%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : KRS272^7 : TPTP v8.1.2. Released v5.5.0.
% 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 : n018.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 07:18:35 EDT 2024

% Result   : Theorem 1.44s 0.60s
% Output   : Refutation 1.44s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : KRS272^7 : TPTP v8.1.2. Released v5.5.0.
% 0.08/0.15  % 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
% 0.16/0.36  % Computer : n018.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Fri May  3 19:52:38 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.16/0.36  This is a TH0_THM_EQU_NAR problem
% 0.16/0.36  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.7LKmvzLAF1/Vampire---4.8_21131
% 0.16/0.39  % (21378)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  % (21376)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  % (21375)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  % (21379)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  % (21377)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  % (21373)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  % (21374)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  % (21380)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)
% 0.23/0.39  % (21376)Instruction limit reached!
% 0.23/0.39  % (21376)------------------------------
% 0.23/0.39  % (21376)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39  % (21377)Instruction limit reached!
% 0.23/0.39  % (21377)------------------------------
% 0.23/0.39  % (21377)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39  % (21377)Termination reason: Unknown
% 0.23/0.39  % (21377)Termination phase: shuffling
% 0.23/0.39  
% 0.23/0.39  % (21377)Memory used [KB]: 1023
% 0.23/0.39  % (21377)Time elapsed: 0.004 s
% 0.23/0.39  % (21377)Instructions burned: 3 (million)
% 0.23/0.39  % (21377)------------------------------
% 0.23/0.39  % (21377)------------------------------
% 0.23/0.39  % (21376)Termination reason: Unknown
% 0.23/0.39  % (21376)Termination phase: shuffling
% 0.23/0.39  
% 0.23/0.39  % (21376)Memory used [KB]: 1023
% 0.23/0.39  % (21376)Time elapsed: 0.003 s
% 0.23/0.39  % (21376)Instructions burned: 3 (million)
% 0.23/0.39  % (21376)------------------------------
% 0.23/0.39  % (21376)------------------------------
% 0.23/0.39  % (21380)Instruction limit reached!
% 0.23/0.39  % (21380)------------------------------
% 0.23/0.39  % (21380)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39  % (21380)Termination reason: Unknown
% 0.23/0.39  % (21380)Termination phase: shuffling
% 0.23/0.39  
% 0.23/0.39  % (21380)Memory used [KB]: 1023
% 0.23/0.39  % (21380)Time elapsed: 0.004 s
% 0.23/0.39  % (21380)Instructions burned: 4 (million)
% 0.23/0.39  % (21380)------------------------------
% 0.23/0.39  % (21380)------------------------------
% 0.23/0.39  % (21374)Instruction limit reached!
% 0.23/0.39  % (21374)------------------------------
% 0.23/0.39  % (21374)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39  % (21374)Termination reason: Unknown
% 0.23/0.39  % (21374)Termination phase: shuffling
% 0.23/0.39  
% 0.23/0.39  % (21374)Memory used [KB]: 1023
% 0.23/0.39  % (21374)Time elapsed: 0.004 s
% 0.23/0.39  % (21374)Instructions burned: 4 (million)
% 0.23/0.39  % (21374)------------------------------
% 0.23/0.39  % (21374)------------------------------
% 0.23/0.40  % (21379)Instruction limit reached!
% 0.23/0.40  % (21379)------------------------------
% 0.23/0.40  % (21379)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40  % (21379)Termination reason: Unknown
% 0.23/0.40  % (21379)Termination phase: Saturation
% 0.23/0.40  
% 0.23/0.40  % (21379)Memory used [KB]: 5628
% 0.23/0.40  % (21379)Time elapsed: 0.012 s
% 0.23/0.40  % (21379)Instructions burned: 20 (million)
% 0.23/0.40  % (21379)------------------------------
% 0.23/0.40  % (21379)------------------------------
% 0.23/0.40  % (21378)Refutation not found, incomplete strategy
% 0.23/0.40  % (21378)------------------------------
% 0.23/0.40  % (21378)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40  % (21378)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.40  
% 0.23/0.40  
% 0.23/0.40  % (21378)Memory used [KB]: 5756
% 0.23/0.40  % (21378)Time elapsed: 0.013 s
% 0.23/0.40  % (21378)Instructions burned: 19 (million)
% 0.23/0.40  % (21378)------------------------------
% 0.23/0.40  % (21378)------------------------------
% 0.23/0.40  % (21375)Instruction limit reached!
% 0.23/0.40  % (21375)------------------------------
% 0.23/0.40  % (21375)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40  % (21375)Termination reason: Unknown
% 0.23/0.40  % (21375)Termination phase: Saturation
% 0.23/0.40  
% 0.23/0.40  % (21375)Memory used [KB]: 5756
% 0.23/0.40  % (21375)Time elapsed: 0.015 s
% 0.23/0.40  % (21375)Instructions burned: 28 (million)
% 0.23/0.40  % (21375)------------------------------
% 0.23/0.40  % (21375)------------------------------
% 0.23/0.40  % (21381)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)
% 0.23/0.40  % (21382)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)
% 0.23/0.40  % (21383)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)
% 0.23/0.40  % (21384)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)
% 0.23/0.40  % (21383)Instruction limit reached!
% 0.23/0.40  % (21383)------------------------------
% 0.23/0.40  % (21383)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40  % (21383)Termination reason: Unknown
% 0.23/0.40  % (21383)Termination phase: shuffling
% 0.23/0.40  
% 0.23/0.40  % (21383)Memory used [KB]: 1023
% 0.23/0.40  % (21383)Time elapsed: 0.004 s
% 0.23/0.40  % (21383)Instructions burned: 4 (million)
% 0.23/0.40  % (21383)------------------------------
% 0.23/0.40  % (21383)------------------------------
% 0.23/0.41  % (21382)Instruction limit reached!
% 0.23/0.41  % (21382)------------------------------
% 0.23/0.41  % (21382)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.41  % (21382)Termination reason: Unknown
% 0.23/0.41  % (21382)Termination phase: Saturation
% 0.23/0.41  
% 0.23/0.41  % (21382)Memory used [KB]: 1151
% 0.23/0.41  % (21382)Time elapsed: 0.010 s
% 0.23/0.41  % (21382)Instructions burned: 16 (million)
% 0.23/0.41  % (21382)------------------------------
% 0.23/0.41  % (21382)------------------------------
% 0.23/0.41  % (21385)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)
% 0.23/0.41  % (21386)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)
% 0.23/0.41  % (21387)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)
% 0.23/0.41  % (21385)Instruction limit reached!
% 0.23/0.41  % (21385)------------------------------
% 0.23/0.41  % (21385)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.41  % (21385)Termination reason: Unknown
% 0.23/0.41  % (21385)Termination phase: SInE selection
% 0.23/0.41  
% 0.23/0.41  % (21385)Memory used [KB]: 1023
% 0.23/0.41  % (21385)Time elapsed: 0.006 s
% 0.23/0.41  % (21385)Instructions burned: 8 (million)
% 0.23/0.41  % (21385)------------------------------
% 0.23/0.41  % (21385)------------------------------
% 0.23/0.42  % (21387)Instruction limit reached!
% 0.23/0.42  % (21387)------------------------------
% 0.23/0.42  % (21387)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.42  % (21387)Termination reason: Unknown
% 0.23/0.42  % (21387)Termination phase: shuffling
% 0.23/0.42  
% 0.23/0.42  % (21387)Memory used [KB]: 1023
% 0.23/0.42  % (21387)Time elapsed: 0.004 s
% 0.23/0.42  % (21387)Instructions burned: 4 (million)
% 0.23/0.42  % (21387)------------------------------
% 0.23/0.42  % (21387)------------------------------
% 0.23/0.42  % (21388)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)
% 0.23/0.42  % (21388)Instruction limit reached!
% 0.23/0.42  % (21388)------------------------------
% 0.23/0.42  % (21388)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.42  % (21381)Instruction limit reached!
% 0.23/0.42  % (21381)------------------------------
% 0.23/0.42  % (21381)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.42  % (21381)Termination reason: Unknown
% 0.23/0.42  % (21381)Termination phase: Saturation
% 0.23/0.42  
% 0.23/0.42  % (21381)Memory used [KB]: 5884
% 0.23/0.42  % (21381)Time elapsed: 0.021 s
% 0.23/0.42  % (21381)Instructions burned: 38 (million)
% 0.23/0.42  % (21381)------------------------------
% 0.23/0.42  % (21381)------------------------------
% 0.23/0.42  % (21388)Termination reason: Unknown
% 0.23/0.42  % (21388)Termination phase: shuffling
% 0.23/0.42  
% 0.23/0.42  % (21388)Memory used [KB]: 1023
% 0.23/0.42  % (21388)Time elapsed: 0.004 s
% 0.23/0.42  % (21388)Instructions burned: 4 (million)
% 0.23/0.42  % (21388)------------------------------
% 0.23/0.42  % (21388)------------------------------
% 0.23/0.42  % (21386)Instruction limit reached!
% 0.23/0.42  % (21386)------------------------------
% 0.23/0.42  % (21386)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.42  % (21386)Termination reason: Unknown
% 0.23/0.42  % (21386)Termination phase: Saturation
% 0.23/0.42  
% 0.23/0.42  % (21386)Memory used [KB]: 5628
% 0.23/0.42  % (21386)Time elapsed: 0.012 s
% 0.23/0.42  % (21386)Instructions burned: 17 (million)
% 0.23/0.42  % (21386)------------------------------
% 0.23/0.42  % (21386)------------------------------
% 0.23/0.43  % (21389)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)
% 0.23/0.43  % (21390)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)
% 0.23/0.43  % (21389)Instruction limit reached!
