16 thf(f125,plain,(
% 37.78/5.16 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))))))))) | ~spl0_2),
% 37.78/5.16 inference(boolean_simplification,[],[f124])).
% 37.78/5.16 thf(f124,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | $false) = $false) | ~spl0_2),
% 37.78/5.16 inference(backward_demodulation,[],[f116,f122])).
% 37.78/5.16 thf(f1735,plain,(
% 37.78/5.16 ~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39 | ~spl0_40),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f1734])).
% 37.78/5.16 thf(f1734,plain,(
% 37.78/5.16 $false | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39 | ~spl0_40)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f1733])).
% 37.78/5.16 thf(f1733,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39 | ~spl0_40)),
% 37.78/5.16 inference(forward_demodulation,[],[f1732,f1494])).
% 37.78/5.16 thf(f1494,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0)))) = $false) | ~spl0_40),
% 37.78/5.16 inference(boolean_simplification,[],[f1493])).
% 37.78/5.16 thf(f1493,plain,(
% 37.78/5.16 (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) = $false) | ~spl0_40),
% 37.78/5.16 inference(backward_demodulation,[],[f1474,f1489])).
% 37.78/5.16 thf(f1489,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))) = $false) | ~spl0_40),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f1474])).
% 37.78/5.16 thf(f1474,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) = $false) | ~spl0_40),
% 37.78/5.16 inference(avatar_component_clause,[],[f1472])).
% 37.78/5.16 thf(f1472,plain,(
% 37.78/5.16 spl0_40 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_40])])).
% 37.78/5.16 thf(f1732,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0)))) = $true) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39 | ~spl0_40)),
% 37.78/5.16 inference(boolean_simplification,[],[f1731])).
% 37.78/5.16 thf(f1731,plain,(
% 37.78/5.16 (($true => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) = $true) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39 | ~spl0_40)),
% 37.78/5.16 inference(forward_demodulation,[],[f1700,f1457])).
% 37.78/5.16 thf(f1700,plain,(
% 37.78/5.16 ($true = ((irel @ sK8 @ sK13) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0)))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39 | ~spl0_40)),
% 37.78/5.16 inference(boolean_simplification,[],[f1699])).
% 37.78/5.16 thf(f1699,plain,(
% 37.78/5.16 ($true = ((irel @ sK8 @ sK13) => ($true & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39 | ~spl0_40)),
% 37.78/5.16 inference(boolean_simplification,[],[f1698])).
% 37.78/5.16 thf(f1698,plain,(
% 37.78/5.16 ($true = ((irel @ sK8 @ sK13) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) | $true) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39 | ~spl0_40)),
% 37.78/5.16 inference(boolean_simplification,[],[f1697])).
% 37.78/5.16 thf(f1697,plain,(
% 37.78/5.16 ($true = ((irel @ sK8 @ sK13) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) | $true) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0)))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39 | ~spl0_40)),
% 37.78/5.16 inference(boolean_simplification,[],[f1682])).
% 37.78/5.16 thf(f1682,plain,(
% 37.78/5.16 ($true = ((irel @ sK8 @ sK13) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) | $true) & ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0)))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_23 | ~spl0_38 | ~spl0_39 | ~spl0_40)),
% 37.78/5.16 inference(superposition,[],[f1671,f1620])).
% 37.78/5.16 thf(f1620,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0)))) = $true) | ~spl0_40),
% 37.78/5.16 inference(not_proxy_clausification,[],[f1489])).
% 37.78/5.16 thf(f1479,plain,(
% 37.78/5.16 spl0_40 | spl0_41 | ~spl0_39),
% 37.78/5.16 inference(avatar_split_clause,[],[f1470,f1364,f1476,f1472])).
% 37.78/5.16 thf(f1470,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))) = $false) | ~spl0_39),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f1459])).
% 37.78/5.16 thf(f1459,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0)))))) = $false) | ~spl0_39),
% 37.78/5.16 inference(boolean_simplification,[],[f1458])).
% 37.78/5.16 thf(f1458,plain,(
% 37.78/5.16 (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK13 @ Y0) => (a1 @ Y0))))))) = $false) | ~spl0_39),
% 37.78/5.16 inference(backward_demodulation,[],[f1449,f1457])).