% 0.23/0.43  % (21389)------------------------------
% 0.23/0.43  % (21389)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.43  % (21389)Termination reason: Unknown
% 0.23/0.43  % (21389)Termination phase: Property scanning
% 0.23/0.43  
% 0.23/0.43  % (21389)Memory used [KB]: 1151
% 0.23/0.43  % (21389)Time elapsed: 0.008 s
% 0.23/0.43  % (21389)Instructions burned: 7 (million)
% 0.23/0.43  % (21389)------------------------------
% 0.23/0.43  % (21389)------------------------------
% 0.23/0.43  % (21391)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)
% 0.23/0.43  % (21390)Instruction limit reached!
% 0.23/0.43  % (21390)------------------------------
% 0.23/0.43  % (21390)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.43  % (21390)Termination reason: Unknown
% 0.23/0.43  % (21390)Termination phase: shuffling
% 0.23/0.43  
% 0.23/0.43  % (21390)Memory used [KB]: 1023
% 0.23/0.43  % (21390)Time elapsed: 0.005 s
% 0.23/0.43  % (21390)Instructions burned: 4 (million)
% 0.23/0.43  % (21390)------------------------------
% 0.23/0.43  % (21390)------------------------------
% 0.23/0.43  % (21391)Instruction limit reached!
% 0.23/0.43  % (21391)------------------------------
% 0.23/0.43  % (21391)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.43  % (21391)Termination reason: Unknown
% 0.23/0.43  % (21391)Termination phase: shuffling
% 0.23/0.43  
% 0.23/0.43  % (21391)Memory used [KB]: 1023
% 0.23/0.43  % (21391)Time elapsed: 0.006 s
% 0.23/0.43  % (21391)Instructions burned: 4 (million)
% 0.23/0.43  % (21391)------------------------------
% 0.23/0.43  % (21391)------------------------------
% 0.23/0.44  % (21392)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)
% 0.23/0.44  % (21393)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)
% 0.23/0.44  % (21394)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.23/0.45  % (21404)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  % (21394)Instruction limit reached!
% 0.23/0.45  % (21394)------------------------------
% 0.23/0.45  % (21394)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.45  % (21394)Termination reason: Unknown
% 0.23/0.45  % (21394)Termination phase: Property scanning
% 0.23/0.45  
% 0.23/0.45  % (21394)Memory used [KB]: 1023
% 0.23/0.45  % (21394)Time elapsed: 0.008 s
% 0.23/0.45  % (21394)Instructions burned: 6 (million)
% 0.23/0.45  % (21394)------------------------------
% 0.23/0.45  % (21394)------------------------------
% 0.23/0.45  % (21404)Refutation not found, incomplete strategy
% 0.23/0.45  % (21404)------------------------------
% 0.23/0.45  % (21404)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.45  % (21404)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.45  
% 0.23/0.45  
% 0.23/0.45  % (21404)Memory used [KB]: 5628
% 0.23/0.45  % (21404)Time elapsed: 0.008 s
% 0.23/0.45  % (21404)Instructions burned: 12 (million)
% 0.23/0.45  % (21404)------------------------------
% 0.23/0.45  % (21404)------------------------------
% 0.23/0.46  % (21392)Instruction limit reached!
% 0.23/0.46  % (21392)------------------------------
% 0.23/0.46  % (21392)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.46  % (21392)Termination reason: Unknown
% 0.23/0.46  % (21392)Termination phase: Saturation
% 0.23/0.46  
% 0.23/0.46  % (21392)Memory used [KB]: 5628
% 0.23/0.46  % (21392)Time elapsed: 0.019 s
% 0.23/0.46  % (21392)Instructions burned: 18 (million)
% 0.23/0.46  % (21392)------------------------------
% 0.23/0.46  % (21392)------------------------------
% 0.23/0.46  % (21406)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on Vampire---4 for (2999ds/5Mi)
% 0.23/0.46  % (21405)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)
% 0.23/0.46  % (21406)Instruction limit reached!
% 0.23/0.46  % (21406)------------------------------
% 0.23/0.46  % (21406)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.46  % (21406)Termination reason: Unknown
% 0.23/0.46  % (21406)Termination phase: Property scanning
% 0.23/0.46  
% 0.23/0.46  % (21406)Memory used [KB]: 1023
% 0.23/0.46  % (21406)Time elapsed: 0.006 s
% 0.23/0.46  % (21406)Instructions burned: 6 (million)
% 0.23/0.46  % (21406)------------------------------
% 0.23/0.46  % (21406)------------------------------
% 0.23/0.47  % (21407)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)
% 0.23/0.47  % (21408)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)
% 0.23/0.47  % (21407)Instruction limit reached!
% 0.23/0.47  % (21407)------------------------------
% 0.23/0.47  % (21407)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.47  % (21405)Instruction limit reached!
% 0.23/0.47  % (21405)------------------------------
% 0.23/0.47  % (21405)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.47  % (21405)Termination reason: Unknown
% 0.23/0.47  % (21405)Termination phase: Saturation
% 0.23/0.47  
% 0.23/0.47  % (21405)Memory used [KB]: 5628
% 0.23/0.47  % (21405)Time elapsed: 0.013 s
% 0.23/0.47  % (21405)Instructions burned: 21 (million)
% 0.23/0.47  % (21405)------------------------------
% 0.23/0.47  % (21405)------------------------------
% 0.23/0.47  % (21407)Termination reason: Unknown
% 0.23/0.47  % (21407)Termination phase: SInE selection
% 0.23/0.47  
% 0.23/0.47  % (21407)Memory used [KB]: 1023
% 0.23/0.47  % (21407)Time elapsed: 0.006 s
% 0.23/0.47  % (21407)Instructions burned: 7 (million)
% 0.23/0.47  % (21407)------------------------------
% 0.23/0.47  % (21407)------------------------------
% 0.23/0.47  % (21409)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)
% 0.23/0.48  % (21411)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)
% 0.23/0.49  % (21412)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 (2998ds/879Mi)
% 0.23/0.49  % (21413)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (2998ds/17Mi)
% 0.23/0.49  % (21411)Instruction limit reached!
% 0.23/0.49  % (21411)------------------------------
% 0.23/0.49  % (21411)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.49  % (21411)Termination reason: Unknown
% 0.23/0.49  % (21411)Termination phase: Saturation
% 0.23/0.49  
% 0.23/0.49  % (21411)Memory used [KB]: 5628
% 0.23/0.49  % (21411)Time elapsed: 0.012 s
% 0.23/0.49  % (21411)Instructions burned: 21 (million)
% 0.23/0.49  % (21411)------------------------------
% 0.23/0.49  % (21411)------------------------------
% 0.23/0.49  % (21413)Instruction limit reached!
% 0.23/0.49  % (21413)------------------------------
% 0.23/0.49  % (21413)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.49  % (21413)Termination reason: Unknown
% 0.23/0.49  % (21413)Termination phase: Saturation
% 0.23/0.49  
% 0.23/0.49  % (21413)Memory used [KB]: 5628
% 0.23/0.49  % (21413)Time elapsed: 0.009 s
% 0.23/0.49  % (21413)Instructions burned: 17 (million)
% 0.23/0.49  % (21413)------------------------------
% 0.23/0.49  % (21413)------------------------------
% 0.23/0.50  % (21373)Instruction limit reached!
% 0.23/0.50  % (21373)------------------------------
% 0.23/0.50  % (21373)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.50  % (21373)Termination reason: Unknown
% 0.23/0.50  % (21373)Termination phase: Saturation
% 0.23/0.50  
% 0.23/0.50  % (21373)Memory used [KB]: 6524
% 0.23/0.50  % (21373)Time elapsed: 0.116 s
% 0.23/0.50  % (21373)Instructions burned: 184 (million)
% 0.23/0.50  % (21373)------------------------------
% 0.23/0.50  % (21373)------------------------------
% 0.23/0.50  % (21415)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on Vampire---4 for (2998ds/30Mi)
% 0.23/0.50  % (21414)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2998ds/3Mi)
% 0.23/0.50  % (21414)Instruction limit reached!
% 0.23/0.50  % (21414)------------------------------
% 0.23/0.50  % (21414)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.50  % (21414)Termination reason: Unknown
% 0.23/0.50  % (21414)Termination phase: shuffling
% 0.23/0.51  
% 0.23/0.51  % (21414)Memory used [KB]: 1023
% 0.23/0.51  % (21414)Time elapsed: 0.004 s
% 0.23/0.51  % (21414)Instructions burned: 4 (million)
% 0.23/0.51  % (21414)------------------------------
% 0.23/0.51  % (21414)------------------------------
% 0.23/0.51  % (21415)Instruction limit reached!
% 0.23/0.51  % (21415)------------------------------
% 0.23/0.51  % (21415)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.51  % (21415)Termination reason: Unknown
% 0.23/0.51  % (21415)Termination phase: Saturation
% 0.23/0.51  
% 0.23/0.51  % (21415)Memory used [KB]: 5756
% 0.23/0.51  % (21415)Time elapsed: 0.010 s
% 0.23/0.51  % (21415)Instructions burned: 30 (million)
% 0.23/0.51  % (21415)------------------------------
% 0.23/0.51  % (21415)------------------------------
% 0.23/0.51  % (21416)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 (2998ds/127Mi)
% 0.23/0.52  % (21418)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 (2998ds/100Mi)
% 1.27/0.52  % (21421)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)
% 1.27/0.52  % (21421)Instruction limit reached!
% 1.27/0.52  % (21421)------------------------------
% 1.27/0.52  % (21421)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.27/0.52  % (21421)Termination reason: Unknown
% 1.27/0.52  % (21421)Termination phase: shuffling
% 1.27/0.52  
% 1.27/0.52  % (21421)Memory used [KB]: 1023
% 1.27/0.52  % (21421)Time elapsed: 0.002 s
% 1.27/0.52  % (21421)Instructions burned: 3 (million)
% 1.27/0.52  % (21421)------------------------------
% 1.27/0.52  % (21421)------------------------------
% 1.27/0.53  % (21426)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)
% 1.27/0.53  % (21426)Instruction limit reached!
% 1.27/0.53  % (21426)------------------------------
% 1.27/0.53  % (21426)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.27/0.53  % (21426)Termination reason: Unknown
% 1.27/0.53  % (21426)Termination phase: Saturation
% 1.27/0.53  
% 1.27/0.53  % (21426)Memory used [KB]: 5628
% 1.27/0.53  % (21426)Time elapsed: 0.007 s
% 1.27/0.53  % (21426)Instructions burned: 21 (million)
% 1.27/0.53  % (21426)------------------------------
% 1.27/0.53  % (21426)------------------------------
% 1.44/0.54  % (21434)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)
% 1.44/0.55  % (21418)Instruction limit reached!
% 1.44/0.55  % (21418)------------------------------
% 1.44/0.55  % (21418)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.44/0.55  % (21418)Termination reason: Unknown
% 1.44/0.55  % (21418)Termination phase: Saturation
% 1.44/0.55  
% 1.44/0.55  % (21418)Memory used [KB]: 6140
% 1.44/0.55  % (21418)Time elapsed: 0.032 s
% 1.44/0.55  % (21418)Instructions burned: 102 (million)
% 1.44/0.55  % (21418)------------------------------
% 1.44/0.55  % (21418)------------------------------
% 1.44/0.56  % (21441)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)
% 1.44/0.56  % (21416)Instruction limit reached!
% 1.44/0.56  % (21416)------------------------------
% 1.44/0.56  % (21416)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.44/0.56  % (21416)Termination reason: Unknown
% 1.44/0.56  % (21416)Termination phase: Saturation
% 1.44/0.56  
% 1.44/0.56  % (21416)Memory used [KB]: 6140
% 1.44/0.56  % (21416)Time elapsed: 0.045 s
% 1.44/0.56  % (21416)Instructions burned: 129 (million)
% 1.44/0.56  % (21416)------------------------------
% 1.44/0.56  % (21416)------------------------------
% 1.44/0.57  % (21446)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)
% 1.44/0.57  % (21434)Instruction limit reached!
% 1.44/0.57  % (21434)------------------------------
% 1.44/0.57  % (21434)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.44/0.57  % (21434)Termination reason: Unknown
% 1.44/0.57  % (21434)Termination phase: Saturation
% 1.44/0.57  
% 1.44/0.57  % (21434)Memory used [KB]: 6140
% 1.44/0.57  % (21434)Time elapsed: 0.028 s
% 1.44/0.57  % (21434)Instructions burned: 87 (million)
% 1.44/0.57  % (21434)------------------------------
% 1.44/0.57  % (21434)------------------------------
% 1.44/0.58  % (21452)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)
% 1.44/0.58  % (21446)Instruction limit reached!
% 1.44/0.58  % (21446)------------------------------
% 1.44/0.58  % (21446)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.44/0.58  % (21446)Termination reason: Unknown
% 1.44/0.58  % (21446)Termination phase: Saturation
% 1.44/0.58  
% 1.44/0.58  % (21446)Memory used [KB]: 5884
% 1.44/0.58  % (21446)Time elapsed: 0.013 s
% 1.44/0.58  % (21446)Instructions burned: 40 (million)
% 1.44/0.58  % (21446)------------------------------
% 1.44/0.58  % (21446)------------------------------
% 1.44/0.59  % (21458)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 (2997ds/46Mi)
% 1.44/0.59  % (21408)First to succeed.
% 1.44/0.59  % (21441)Instruction limit reached!
% 1.44/0.59  % (21441)------------------------------
% 1.44/0.59  % (21441)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.44/0.59  % (21441)Termination reason: Unknown
% 1.44/0.59  % (21441)Termination phase: Saturation
% 1.44/0.59  
% 1.44/0.59  % (21441)Memory used [KB]: 6140
% 1.44/0.59  % (21441)Time elapsed: 0.036 s
% 1.44/0.59  % (21441)Instructions burned: 109 (million)
% 1.44/0.59  % (21441)------------------------------
% 1.44/0.59  % (21441)------------------------------
% 1.44/0.60  % (21465)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 (2997ds/98Mi)
% 1.44/0.60  % (21408)Refutation found. Thanks to Tanya!
% 1.44/0.60  % SZS status Theorem for Vampire---4
% 1.44/0.60  % SZS output start Proof for Vampire---4
% 1.44/0.60  thf(type_def_5, type, mu: $tType).
% 1.44/0.60  thf(func_def_0, type, mu: $tType).
% 1.44/0.60  thf(func_def_1, type, qmltpeq: mu > mu > $i > $o).
% 1.44/0.60  thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 1.44/0.60  thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 1.44/0.60  thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 1.44/0.60  thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 1.44/0.60  thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 1.44/0.60  thf(func_def_8, type, mtrue: $i > $o).
% 1.44/0.60  thf(func_def_9, type, mfalse: $i > $o).
% 1.44/0.60  thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 1.44/0.60  thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 1.44/0.60  thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 1.44/0.60  thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 1.44/0.60  thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 1.44/0.60  thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 1.44/0.60  thf(func_def_16, type, exists_in_world: mu > $i > $o).
% 1.44/0.60  thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 1.44/0.60  thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 1.44/0.60  thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 1.44/0.60  thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o).
% 1.44/0.60  thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o).
% 1.44/0.60  thf(func_def_22, type, mserial: ($i > $i > $o) > $o).
% 1.44/0.60  thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o).
% 1.44/0.60  thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o).
% 1.44/0.60  thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o).
% 1.44/0.60  thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o).
% 1.44/0.60  thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o).
% 1.44/0.60  thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o).
% 1.44/0.60  thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o).
% 1.44/0.60  thf(func_def_30, type, mvalid: ($i > $o) > $o).
% 1.44/0.60  thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 1.44/0.60  thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 1.44/0.60  thf(func_def_33, type, minvalid: ($i > $o) > $o).
% 1.44/0.60  thf(func_def_34, type, rel_s4: $i > $i > $o).
% 1.44/0.60  thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o).
% 1.44/0.60  thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o).
% 1.44/0.60  thf(func_def_37, type, string: mu > $i > $o).
% 1.44/0.60  thf(func_def_38, type, in: mu > mu > mu > $i > $o).
% 1.44/0.60  thf(func_def_39, type, do: mu > mu > mu > $i > $o).
% 1.44/0.60  thf(func_def_40, type, number: mu > mu > $i > $o).
% 1.44/0.60  thf(func_def_41, type, entry_box: mu > $i > $o).
% 1.44/0.60  thf(func_def_42, type, userid: mu > mu > $i > $o).
% 1.44/0.60  thf(func_def_43, type, one: mu).
% 1.44/0.60  thf(func_def_44, type, u: mu).
% 1.44/0.60  thf(func_def_60, type, sK0: $i > mu).
% 1.44/0.60  thf(func_def_62, type, sK2: $i > mu).
% 1.44/0.60  thf(func_def_66, type, sK3: mu > mu > $i > mu > mu).
% 1.44/0.60  thf(func_def_67, type, sK4: $i > mu).
% 1.44/0.60  thf(func_def_70, type, sK7: mu > mu > $i).
% 1.44/0.60  thf(func_def_71, type, sK8: mu > mu > mu > mu > $i).
% 1.44/0.60  thf(func_def_72, type, sK9: mu > mu > mu > mu > mu).
% 1.44/0.60  thf(func_def_73, type, sK10: mu > mu > mu > mu > $i).
% 1.44/0.60  thf(func_def_74, type, sK11: mu > mu > mu > mu > mu).
% 1.44/0.60  thf(f1158,plain,(
% 1.44/0.60    $false),
% 1.44/0.60    inference(avatar_sat_refutation,[],[f519,f550,f554,f743,f763,f840,f904,f918,f932,f942,f1146,f1157])).
% 1.44/0.60  thf(f1157,plain,(
% 1.44/0.60    spl1_24 | ~spl1_30),
% 1.44/0.60    inference(avatar_split_clause,[],[f1154,f1137,f914])).
% 1.44/0.60  thf(f914,plain,(
% 1.44/0.60    spl1_24 <=> ($false = (rel_s4 @ sK6 @ sK6))),
% 1.44/0.60    introduced(avatar_definition,[new_symbols(naming,[spl1_24])])).