% 37.78/5.16 thf(f1401,plain,(
% 37.78/5.16 spl0_38 | ~spl0_23 | ~spl0_39),
% 37.78/5.16 inference(avatar_split_clause,[],[f1396,f1364,f770,f1360])).
% 37.78/5.16 thf(f1396,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | (~spl0_23 | ~spl0_39)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f1377])).
% 37.78/5.16 thf(f1351,plain,(
% 37.78/5.16 ~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | ~spl0_36),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f1350])).
% 37.78/5.16 thf(f1350,plain,(
% 37.78/5.16 $false | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | ~spl0_36)),
% 37.78/5.16 inference(trivial_inequality_removal,[],[f1349])).
% 37.78/5.16 thf(f1349,plain,(
% 37.78/5.16 ($true = $false) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | ~spl0_36)),
% 37.78/5.16 inference(boolean_simplification,[],[f1346])).
% 37.78/5.16 thf(f1346,plain,(
% 37.78/5.16 ($true = ($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22 | ~spl0_36)),
% 37.78/5.16 inference(backward_demodulation,[],[f1208,f1340])).
% 37.78/5.16 thf(f1340,plain,(
% 37.78/5.16 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0)))))) | ~spl0_36),
% 37.78/5.16 inference(avatar_component_clause,[],[f1338])).
% 37.78/5.16 thf(f1338,plain,(
% 37.78/5.16 spl0_36 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))))),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_36])])).
% 37.78/5.16 thf(f1208,plain,(
% 37.78/5.16 ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22)),
% 37.78/5.16 inference(boolean_simplification,[],[f1203])).
% 37.78/5.16 thf(f1203,plain,(
% 37.78/5.16 (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))))) = $true) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22)),
% 37.78/5.16 inference(superposition,[],[f827,f1198])).
% 37.78/5.16 thf(f1198,plain,(
% 37.78/5.16 ($true = (irel @ sK8 @ sK11)) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22)),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f1189])).
% 37.78/5.16 thf(f1189,plain,(
% 37.78/5.16 ($false = ((irel @ sK8 @ sK11) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0)))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22)),
% 37.78/5.16 inference(beta_eta_normalization,[],[f1183])).
% 37.78/5.16 thf(f1183,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ sK11) = $false) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22)),
% 37.78/5.16 inference(sigma_clausification,[],[f1156])).
% 37.78/5.16 thf(f1156,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))) = $false) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f795])).
% 37.78/5.16 thf(f795,plain,(
% 37.78/5.16 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22)),
% 37.78/5.16 inference(boolean_simplification,[],[f794])).
% 37.78/5.16 thf(f794,plain,(
% 37.78/5.16 ($true = ($true & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22)),
% 37.78/5.16 inference(boolean_simplification,[],[f793])).
% 37.78/5.16 thf(f793,plain,(
% 37.78/5.16 ($true = (($true | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22)),
% 37.78/5.16 inference(boolean_simplification,[],[f792])).
% 37.78/5.16 thf(f792,plain,(
% 37.78/5.16 ($true = (((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22)),
% 37.78/5.16 inference(boolean_simplification,[],[f791])).
% 37.78/5.16 thf(f791,plain,(
% 37.78/5.16 ((((~ $false) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $false)) = $true) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22)),
% 37.78/5.16 inference(backward_demodulation,[],[f763,f788])).
% 37.78/5.16 thf(f788,plain,(
% 37.78/5.16 ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | ~spl0_22),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f768])).
% 37.78/5.16 thf(f827,plain,(
% 37.78/5.16 ( ! [X1 : $i] : (($true = ((irel @ sK8 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))))))) ) | ~spl0_22),
% 37.78/5.16 inference(beta_eta_normalization,[],[f826])).
% 37.78/5.16 thf(f826,plain,(
% 37.78/5.16 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ X1) = $true)) ) | ~spl0_22),
% 37.78/5.16 inference(pi_clausification,[],[f810])).
% 37.78/5.16 thf(f810,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))) = $true) | ~spl0_22),
% 37.78/5.16 inference(not_proxy_clausification,[],[f796])).
% 37.78/5.16 thf(f796,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) = $false) | ~spl0_22),
% 37.78/5.16 inference(boolean_simplification,[],[f790])).