% 1.44/0.60  thf(f1137,plain,(
% 1.44/0.60    spl1_30 <=> ((entry_box @ (sK4 @ sK6) @ sK6) = $false)),
% 1.44/0.60    introduced(avatar_definition,[new_symbols(naming,[spl1_30])])).
% 1.44/0.60  thf(f1154,plain,(
% 1.44/0.60    ($false = (rel_s4 @ sK6 @ sK6)) | ~spl1_30),
% 1.44/0.60    inference(trivial_inequality_removal,[],[f1152])).
% 1.44/0.60  thf(f1152,plain,(
% 1.44/0.60    ($false = $true) | ($false = (rel_s4 @ sK6 @ sK6)) | ~spl1_30),
% 1.44/0.60    inference(superposition,[],[f276,f1139])).
% 1.44/0.60  thf(f1139,plain,(
% 1.44/0.60    ((entry_box @ (sK4 @ sK6) @ sK6) = $false) | ~spl1_30),
% 1.44/0.60    inference(avatar_component_clause,[],[f1137])).
% 1.44/0.60  thf(f276,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (($true = (entry_box @ (sK4 @ X1) @ X2)) | ($false = (rel_s4 @ X1 @ X2))) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f275])).
% 1.44/0.60  thf(f275,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (((~ (rel_s4 @ X1 @ X2)) = $true) | ($true = (entry_box @ (sK4 @ X1) @ X2))) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f274])).
% 1.44/0.60  thf(f274,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (($false = (~ (entry_box @ (sK4 @ X1) @ X2))) | ((~ (rel_s4 @ X1 @ X2)) = $true)) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f272])).
% 1.44/0.60  thf(f272,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (($false = ((~ (entry_box @ (sK4 @ X1) @ X2)) | (~ (number @ (sK4 @ X1) @ one @ X2)))) | ((~ (rel_s4 @ X1 @ X2)) = $true)) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f271])).
% 1.44/0.60  thf(f271,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (($true = (~ ((~ (entry_box @ (sK4 @ X1) @ X2)) | (~ (number @ (sK4 @ X1) @ one @ X2))))) | ((~ (rel_s4 @ X1 @ X2)) = $true)) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f270])).
% 1.44/0.60  thf(f270,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (($true = ((~ (rel_s4 @ X1 @ X2)) | (~ ((~ (entry_box @ (sK4 @ X1) @ X2)) | (~ (number @ (sK4 @ X1) @ one @ X2))))))) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f269])).
% 1.44/0.60  thf(f269,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ ((~ (entry_box @ (sK4 @ X1) @ Y0)) | (~ (number @ (sK4 @ X1) @ one @ Y0)))))) @ X2) = $true)) )),
% 1.44/0.60    inference(pi_clausification,[],[f268])).
% 1.44/0.60  thf(f268,plain,(
% 1.44/0.60    ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ ((~ (entry_box @ (sK4 @ X1) @ Y0)) | (~ (number @ (sK4 @ X1) @ one @ Y0))))))) = $true)) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f266])).
% 1.44/0.60  thf(f266,plain,(
% 1.44/0.60    ( ! [X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ ((~ (entry_box @ (sK4 @ X1) @ Y0)) | (~ (number @ (sK4 @ X1) @ one @ Y0)))))))))) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f265])).
% 1.44/0.60  thf(f265,plain,(
% 1.44/0.60    ( ! [X1 : $i] : (($false = ((exists_in_world @ (sK4 @ X1) @ X1) => (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ ((~ (entry_box @ (sK4 @ X1) @ Y0)) | (~ (number @ (sK4 @ X1) @ one @ Y0))))))))))) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f264])).
% 1.44/0.60  thf(f264,plain,(
% 1.44/0.60    ( ! [X1 : $i] : (($false = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X1 @ Y1)) | (~ ((~ (entry_box @ Y0 @ Y1)) | (~ (number @ Y0 @ one @ Y1)))))))))) @ (sK4 @ X1)))) )),
% 1.44/0.60    inference(sigma_clausification,[],[f263])).
% 1.44/0.60  thf(f263,plain,(
% 1.44/0.60    ( ! [X1 : $i] : (($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X1 @ Y1)) | (~ ((~ (entry_box @ Y0 @ Y1)) | (~ (number @ Y0 @ one @ Y1))))))))))))) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f262])).
% 1.44/0.60  thf(f262,plain,(
% 1.44/0.60    ( ! [X1 : $i] : (((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X1 @ Y1)) | (~ ((~ (entry_box @ Y0 @ Y1)) | (~ (number @ Y0 @ one @ Y1)))))))))))) = $true)) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f261])).
% 1.44/0.60  thf(f261,plain,(
% 1.44/0.60    ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (~ ((~ (entry_box @ Y1 @ Y2)) | (~ (number @ Y1 @ one @ Y2))))))))))))) @ X1))) )),
% 1.44/0.60    inference(pi_clausification,[],[f260])).
% 1.44/0.60  thf(f260,plain,(
% 1.44/0.60    ((!! @ $i @ (^[Y0 : $i]: (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (~ ((~ (entry_box @ Y1 @ Y2)) | (~ (number @ Y1 @ one @ Y2)))))))))))))) = $true)),
% 1.44/0.60    inference(beta_eta_normalization,[],[f184])).
% 1.44/0.60  thf(f184,plain,(
% 1.44/0.60    ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) | (Y4 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y2)))))) @ (entry_box @ Y0) @ (number @ Y0 @ one)))))))),
% 1.44/0.60    inference(definition_unfolding,[],[f152,f137,f180,f170,f174])).
% 1.44/0.60  thf(f174,plain,(
% 1.44/0.60    (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 1.44/0.60    inference(definition_unfolding,[],[f141,f148,f156,f148,f148])).
% 1.44/0.60  thf(f156,plain,(
% 1.44/0.60    (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 1.44/0.60    inference(cnf_transformation,[],[f107])).
% 1.44/0.60  thf(f107,plain,(
% 1.44/0.60    (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 1.44/0.60    inference(fool_elimination,[],[f106])).
% 1.44/0.60  thf(f106,plain,(
% 1.44/0.60    ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 1.44/0.60    inference(rectify,[],[f3])).
% 1.44/0.60  thf(f3,axiom,(
% 1.44/0.60    ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 1.44/0.60    file('/export/starexec/sandbox/tmp/tmp.7LKmvzLAF1/Vampire---4.8_21131',mor)).
% 1.44/0.60  thf(f148,plain,(
% 1.44/0.60    (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 1.44/0.60    inference(cnf_transformation,[],[f105])).
% 1.44/0.60  thf(f105,plain,(
% 1.44/0.60    (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 1.44/0.60    inference(fool_elimination,[],[f104])).
% 1.44/0.60  thf(f104,plain,(
% 1.44/0.60    ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 1.44/0.60    inference(rectify,[],[f2])).
% 1.44/0.60  thf(f2,axiom,(
% 1.44/0.60    ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 1.44/0.60    file('/export/starexec/sandbox/tmp/tmp.7LKmvzLAF1/Vampire---4.8_21131',mnot)).
% 1.44/0.60  thf(f141,plain,(
% 1.44/0.60    (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 1.44/0.60    inference(cnf_transformation,[],[f86])).
% 1.44/0.60  thf(f86,plain,(
% 1.44/0.60    (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 1.44/0.60    inference(fool_elimination,[],[f85])).
% 1.44/0.60  thf(f85,plain,(
% 1.44/0.60    ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 1.44/0.60    inference(rectify,[],[f8])).
% 1.44/0.60  thf(f8,axiom,(
% 1.44/0.60    ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 1.44/0.60    file('/export/starexec/sandbox/tmp/tmp.7LKmvzLAF1/Vampire---4.8_21131',mand)).
% 1.44/0.60  thf(f170,plain,(
% 1.44/0.60    (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 1.44/0.60    inference(cnf_transformation,[],[f94])).
% 1.44/0.60  thf(f94,plain,(
% 1.44/0.60    (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 1.44/0.60    inference(fool_elimination,[],[f93])).
% 1.44/0.60  thf(f93,plain,(
% 1.44/0.60    (mbox_s4 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s4 @ X1 @ X2)))))),
% 1.44/0.60    inference(rectify,[],[f32])).
% 1.44/0.60  thf(f32,axiom,(
% 1.44/0.60    (mbox_s4 = (^[X3 : $i > $o, X2 : $i] : (! [X6] : ((X3 @ X6) | ~(rel_s4 @ X2 @ X6)))))),
% 1.44/0.60    file('/export/starexec/sandbox/tmp/tmp.7LKmvzLAF1/Vampire---4.8_21131',mbox_s4)).
% 1.44/0.60  thf(f180,plain,(
% 1.44/0.60    (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))))),
% 1.44/0.60    inference(definition_unfolding,[],[f161,f148,f166,f148])).
% 1.44/0.60  thf(f166,plain,(
% 1.44/0.60    (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 1.44/0.60    inference(cnf_transformation,[],[f54])).
% 1.44/0.60  thf(f54,plain,(
% 1.44/0.60    (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 1.44/0.60    inference(fool_elimination,[],[f53])).
% 1.44/0.60  thf(f53,plain,(
% 1.44/0.60    (mforall_ind = (^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : ((exists_in_world @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 1.44/0.60    inference(rectify,[],[f15])).