% 37.78/5.16 thf(f790,plain,(
% 37.78/5.16 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | $false)) | ~spl0_22),
% 37.78/5.16 inference(backward_demodulation,[],[f768,f788])).
% 37.78/5.16 thf(f1345,plain,(
% 37.78/5.16 spl0_36 | spl0_37 | ~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22),
% 37.78/5.16 inference(avatar_split_clause,[],[f1334,f766,f296,f292,f114,f1342,f1338])).
% 37.78/5.16 thf(f1334,plain,(
% 37.78/5.16 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0)))))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) = $false) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22)),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f1197])).
% 37.78/5.16 thf(f1197,plain,(
% 37.78/5.16 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK11 @ Y0) => (a2 @ Y0))))))) | (~spl0_2 | ~spl0_9 | ~spl0_10 | ~spl0_22)),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f1189])).
% 37.78/5.16 thf(f1063,plain,(
% 37.78/5.16 spl0_29 | spl0_30 | spl0_27),
% 37.78/5.16 inference(avatar_split_clause,[],[f1052,f905,f1060,f1056])).
% 37.78/5.16 thf(f1052,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) = $false) | spl0_27),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f981])).
% 37.78/5.16 thf(f981,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK10 @ Y0) => (a2 @ Y0)))))) = $false) | spl0_27),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f977])).
% 37.78/5.16 thf(f773,plain,(
% 37.78/5.16 spl0_22 | spl0_23 | ~spl0_2 | ~spl0_10),
% 37.78/5.16 inference(avatar_split_clause,[],[f764,f296,f114,f770,f766])).
% 37.78/5.16 thf(f764,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) = $false) | (~spl0_2 | ~spl0_10)),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f751])).
% 37.78/5.16 thf(f751,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) = $false) | (~spl0_2 | ~spl0_10)),
% 37.78/5.16 inference(boolean_simplification,[],[f750])).
% 37.78/5.16 thf(f750,plain,(
% 37.78/5.16 (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK8 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))) = $false) | (~spl0_2 | ~spl0_10)),
% 37.78/5.16 inference(backward_demodulation,[],[f735,f749])).
% 37.78/5.16 thf(f681,plain,(
% 37.78/5.16 spl0_19 | spl0_20 | spl0_7),
% 37.78/5.16 inference(avatar_split_clause,[],[f672,f271,f678,f674])).
% 37.78/5.16 thf(f672,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | spl0_7),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f272])).
% 37.78/5.16 thf(f272,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) != $false) | spl0_7),
% 37.78/5.16 inference(avatar_component_clause,[],[f271])).
% 37.78/5.16 thf(f557,plain,(
% 37.78/5.16 ~spl0_6 | spl0_9 | ~spl0_10),
% 37.78/5.16 inference(avatar_contradiction_clause,[],[f556])).
% 37.78/5.16 thf(f556,plain,(
% 37.78/5.16 $false | (~spl0_6 | spl0_9 | ~spl0_10)),
% 37.78/5.16 inference(subsumption_resolution,[],[f555,f293])).
% 37.78/5.16 thf(f293,plain,(
% 37.78/5.16 ($true != (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | spl0_9),
% 37.78/5.16 inference(avatar_component_clause,[],[f292])).
% 37.78/5.16 thf(f555,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (~spl0_6 | ~spl0_10)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f460])).
% 37.78/5.16 thf(f460,plain,(
% 37.78/5.16 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) | (~spl0_6 | ~spl0_10)),
% 37.78/5.16 inference(boolean_simplification,[],[f456])).
% 37.78/5.16 thf(f456,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | $false) = $false) | (~spl0_6 | ~spl0_10)),
% 37.78/5.16 inference(backward_demodulation,[],[f191,f452])).
% 37.78/5.16 thf(f191,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) = $false) | ~spl0_6),
% 37.78/5.16 inference(avatar_component_clause,[],[f189])).
% 37.78/5.16 thf(f189,plain,(
% 37.78/5.16 spl0_6 <=> (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) = $false)),
% 37.78/5.16 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 37.78/5.16 thf(f299,plain,(
% 37.78/5.16 spl0_9 | spl0_10 | spl0_5),
% 37.78/5.16 inference(avatar_split_clause,[],[f290,f185,f296,f292])).