% 1.44/0.60  thf(f15,axiom,(
% 1.44/0.60    (mforall_ind = (^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : ((exists_in_world @ X0 @ X2) => (X3 @ X0 @ X2)))))),
% 1.44/0.60    file('/export/starexec/sandbox/tmp/tmp.7LKmvzLAF1/Vampire---4.8_21131',mforall_ind)).
% 1.44/0.60  thf(f161,plain,(
% 1.44/0.60    (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 1.44/0.60    inference(cnf_transformation,[],[f113])).
% 1.44/0.60  thf(f113,plain,(
% 1.44/0.60    (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 1.44/0.60    inference(fool_elimination,[],[f112])).
% 1.44/0.60  thf(f112,plain,(
% 1.44/0.60    ((^[X0 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X1 : mu] : (mnot @ (X0 @ X1)))))) = mexists_ind)),
% 1.44/0.60    inference(rectify,[],[f16])).
% 1.44/0.60  thf(f16,axiom,(
% 1.44/0.60    ((^[X3 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X0 : mu] : (mnot @ (X3 @ X0)))))) = mexists_ind)),
% 1.44/0.60    file('/export/starexec/sandbox/tmp/tmp.7LKmvzLAF1/Vampire---4.8_21131',mexists_ind)).
% 1.44/0.60  thf(f137,plain,(
% 1.44/0.60    (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 1.44/0.60    inference(cnf_transformation,[],[f96])).
% 1.44/0.60  thf(f96,plain,(
% 1.44/0.60    (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 1.44/0.60    inference(fool_elimination,[],[f95])).
% 1.44/0.60  thf(f95,plain,(
% 1.44/0.60    (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 1.44/0.60    inference(rectify,[],[f28])).
% 1.44/0.60  thf(f28,axiom,(
% 1.44/0.60    (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 1.44/0.60    file('/export/starexec/sandbox/tmp/tmp.7LKmvzLAF1/Vampire---4.8_21131',mvalid)).
% 1.44/0.60  thf(f152,plain,(
% 1.44/0.60    ($true = (mvalid @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (mand @ (entry_box @ Y0) @ (number @ Y0 @ one)))))))),
% 1.44/0.60    inference(cnf_transformation,[],[f50])).
% 1.44/0.60  thf(f50,plain,(
% 1.44/0.60    ($true = (mvalid @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (mand @ (entry_box @ Y0) @ (number @ Y0 @ one)))))))),
% 1.44/0.60    inference(fool_elimination,[],[f49])).
% 1.44/0.60  thf(f49,plain,(
% 1.44/0.60    (mvalid @ (mexists_ind @ (^[X0 : mu] : (mbox_s4 @ (mand @ (entry_box @ X0) @ (number @ X0 @ one))))))),
% 1.44/0.60    inference(rectify,[],[f40])).
% 1.44/0.60  thf(f40,axiom,(
% 1.44/0.60    (mvalid @ (mexists_ind @ (^[X12 : mu] : (mbox_s4 @ (mand @ (entry_box @ X12) @ (number @ X12 @ one))))))),
% 1.44/0.60    file('/export/starexec/sandbox/tmp/tmp.7LKmvzLAF1/Vampire---4.8_21131',ax2)).
% 1.44/0.60  thf(f1146,plain,(
% 1.44/0.60    spl1_13 | spl1_12 | spl1_30 | ~spl1_5 | ~spl1_14),
% 1.44/0.60    inference(avatar_split_clause,[],[f1145,f824,f544,f1137,f816,f820])).
% 1.44/0.60  thf(f820,plain,(
% 1.44/0.60    spl1_13 <=> ((exists_in_world @ (sK2 @ sK6) @ sK6) = $false)),
% 1.44/0.60    introduced(avatar_definition,[new_symbols(naming,[spl1_13])])).
% 1.44/0.60  thf(f816,plain,(
% 1.44/0.60    spl1_12 <=> ($false = (string @ (sK2 @ sK6) @ sK6))),
% 1.44/0.60    introduced(avatar_definition,[new_symbols(naming,[spl1_12])])).
% 1.44/0.60  thf(f544,plain,(
% 1.44/0.60    spl1_5 <=> ! [X2 : mu,X1 : mu] : (($false = (entry_box @ X2 @ sK6)) | ((string @ X1 @ sK6) = $false) | ((exists_in_world @ X1 @ sK6) = $false) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X2 @ sK6)))),
% 1.44/0.60    introduced(avatar_definition,[new_symbols(naming,[spl1_5])])).
% 1.44/0.60  thf(f824,plain,(
% 1.44/0.60    spl1_14 <=> ! [X0] : (($false = (exists_in_world @ (sK4 @ X0) @ sK6)) | ($false = (rel_s4 @ X0 @ (sK7 @ (sK2 @ sK6) @ (sK4 @ X0)))) | ($false = (entry_box @ (sK4 @ X0) @ sK6)))),
% 1.44/0.60    introduced(avatar_definition,[new_symbols(naming,[spl1_14])])).
% 1.44/0.60  thf(f1145,plain,(
% 1.44/0.60    ((entry_box @ (sK4 @ sK6) @ sK6) = $false) | ($false = (string @ (sK2 @ sK6) @ sK6)) | ((exists_in_world @ (sK2 @ sK6) @ sK6) = $false) | (~spl1_5 | ~spl1_14)),
% 1.44/0.60    inference(trivial_inequality_removal,[],[f1144])).
% 1.44/0.60  thf(f1144,plain,(
% 1.44/0.60    ($false = $true) | ((entry_box @ (sK4 @ sK6) @ sK6) = $false) | ((exists_in_world @ (sK2 @ sK6) @ sK6) = $false) | ($false = (string @ (sK2 @ sK6) @ sK6)) | (~spl1_5 | ~spl1_14)),
% 1.44/0.60    inference(forward_demodulation,[],[f1125,f267])).
% 1.44/0.60  thf(f267,plain,(
% 1.44/0.60    ( ! [X1 : $i] : (($true = (exists_in_world @ (sK4 @ X1) @ X1))) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f265])).
% 1.44/0.60  thf(f1125,plain,(
% 1.44/0.60    ((entry_box @ (sK4 @ sK6) @ sK6) = $false) | ((exists_in_world @ (sK4 @ sK6) @ sK6) = $false) | ((exists_in_world @ (sK2 @ sK6) @ sK6) = $false) | ($false = (string @ (sK2 @ sK6) @ sK6)) | (~spl1_5 | ~spl1_14)),
% 1.44/0.60    inference(trivial_inequality_removal,[],[f1124])).
% 1.44/0.60  thf(f1124,plain,(
% 1.44/0.60    ((exists_in_world @ (sK4 @ sK6) @ sK6) = $false) | ((exists_in_world @ (sK2 @ sK6) @ sK6) = $false) | ((entry_box @ (sK4 @ sK6) @ sK6) = $false) | ($false = (string @ (sK2 @ sK6) @ sK6)) | ($false = $true) | (~spl1_5 | ~spl1_14)),
% 1.44/0.60    inference(duplicate_literal_removal,[],[f1118])).
% 1.44/0.60  thf(f1118,plain,(
% 1.44/0.60    ((exists_in_world @ (sK2 @ sK6) @ sK6) = $false) | ((entry_box @ (sK4 @ sK6) @ sK6) = $false) | ($false = $true) | ((exists_in_world @ (sK4 @ sK6) @ sK6) = $false) | ((entry_box @ (sK4 @ sK6) @ sK6) = $false) | ($false = (string @ (sK2 @ sK6) @ sK6)) | ((exists_in_world @ (sK4 @ sK6) @ sK6) = $false) | (~spl1_5 | ~spl1_14)),
% 1.44/0.60    inference(superposition,[],[f825,f545])).
% 1.44/0.60  thf(f545,plain,(
% 1.44/0.60    ( ! [X2 : mu,X1 : mu] : (((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true) | ((string @ X1 @ sK6) = $false) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (entry_box @ X2 @ sK6))) ) | ~spl1_5),
% 1.44/0.60    inference(avatar_component_clause,[],[f544])).
% 1.44/0.60  thf(f825,plain,(
% 1.44/0.60    ( ! [X0 : $i] : (($false = (rel_s4 @ X0 @ (sK7 @ (sK2 @ sK6) @ (sK4 @ X0)))) | ($false = (entry_box @ (sK4 @ X0) @ sK6)) | ($false = (exists_in_world @ (sK4 @ X0) @ sK6))) ) | ~spl1_14),
% 1.44/0.60    inference(avatar_component_clause,[],[f824])).
% 1.44/0.60  thf(f942,plain,(
% 1.44/0.60    ~spl1_24),
% 1.44/0.60    inference(avatar_contradiction_clause,[],[f941])).
% 1.44/0.60  thf(f941,plain,(
% 1.44/0.60    $false | ~spl1_24),
% 1.44/0.60    inference(trivial_inequality_removal,[],[f934])).
% 1.44/0.60  thf(f934,plain,(
% 1.44/0.60    ($false = $true) | ~spl1_24),
% 1.44/0.60    inference(superposition,[],[f916,f213])).
% 1.44/0.60  thf(f213,plain,(
% 1.44/0.60    ( ! [X1 : $i] : (((rel_s4 @ X1 @ X1) = $true)) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f212])).
% 1.44/0.60  thf(f212,plain,(
% 1.44/0.60    ( ! [X1 : $i] : ((((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1) = $true)) )),
% 1.44/0.60    inference(pi_clausification,[],[f211])).