% 37.78/5.16 thf(f290,plain,(
% 37.78/5.16 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) = $true) | spl0_5),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f186])).
% 37.78/5.16 thf(f186,plain,(
% 37.78/5.16 ($false != ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) | spl0_5),
% 37.78/5.16 inference(avatar_component_clause,[],[f185])).
% 37.78/5.16 thf(f278,plain,(
% 37.78/5.16 spl0_7 | spl0_8 | ~spl0_5),
% 37.78/5.16 inference(avatar_split_clause,[],[f269,f185,f275,f271])).
% 37.78/5.16 thf(f269,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) = $false) | ~spl0_5),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f253])).
% 37.78/5.16 thf(f253,plain,(
% 37.78/5.16 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0)))))) = $false) | ~spl0_5),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f240])).
% 37.78/5.16 thf(f240,plain,(
% 37.78/5.16 (((irel @ sK3 @ sK4) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK4 @ Y0) => (a3 @ Y0))))))) = $false) | ~spl0_5),
% 37.78/5.16 inference(beta_eta_normalization,[],[f239])).
% 37.78/5.16 thf(f239,plain,(
% 37.78/5.16 (((^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))) @ sK4) = $false) | ~spl0_5),
% 37.78/5.16 inference(sigma_clausification,[],[f202])).
% 37.78/5.16 thf(f202,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))) = $false) | ~spl0_5),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f187])).
% 37.78/5.16 thf(f192,plain,(
% 37.78/5.16 spl0_5 | spl0_6 | ~spl0_2),
% 37.78/5.16 inference(avatar_split_clause,[],[f183,f114,f189,f185])).
% 37.78/5.16 thf(f183,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) = $false) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))))))))) | ~spl0_2),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f174])).
% 37.78/5.16 thf(f174,plain,(
% 37.78/5.16 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))))) | ~spl0_2),
% 37.78/5.16 inference(boolean_simplification,[],[f173])).
% 37.78/5.16 thf(f173,plain,(
% 37.78/5.16 (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a3 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a4 @ Y0))))))) = $false) | ~spl0_2),
% 37.78/5.16 inference(backward_demodulation,[],[f154,f172])).
% 37.78/5.16 thf(f117,plain,(
% 37.78/5.16 spl0_1 | spl0_2),
% 37.78/5.16 inference(avatar_split_clause,[],[f108,f114,f110])).
% 37.78/5.16 thf(f108,plain,(
% 37.78/5.16 (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) = $false)),
% 37.78/5.16 inference(binary_proxy_clausification,[],[f107])).
% 37.78/5.16 thf(f107,plain,(
% 37.78/5.16 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a3 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a1 @ Y3))))))))))))))))))))))),
% 37.78/5.16 inference(beta_eta_normalization,[],[f106])).
% 37.78/5.16 thf(f106,plain,(
% 37.78/5.16 (((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))))))))))))))) @ sK2) = $false)),
% 37.78/5.16 inference(sigma_clausification,[],[f101])).
% 37.78/5.16 thf(f101,plain,(
% 37.78/5.16 ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))))))))))) = $false)),
% 37.78/5.16 inference(not_proxy_clausification,[],[f100])).
% 37.78/5.16 thf(f100,plain,(
% 37.78/5.16 ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (a3 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((irel @ Y2 @ Y3) => (((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) & ((~ (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (a1 @ Y4)))))))))))))))))))))))) = $true)),
% 37.78/5.17 inference(beta_eta_normalization,[],[f99])).
% 37.78/5.17 thf(f99,plain,(
% 37.78/5.17 ((~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: (Y0)) @ a1) @ ((^[Y0 : $i > $o]: (Y0)) @ a2)) @ ((^[Y0 : $i > $o]: (Y0)) @ a3)) @ ((^[Y0 : $i > $o]: (Y0)) @ a4)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: (Y0)) @ a4) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: (Y0)) @ a3) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: (Y0)) @ a2) @ ((^[Y0 : $i > $o]: (Y0)) @ a1))))))) = $true)),
% 37.78/5.17 inference(definition_unfolding,[],[f75,f80,f97,f97,f97,f97,f68,f68,f68,f68,f97,f68,f97,f68,f97,f68,f68])).