% 1.44/0.60  thf(f211,plain,(
% 1.44/0.60    ((!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))) = $true)),
% 1.44/0.60    inference(beta_eta_normalization,[],[f187])).
% 1.44/0.60  thf(f187,plain,(
% 1.44/0.60    (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4) = $true)),
% 1.44/0.60    inference(definition_unfolding,[],[f165,f146])).
% 1.44/0.60  thf(f146,plain,(
% 1.44/0.60    (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 1.44/0.60    inference(cnf_transformation,[],[f58])).
% 1.44/0.60  thf(f58,plain,(
% 1.44/0.60    (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 1.44/0.60    inference(fool_elimination,[],[f57])).
% 1.44/0.60  thf(f57,plain,(
% 1.44/0.60    ((^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))) = mreflexive)),
% 1.44/0.60    inference(rectify,[],[f18])).
% 1.44/0.60  thf(f18,axiom,(
% 1.44/0.60    ((^[X5 : $i > $i > $o] : (! [X8] : (X5 @ X8 @ X8))) = mreflexive)),
% 1.44/0.60    file('/export/starexec/sandbox/tmp/tmp.7LKmvzLAF1/Vampire---4.8_21131',mreflexive)).
% 1.44/0.60  thf(f165,plain,(
% 1.44/0.60    ((mreflexive @ rel_s4) = $true)),
% 1.44/0.60    inference(cnf_transformation,[],[f92])).
% 1.44/0.60  thf(f92,plain,(
% 1.44/0.60    ((mreflexive @ rel_s4) = $true)),
% 1.44/0.60    inference(fool_elimination,[],[f91])).
% 1.44/0.60  thf(f91,plain,(
% 1.44/0.60    (mreflexive @ rel_s4)),
% 1.44/0.60    inference(rectify,[],[f34])).
% 1.44/0.60  thf(f34,axiom,(
% 1.44/0.60    (mreflexive @ rel_s4)),
% 1.44/0.60    file('/export/starexec/sandbox/tmp/tmp.7LKmvzLAF1/Vampire---4.8_21131',a1)).
% 1.44/0.60  thf(f916,plain,(
% 1.44/0.60    ($false = (rel_s4 @ sK6 @ sK6)) | ~spl1_24),
% 1.44/0.60    inference(avatar_component_clause,[],[f914])).
% 1.44/0.60  thf(f932,plain,(
% 1.44/0.60    spl1_4 | ~spl1_13),
% 1.44/0.60    inference(avatar_split_clause,[],[f926,f820,f515])).
% 1.44/0.60  thf(f515,plain,(
% 1.44/0.60    spl1_4 <=> ! [X3] : ((rel_s4 @ X3 @ sK6) = $false)),
% 1.44/0.60    introduced(avatar_definition,[new_symbols(naming,[spl1_4])])).
% 1.44/0.60  thf(f926,plain,(
% 1.44/0.60    ( ! [X0 : $i] : (($false = (rel_s4 @ X0 @ sK6))) ) | ~spl1_13),
% 1.44/0.60    inference(trivial_inequality_removal,[],[f922])).
% 1.44/0.60  thf(f922,plain,(
% 1.44/0.60    ( ! [X0 : $i] : (($false = $true) | ($false = (rel_s4 @ X0 @ sK6))) ) | ~spl1_13),
% 1.44/0.60    inference(superposition,[],[f822,f200])).
% 1.44/0.60  thf(f200,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (((exists_in_world @ (sK2 @ X2) @ X2) = $true) | ($false = (rel_s4 @ X1 @ X2))) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f198])).
% 1.44/0.60  thf(f198,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (($false = (rel_s4 @ X1 @ X2)) | ($false = ((exists_in_world @ (sK2 @ X2) @ X2) => (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (~ ((~ (userid @ u @ (sK2 @ X2) @ Y0)) | (~ (string @ (sK2 @ X2) @ Y0))))))))))) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f197])).
% 1.44/0.60  thf(f197,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (($false = (rel_s4 @ X1 @ X2)) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (~ ((~ (userid @ u @ Y0 @ Y1)) | (~ (string @ Y0 @ Y1)))))))))) @ (sK2 @ X2)) = $false)) )),
% 1.44/0.60    inference(sigma_clausification,[],[f196])).
% 1.44/0.60  thf(f196,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (~ ((~ (userid @ u @ Y0 @ Y1)) | (~ (string @ Y0 @ Y1)))))))))))) | ($false = (rel_s4 @ X1 @ X2))) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f195])).
% 1.44/0.60  thf(f195,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (~ ((~ (userid @ u @ Y0 @ Y1)) | (~ (string @ Y0 @ Y1)))))))))))) = $true) | ($false = (rel_s4 @ X1 @ X2))) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f194])).
% 1.44/0.60  thf(f194,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (((~ (rel_s4 @ X1 @ X2)) = $true) | ((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (~ ((~ (userid @ u @ Y0 @ Y1)) | (~ (string @ Y0 @ Y1)))))))))))) = $true)) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f193])).
% 1.44/0.60  thf(f193,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (($true = ((~ (rel_s4 @ X1 @ X2)) | (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (~ ((~ (userid @ u @ Y0 @ Y1)) | (~ (string @ Y0 @ Y1))))))))))))))) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f192])).
% 1.44/0.60  thf(f192,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (~ ((~ (userid @ u @ Y1 @ Y2)) | (~ (string @ Y1 @ Y2)))))))))))))) @ X2) = $true)) )),
% 1.44/0.60    inference(pi_clausification,[],[f191])).
% 1.44/0.60  thf(f191,plain,(
% 1.44/0.60    ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (~ ((~ (userid @ u @ Y1 @ Y2)) | (~ (string @ Y1 @ Y2))))))))))))))))) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f190])).
% 1.44/0.60  thf(f190,plain,(
% 1.44/0.60    ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (~ ((~ (userid @ u @ Y2 @ Y3)) | (~ (string @ Y2 @ Y3)))))))))))))))) @ X1) = $true)) )),
% 1.44/0.60    inference(pi_clausification,[],[f189])).
% 1.44/0.60  thf(f189,plain,(
% 1.44/0.60    ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (~ ((~ (userid @ u @ Y2 @ Y3)) | (~ (string @ Y2 @ Y3))))))))))))))))) = $true)),
% 1.44/0.60    inference(beta_eta_normalization,[],[f185])).
% 1.44/0.60  thf(f185,plain,(
% 1.44/0.60    ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) | (Y4 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y2)))))) @ (userid @ u @ Y0) @ (string @ Y0))))))))),
% 1.44/0.60    inference(definition_unfolding,[],[f158,f137,f170,f180,f170,f174])).
% 1.44/0.60  thf(f158,plain,(
% 1.44/0.60    ($true = (mvalid @ (mbox_s4 @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (mand @ (userid @ u @ Y0) @ (string @ Y0))))))))),
% 1.44/0.60    inference(cnf_transformation,[],[f78])).
% 1.44/0.60  thf(f78,plain,(
% 1.44/0.60    ($true = (mvalid @ (mbox_s4 @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (mand @ (userid @ u @ Y0) @ (string @ Y0))))))))),
% 1.44/0.60    inference(fool_elimination,[],[f77])).
% 1.44/0.60  thf(f77,plain,(
% 1.44/0.60    (mvalid @ (mbox_s4 @ (mexists_ind @ (^[X0 : mu] : (mbox_s4 @ (mand @ (userid @ u @ X0) @ (string @ X0)))))))),
% 1.44/0.60    inference(rectify,[],[f39])).
% 1.44/0.60  thf(f39,axiom,(
% 1.44/0.60    (mvalid @ (mbox_s4 @ (mexists_ind @ (^[X11 : mu] : (mbox_s4 @ (mand @ (userid @ u @ X11) @ (string @ X11)))))))),
% 1.44/0.60    file('/export/starexec/sandbox/tmp/tmp.7LKmvzLAF1/Vampire---4.8_21131',ax1)).
% 1.44/0.60  thf(f822,plain,(
% 1.44/0.60    ((exists_in_world @ (sK2 @ sK6) @ sK6) = $false) | ~spl1_13),
% 1.44/0.60    inference(avatar_component_clause,[],[f820])).
% 1.44/0.60  thf(f918,plain,(
% 1.44/0.60    spl1_4 | spl1_24 | ~spl1_12),
% 1.44/0.60    inference(avatar_split_clause,[],[f910,f816,f914,f515])).
% 1.44/0.60  thf(f910,plain,(
% 1.44/0.60    ( ! [X0 : $i] : (($false = (rel_s4 @ sK6 @ sK6)) | ($false = (rel_s4 @ X0 @ sK6))) ) | ~spl1_12),
% 1.44/0.60    inference(trivial_inequality_removal,[],[f908])).
% 1.44/0.60  thf(f908,plain,(
% 1.44/0.60    ( ! [X0 : $i] : (($false = (rel_s4 @ X0 @ sK6)) | ($false = (rel_s4 @ sK6 @ sK6)) | ($false = $true)) ) | ~spl1_12),
% 1.44/0.60    inference(superposition,[],[f818,f210])).
% 1.44/0.60  thf(f210,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : $i,X1 : $i] : (((string @ (sK2 @ X2) @ X3) = $true) | ((rel_s4 @ X2 @ X3) = $false) | ($false = (rel_s4 @ X1 @ X2))) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f207])).
% 1.44/0.60  thf(f207,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : $i,X1 : $i] : (((~ (string @ (sK2 @ X2) @ X3)) = $false) | ($false = (rel_s4 @ X1 @ X2)) | ((rel_s4 @ X2 @ X3) = $false)) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f206])).
% 1.44/0.60  thf(f206,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : $i,X1 : $i] : (((rel_s4 @ X2 @ X3) = $false) | ($false = (rel_s4 @ X1 @ X2)) | (((~ (userid @ u @ (sK2 @ X2) @ X3)) | (~ (string @ (sK2 @ X2) @ X3))) = $false)) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f205])).
% 1.44/0.60  thf(f205,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (rel_s4 @ X1 @ X2)) | ((~ (rel_s4 @ X2 @ X3)) = $true) | (((~ (userid @ u @ (sK2 @ X2) @ X3)) | (~ (string @ (sK2 @ X2) @ X3))) = $false)) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f204])).
% 1.44/0.60  thf(f204,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ ((~ (userid @ u @ (sK2 @ X2) @ X3)) | (~ (string @ (sK2 @ X2) @ X3))))) | ((~ (rel_s4 @ X2 @ X3)) = $true) | ($false = (rel_s4 @ X1 @ X2))) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f203])).
% 1.44/0.60  thf(f203,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (rel_s4 @ X1 @ X2)) | (((~ (rel_s4 @ X2 @ X3)) | (~ ((~ (userid @ u @ (sK2 @ X2) @ X3)) | (~ (string @ (sK2 @ X2) @ X3))))) = $true)) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f202])).
% 1.44/0.60  thf(f202,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (rel_s4 @ X1 @ X2)) | ($true = ((^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (~ ((~ (userid @ u @ (sK2 @ X2) @ Y0)) | (~ (string @ (sK2 @ X2) @ Y0)))))) @ X3))) )),
% 1.44/0.60    inference(pi_clausification,[],[f201])).
% 1.44/0.60  thf(f201,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (($false = (rel_s4 @ X1 @ X2)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (~ ((~ (userid @ u @ (sK2 @ X2) @ Y0)) | (~ (string @ (sK2 @ X2) @ Y0))))))))) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f199])).
% 1.44/0.60  thf(f199,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (~ ((~ (userid @ u @ (sK2 @ X2) @ Y0)) | (~ (string @ (sK2 @ X2) @ Y0))))))))) | ($false = (rel_s4 @ X1 @ X2))) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f198])).
% 1.44/0.60  thf(f818,plain,(
% 1.44/0.60    ($false = (string @ (sK2 @ sK6) @ sK6)) | ~spl1_12),
% 1.44/0.60    inference(avatar_component_clause,[],[f816])).
% 1.44/0.60  thf(f904,plain,(
% 1.44/0.60    ~spl1_6),
% 1.44/0.60    inference(avatar_contradiction_clause,[],[f903])).
% 1.44/0.60  thf(f903,plain,(
% 1.44/0.60    $false | ~spl1_6),
% 1.44/0.60    inference(trivial_inequality_removal,[],[f870])).
% 1.44/0.60  thf(f870,plain,(
% 1.44/0.60    ($false = $true) | ~spl1_6),
% 1.44/0.60    inference(superposition,[],[f548,f144])).
% 1.44/0.60  thf(f144,plain,(
% 1.44/0.60    ( ! [X0 : $i] : (((exists_in_world @ (sK0 @ X0) @ X0) = $true)) )),
% 1.44/0.60    inference(cnf_transformation,[],[f130])).
% 1.44/0.60  thf(f130,plain,(
% 1.44/0.60    ! [X0] : ((exists_in_world @ (sK0 @ X0) @ X0) = $true)),
% 1.44/0.60    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f111,f129])).
% 1.44/0.60  thf(f129,plain,(
% 1.44/0.60    ! [X0] : (? [X1 : mu] : ($true = (exists_in_world @ X1 @ X0)) => ((exists_in_world @ (sK0 @ X0) @ X0) = $true))),
% 1.44/0.60    introduced(choice_axiom,[])).
% 1.44/0.60  thf(f111,plain,(
% 1.44/0.60    ! [X0] : ? [X1 : mu] : ($true = (exists_in_world @ X1 @ X0))),
% 1.44/0.60    inference(fool_elimination,[],[f110])).
% 1.44/0.60  thf(f110,plain,(
% 1.44/0.60    ! [X0] : ? [X1 : mu] : (exists_in_world @ X1 @ X0)),
% 1.44/0.60    inference(rectify,[],[f14])).
% 1.44/0.60  thf(f14,axiom,(
% 1.44/0.60    ! [X6] : ? [X0 : mu] : (exists_in_world @ X0 @ X6)),
% 1.44/0.60    file('/export/starexec/sandbox/tmp/tmp.7LKmvzLAF1/Vampire---4.8_21131',nonempty_ax)).
% 1.44/0.60  thf(f548,plain,(
% 1.44/0.60    ( ! [X0 : mu] : (($false = (exists_in_world @ X0 @ sK6))) ) | ~spl1_6),
% 1.44/0.60    inference(avatar_component_clause,[],[f547])).
% 1.44/0.60  thf(f547,plain,(
% 1.44/0.60    spl1_6 <=> ! [X0 : mu] : ($false = (exists_in_world @ X0 @ sK6))),
% 1.44/0.60    introduced(avatar_definition,[new_symbols(naming,[spl1_6])])).
% 1.44/0.60  thf(f840,plain,(
% 1.44/0.60    spl1_12 | spl1_14 | spl1_4 | spl1_13 | ~spl1_5 | ~spl1_11),
% 1.44/0.60    inference(avatar_split_clause,[],[f806,f760,f544,f820,f515,f824,f816])).
% 1.44/0.60  thf(f760,plain,(
% 1.44/0.60    spl1_11 <=> ! [X2 : mu,X1 : mu] : (($false = (exists_in_world @ X2 @ sK6)) | ((string @ X1 @ sK6) = $false) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (entry_box @ X2 @ (sK7 @ X1 @ X2))) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | ($false = (entry_box @ X2 @ sK6)))),
% 1.44/0.60    introduced(avatar_definition,[new_symbols(naming,[spl1_11])])).
% 1.44/0.60  thf(f806,plain,(
% 1.44/0.60    ( ! [X0 : $i,X1 : $i] : (($false = (exists_in_world @ (sK4 @ X0) @ sK6)) | ((exists_in_world @ (sK2 @ sK6) @ sK6) = $false) | ($false = (string @ (sK2 @ sK6) @ sK6)) | ($false = (entry_box @ (sK4 @ X0) @ sK6)) | ($false = (rel_s4 @ X0 @ (sK7 @ (sK2 @ sK6) @ (sK4 @ X0)))) | ((rel_s4 @ X1 @ sK6) = $false)) ) | (~spl1_5 | ~spl1_11)),
% 1.44/0.60    inference(trivial_inequality_removal,[],[f805])).
% 1.44/0.60  thf(f805,plain,(
% 1.44/0.60    ( ! [X0 : $i,X1 : $i] : (($false = $true) | ((exists_in_world @ (sK2 @ sK6) @ sK6) = $false) | ($false = (string @ (sK2 @ sK6) @ sK6)) | ((rel_s4 @ X1 @ sK6) = $false) | ($false = (rel_s4 @ X0 @ (sK7 @ (sK2 @ sK6) @ (sK4 @ X0)))) | ($false = (exists_in_world @ (sK4 @ X0) @ sK6)) | ($false = (entry_box @ (sK4 @ X0) @ sK6))) ) | (~spl1_5 | ~spl1_11)),
% 1.44/0.60    inference(duplicate_literal_removal,[],[f791])).
% 1.44/0.60  thf(f791,plain,(
% 1.44/0.60    ( ! [X0 : $i,X1 : $i] : (($false = (exists_in_world @ (sK4 @ X0) @ sK6)) | ($false = (exists_in_world @ (sK4 @ X0) @ sK6)) | ($false = (entry_box @ (sK4 @ X0) @ sK6)) | ((exists_in_world @ (sK2 @ sK6) @ sK6) = $false) | ((exists_in_world @ (sK2 @ sK6) @ sK6) = $false) | ($false = (string @ (sK2 @ sK6) @ sK6)) | ($false = $true) | ($false = (string @ (sK2 @ sK6) @ sK6)) | ($false = (entry_box @ (sK4 @ X0) @ sK6)) | ($false = (rel_s4 @ X0 @ (sK7 @ (sK2 @ sK6) @ (sK4 @ X0)))) | ((rel_s4 @ X1 @ sK6) = $false)) ) | (~spl1_5 | ~spl1_11)),
% 1.44/0.60    inference(superposition,[],[f545,f782])).
% 1.44/0.60  thf(f782,plain,(
% 1.44/0.60    ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (rel_s4 @ X1 @ (sK7 @ (sK2 @ X1) @ (sK4 @ X0)))) | ($false = (rel_s4 @ X2 @ X1)) | ($false = (exists_in_world @ (sK2 @ X1) @ sK6)) | ($false = (exists_in_world @ (sK4 @ X0) @ sK6)) | ((string @ (sK2 @ X1) @ sK6) = $false) | ($false = (rel_s4 @ X0 @ (sK7 @ (sK2 @ X1) @ (sK4 @ X0)))) | ($false = (entry_box @ (sK4 @ X0) @ sK6))) ) | ~spl1_11),
% 1.44/0.60    inference(trivial_inequality_removal,[],[f781])).