% 37.78/5.17 thf(f68,plain,(
% 37.78/5.17 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 37.78/5.17 inference(cnf_transformation,[],[f40])).
% 37.78/5.17 thf(f40,plain,(
% 37.78/5.17 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 37.78/5.17 inference(fool_elimination,[],[f39])).
% 37.78/5.17 thf(f39,plain,(
% 37.78/5.17 ((^[X0 : $i > $o] : (X0)) = iatom)),
% 37.78/5.17 inference(rectify,[],[f8])).
% 37.78/5.17 thf(f8,axiom,(
% 37.78/5.17 ((^[X5 : $i > $o] : (X5)) = iatom)),
% 37.78/5.17 file('/export/starexec/sandbox/tmp/tmp.C36a6lzdu4/Vampire---4.8_19757',iatom)).
% 37.78/5.17 thf(f97,plain,(
% 37.78/5.17 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))))),
% 37.78/5.17 inference(definition_unfolding,[],[f77,f93,f95,f95])).
% 37.78/5.17 thf(f95,plain,(
% 37.78/5.17 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))))),
% 37.78/5.17 inference(definition_unfolding,[],[f87,f90,f78,f78])).
% 37.78/5.17 thf(f78,plain,(
% 37.78/5.17 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 37.78/5.17 inference(cnf_transformation,[],[f36])).
% 37.78/5.17 thf(f36,plain,(
% 37.78/5.17 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 37.78/5.17 inference(fool_elimination,[],[f35])).
% 37.78/5.17 thf(f35,plain,(
% 37.78/5.17 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((irel @ X1 @ X2) => (X0 @ X2)))) = mbox_s4)),
% 37.78/5.17 inference(rectify,[],[f7])).
% 37.78/5.17 thf(f7,axiom,(
% 37.78/5.17 ((^[X5 : $i > $o, X0 : $i] : (! [X1] : ((irel @ X0 @ X1) => (X5 @ X1)))) = mbox_s4)),
% 37.78/5.17 file('/export/starexec/sandbox/tmp/tmp.C36a6lzdu4/Vampire---4.8_19757',mbox_s4)).
% 37.78/5.17 thf(f90,plain,(
% 37.78/5.17 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 37.78/5.17 inference(definition_unfolding,[],[f84,f83,f85])).
% 37.78/5.17 thf(f85,plain,(
% 37.78/5.17 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 37.78/5.17 inference(cnf_transformation,[],[f30])).
% 37.78/5.17 thf(f30,plain,(
% 37.78/5.17 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 37.78/5.17 inference(fool_elimination,[],[f29])).
% 37.78/5.17 thf(f29,plain,(
% 37.78/5.17 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 37.78/5.17 inference(rectify,[],[f3])).
% 37.78/5.17 thf(f3,axiom,(
% 37.78/5.17 ((^[X0 : $i > $o, X3 : $i] : (~(X0 @ X3))) = mnot)),
% 37.78/5.17 file('/export/starexec/sandbox/tmp/tmp.C36a6lzdu4/Vampire---4.8_19757',mnot)).
% 37.78/5.17 thf(f83,plain,(
% 37.78/5.17 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 37.78/5.17 inference(cnf_transformation,[],[f42])).
% 37.78/5.17 thf(f42,plain,(
% 37.78/5.17 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 37.78/5.17 inference(fool_elimination,[],[f41])).
% 37.78/5.17 thf(f41,plain,(
% 37.78/5.17 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 37.78/5.17 inference(rectify,[],[f4])).
% 37.78/5.17 thf(f4,axiom,(
% 37.78/5.17 ((^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X1 @ X3) | (X0 @ X3))) = mor)),
% 37.78/5.17 file('/export/starexec/sandbox/tmp/tmp.C36a6lzdu4/Vampire---4.8_19757',mor)).
% 37.78/5.17 thf(f84,plain,(
% 37.78/5.17 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 37.78/5.17 inference(cnf_transformation,[],[f48])).
% 37.78/5.17 thf(f48,plain,(
% 37.78/5.17 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 37.78/5.17 inference(fool_elimination,[],[f47])).
% 37.78/5.17 thf(f47,plain,(
% 37.78/5.17 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 37.78/5.17 inference(rectify,[],[f6])).
% 37.78/5.17 thf(f6,axiom,(
% 37.78/5.17 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 37.78/5.17 file('/export/starexec/sandbox/tmp/tmp.C36a6lzdu4/Vampire---4.8_19757',mimplies)).
% 37.78/5.17 thf(f87,plain,(
% 37.78/5.17 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 37.78/5.17 inference(cnf_transformation,[],[f38])).
% 37.78/5.17 thf(f38,plain,(
% 37.78/5.17 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 37.78/5.17 inference(fool_elimination,[],[f37])).
% 37.78/5.17 thf(f37,plain,(
% 37.78/5.17 ((^[X0 : $i > $o, X1 : $i > $o] : (mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))) = iimplies)),
% 37.78/5.17 inference(rectify,[],[f14])).
% 37.78/5.17 thf(f14,axiom,(
% 37.78/5.17 ((^[X5 : $i > $o, X7 : $i > $o] : (mimplies @ (mbox_s4 @ X5) @ (mbox_s4 @ X7))) = iimplies)),
% 37.78/5.17 file('/export/starexec/sandbox/tmp/tmp.C36a6lzdu4/Vampire---4.8_19757',iimplies)).
% 37.78/5.17 thf(f93,plain,(
% 37.78/5.17 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ Y0 @ Y1)))))),
% 37.78/5.17 inference(definition_unfolding,[],[f89,f70])).
% 37.78/5.17 thf(f70,plain,(
% 37.78/5.17 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 37.78/5.17 inference(cnf_transformation,[],[f54])).
% 37.78/5.17 thf(f54,plain,(
% 37.78/5.17 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 37.78/5.17 inference(fool_elimination,[],[f53])).
% 37.78/5.17 thf(f53,plain,(
% 37.78/5.17 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) & (X1 @ X2))) = mand)),
% 37.78/5.17 inference(rectify,[],[f5])).
% 37.78/5.17 thf(f5,axiom,(
% 37.78/5.17 ((^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X0 @ X3) & (X1 @ X3))) = mand)),
% 37.78/5.17 file('/export/starexec/sandbox/tmp/tmp.C36a6lzdu4/Vampire---4.8_19757',mand)).
% 37.78/5.17 thf(f89,plain,(
% 37.78/5.17 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ Y0 @ Y1)))))),
% 37.78/5.17 inference(cnf_transformation,[],[f58])).
% 37.78/5.17 thf(f58,plain,(
% 37.78/5.17 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ Y0 @ Y1)))))),
% 37.78/5.17 inference(fool_elimination,[],[f57])).
% 37.78/5.17 thf(f57,plain,(
% 37.78/5.17 (iand = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ X0 @ X1)))),
% 37.78/5.17 inference(rectify,[],[f12])).
% 37.78/5.17 thf(f12,axiom,(
% 37.78/5.17 (iand = (^[X5 : $i > $o, X7 : $i > $o] : (mand @ X5 @ X7)))),
% 37.78/5.17 file('/export/starexec/sandbox/tmp/tmp.C36a6lzdu4/Vampire---4.8_19757',iand)).
% 37.78/5.17 thf(f77,plain,(
% 37.78/5.17 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 37.78/5.17 inference(cnf_transformation,[],[f61])).
% 37.78/5.17 thf(f61,plain,(
% 37.78/5.17 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 37.78/5.17 inference(fool_elimination,[],[f60])).
% 37.78/5.17 thf(f60,plain,(
% 37.78/5.17 ((^[X0 : $i > $o, X1 : $i > $o] : (iand @ (iimplies @ X0 @ X1) @ (iimplies @ X1 @ X0))) = iequiv)),
% 37.78/5.17 inference(rectify,[],[f16])).
% 37.78/5.17 thf(f16,axiom,(
% 37.78/5.17 ((^[X5 : $i > $o, X7 : $i > $o] : (iand @ (iimplies @ X5 @ X7) @ (iimplies @ X7 @ X5))) = iequiv)),
% 37.78/5.17 file('/export/starexec/sandbox/tmp/tmp.C36a6lzdu4/Vampire---4.8_19757',iequiv)).
% 37.78/5.17 thf(f80,plain,(
% 37.78/5.17 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 37.78/5.17 inference(cnf_transformation,[],[f65])).
% 37.78/5.17 thf(f65,plain,(
% 37.78/5.17 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 37.78/5.17 inference(fool_elimination,[],[f64])).
% 37.78/5.17 thf(f64,plain,(
% 37.78/5.17 (ivalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 37.78/5.17 inference(rectify,[],[f18])).
% 37.78/5.17 thf(f18,axiom,(
% 37.78/5.17 (ivalid = (^[X8 : $i > $o] : (! [X6] : (X8 @ X6))))),
% 37.78/5.17 file('/export/starexec/sandbox/tmp/tmp.C36a6lzdu4/Vampire---4.8_19757',ivalid)).
% 37.78/5.17 thf(f75,plain,(
% 37.78/5.17 ($true = (~ (ivalid @ (iequiv @ (iequiv @ (iequiv @ (iequiv @ (iatom @ a1) @ (iatom @ a2)) @ (iatom @ a3)) @ (iatom @ a4)) @ (iequiv @ (iatom @ a4) @ (iequiv @ (iatom @ a3) @ (iequiv @ (iatom @ a2) @ (iatom @ a1))))))))),
% 37.78/5.17 inference(cnf_transformation,[],[f50])).
% 37.78/5.17 thf(f50,plain,(
% 37.78/5.17 ($true = (~ (ivalid @ (iequiv @ (iequiv @ (iequiv @ (iequiv @ (iatom @ a1) @ (iatom @ a2)) @ (iatom @ a3)) @ (iatom @ a4)) @ (iequiv @ (iatom @ a4) @ (iequiv @ (iatom @ a3) @ (iequiv @ (iatom @ a2) @ (iatom @ a1))))))))),
% 37.78/5.17 inference(fool_elimination,[],[f49])).
% 37.78/5.17 thf(f49,plain,(
% 37.78/5.17 ~(ivalid @ (iequiv @ (iequiv @ (iequiv @ (iequiv @ (iatom @ a1) @ (iatom @ a2)) @ (iatom @ a3)) @ (iatom @ a4)) @ (iequiv @ (iatom @ a4) @ (iequiv @ (iatom @ a3) @ (iequiv @ (iatom @ a2) @ (iatom @ a1))))))),
% 37.78/5.17 inference(rectify,[],[f23])).
% 37.78/5.17 thf(f23,negated_conjecture,(
% 37.78/5.17 ~(ivalid @ (iequiv @ (iequiv @ (iequiv @ (iequiv @ (iatom @ a1) @ (iatom @ a2)) @ (iatom @ a3)) @ (iatom @ a4)) @ (iequiv @ (iatom @ a4) @ (iequiv @ (iatom @ a3) @ (iequiv @ (iatom @ a2) @ (iatom @ a1))))))),
% 37.78/5.17 inference(negated_conjecture,[],[f22])).
% 37.78/5.17 thf(f22,conjecture,(
% 37.78/5.17 (ivalid @ (iequiv @ (iequiv @ (iequiv @ (iequiv @ (iatom @ a1) @ (iatom @ a2)) @ (iatom @ a3)) @ (iatom @ a4)) @ (iequiv @ (iatom @ a4) @ (iequiv @ (iatom @ a3) @ (iequiv @ (iatom @ a2) @ (iatom @ a1))))))),
% 37.78/5.17 file('/export/starexec/sandbox/tmp/tmp.C36a6lzdu4/Vampire---4.8_19757',con)).
% 37.78/5.17 % SZS output end Proof for Vampire---4
% 37.78/5.17 % (20457)------------------------------
% 37.78/5.17 % (20457)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 37.78/5.17 % (20457)Termination reason: Refutation
% 37.78/5.17
% 37.78/5.17 % (20457)Memory used [KB]: 10106
% 37.78/5.17 % (20457)Time elapsed: 0.870 s
% 37.78/5.17 % (20457)Instructions burned: 2803 (million)
% 37.78/5.17 % (20457)------------------------------
% 37.78/5.17 % (20457)------------------------------
% 37.78/5.17 % (20015)Success in time 4.77 s
% 37.78/5.17 % Vampire---4.8 exiting
%------------------------------------------------------------------------------