% 1.44/0.60  thf(f781,plain,(
% 1.44/0.60    ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (exists_in_world @ (sK4 @ X0) @ sK6)) | ($false = (rel_s4 @ X0 @ (sK7 @ (sK2 @ X1) @ (sK4 @ X0)))) | ($false = $true) | ((string @ (sK2 @ X1) @ sK6) = $false) | ($false = (entry_box @ (sK4 @ X0) @ sK6)) | ($false = (rel_s4 @ X2 @ X1)) | ($false = (rel_s4 @ X1 @ (sK7 @ (sK2 @ X1) @ (sK4 @ X0)))) | ($false = (exists_in_world @ (sK2 @ X1) @ sK6))) ) | ~spl1_11),
% 1.44/0.60    inference(duplicate_literal_removal,[],[f777])).
% 1.44/0.60  thf(f777,plain,(
% 1.44/0.60    ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (exists_in_world @ (sK2 @ X1) @ sK6)) | ($false = (exists_in_world @ (sK4 @ X0) @ sK6)) | ($false = (rel_s4 @ X0 @ (sK7 @ (sK2 @ X1) @ (sK4 @ X0)))) | ($false = (entry_box @ (sK4 @ X0) @ sK6)) | ($false = (rel_s4 @ X2 @ X1)) | ($false = (rel_s4 @ X1 @ (sK7 @ (sK2 @ X1) @ (sK4 @ X0)))) | ((string @ (sK2 @ X1) @ sK6) = $false) | ($false = $true) | ($false = (rel_s4 @ X0 @ (sK7 @ (sK2 @ X1) @ (sK4 @ X0))))) ) | ~spl1_11),
% 1.44/0.60    inference(superposition,[],[f775,f276])).
% 1.44/0.60  thf(f775,plain,(
% 1.44/0.60    ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (entry_box @ (sK4 @ X0) @ (sK7 @ (sK2 @ X1) @ (sK4 @ X0)))) | ($false = (rel_s4 @ X1 @ (sK7 @ (sK2 @ X1) @ (sK4 @ X0)))) | ($false = (rel_s4 @ X2 @ X1)) | ((string @ (sK2 @ X1) @ sK6) = $false) | ($false = (entry_box @ (sK4 @ X0) @ sK6)) | ($false = (rel_s4 @ X0 @ (sK7 @ (sK2 @ X1) @ (sK4 @ X0)))) | ($false = (exists_in_world @ (sK4 @ X0) @ sK6)) | ($false = (exists_in_world @ (sK2 @ X1) @ sK6))) ) | ~spl1_11),
% 1.44/0.60    inference(trivial_inequality_removal,[],[f771])).
% 1.44/0.60  thf(f771,plain,(
% 1.44/0.60    ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (rel_s4 @ X1 @ (sK7 @ (sK2 @ X1) @ (sK4 @ X0)))) | ($false = (exists_in_world @ (sK4 @ X0) @ sK6)) | ($false = $true) | ($false = (rel_s4 @ X2 @ X1)) | ($false = (entry_box @ (sK4 @ X0) @ sK6)) | ((string @ (sK2 @ X1) @ sK6) = $false) | ($false = (exists_in_world @ (sK2 @ X1) @ sK6)) | ($false = (rel_s4 @ X0 @ (sK7 @ (sK2 @ X1) @ (sK4 @ X0)))) | ($false = (entry_box @ (sK4 @ X0) @ (sK7 @ (sK2 @ X1) @ (sK4 @ X0))))) ) | ~spl1_11),
% 1.44/0.60    inference(superposition,[],[f769,f278])).
% 1.44/0.60  thf(f278,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (((number @ (sK4 @ X1) @ one @ X2) = $true) | ($false = (rel_s4 @ X1 @ X2))) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f277])).
% 1.44/0.60  thf(f277,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (((number @ (sK4 @ X1) @ one @ X2) = $true) | ((~ (rel_s4 @ X1 @ X2)) = $true)) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f273])).
% 1.44/0.60  thf(f273,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (($false = (~ (number @ (sK4 @ X1) @ one @ X2))) | ((~ (rel_s4 @ X1 @ X2)) = $true)) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f272])).
% 1.44/0.60  thf(f769,plain,(
% 1.44/0.60    ( ! [X2 : $i,X0 : $i,X1 : mu] : (($false = (number @ X1 @ one @ (sK7 @ (sK2 @ X0) @ X1))) | ($false = (rel_s4 @ X0 @ (sK7 @ (sK2 @ X0) @ X1))) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (string @ (sK2 @ X0) @ sK6)) | ($false = (exists_in_world @ (sK2 @ X0) @ sK6)) | ($false = (entry_box @ X1 @ sK6)) | ($false = (rel_s4 @ X2 @ X0)) | ((entry_box @ X1 @ (sK7 @ (sK2 @ X0) @ X1)) = $false)) ) | ~spl1_11),
% 1.44/0.60    inference(trivial_inequality_removal,[],[f766])).
% 1.44/0.60  thf(f766,plain,(
% 1.44/0.60    ( ! [X2 : $i,X0 : $i,X1 : mu] : (($false = (exists_in_world @ (sK2 @ X0) @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ((entry_box @ X1 @ (sK7 @ (sK2 @ X0) @ X1)) = $false) | ($false = (entry_box @ X1 @ sK6)) | ($false = $true) | ($false = (rel_s4 @ X0 @ (sK7 @ (sK2 @ X0) @ X1))) | ($false = (number @ X1 @ one @ (sK7 @ (sK2 @ X0) @ X1))) | ($false = (string @ (sK2 @ X0) @ sK6)) | ($false = (rel_s4 @ X2 @ X0))) ) | ~spl1_11),
% 1.44/0.60    inference(superposition,[],[f209,f761])).
% 1.44/0.60  thf(f761,plain,(
% 1.44/0.60    ( ! [X2 : mu,X1 : mu] : (($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((exists_in_world @ X1 @ sK6) = $false) | ((string @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (entry_box @ X2 @ sK6)) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | ($false = (entry_box @ X2 @ (sK7 @ X1 @ X2)))) ) | ~spl1_11),
% 1.44/0.60    inference(avatar_component_clause,[],[f760])).
% 1.44/0.60  thf(f209,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : $i,X1 : $i] : (((userid @ u @ (sK2 @ X2) @ X3) = $true) | ($false = (rel_s4 @ X1 @ X2)) | ((rel_s4 @ X2 @ X3) = $false)) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f208])).
% 1.44/0.60  thf(f208,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (rel_s4 @ X1 @ X2)) | ((~ (userid @ u @ (sK2 @ X2) @ X3)) = $false) | ((rel_s4 @ X2 @ X3) = $false)) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f206])).
% 1.44/0.60  thf(f763,plain,(
% 1.44/0.60    spl1_11 | spl1_4 | spl1_6 | ~spl1_9),
% 1.44/0.60    inference(avatar_split_clause,[],[f752,f736,f547,f515,f760])).
% 1.44/0.60  thf(f736,plain,(
% 1.44/0.60    spl1_9 <=> ! [X2 : mu,X0 : mu,X1 : mu] : (($false = (userid @ u @ X0 @ (sK7 @ X0 @ X2))) | ($false = (entry_box @ X2 @ (sK7 @ X0 @ X2))) | ($false = (number @ X2 @ one @ (sK7 @ X0 @ X2))) | ($false = (entry_box @ X2 @ sK6)) | ($false = (exists_in_world @ X0 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (string @ X0 @ sK6)) | ($false = (exists_in_world @ (sK3 @ X1 @ X0 @ sK6 @ X2) @ sK6)) | ($false = (exists_in_world @ X2 @ sK6)))),
% 1.44/0.60    introduced(avatar_definition,[new_symbols(naming,[spl1_9])])).
% 1.44/0.60  thf(f752,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (($false = (exists_in_world @ X2 @ sK6)) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | ($false = (entry_box @ X2 @ sK6)) | ((string @ X1 @ sK6) = $false) | ((rel_s4 @ X3 @ sK6) = $false) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ($false = (exists_in_world @ X0 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (entry_box @ X2 @ (sK7 @ X1 @ X2)))) ) | ~spl1_9),
% 1.44/0.60    inference(trivial_inequality_removal,[],[f751])).
% 1.44/0.60  thf(f751,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (((string @ X1 @ sK6) = $false) | ($false = (entry_box @ X2 @ (sK7 @ X1 @ X2))) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | ($false = (exists_in_world @ X0 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (entry_box @ X2 @ sK6)) | ((rel_s4 @ X3 @ sK6) = $false) | ($false = $true) | ($false = (exists_in_world @ X2 @ sK6))) ) | ~spl1_9),
% 1.44/0.60    inference(duplicate_literal_removal,[],[f747])).
% 1.44/0.60  thf(f747,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (((rel_s4 @ X3 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((string @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X0 @ sK6)) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | ($false = $true) | ($false = (exists_in_world @ X0 @ sK6)) | ($false = (entry_box @ X2 @ sK6)) | ($false = (entry_box @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ((string @ X1 @ sK6) = $false) | ($false = (entry_box @ X2 @ (sK7 @ X1 @ X2))) | ($false = (exists_in_world @ X2 @ sK6))) ) | ~spl1_9),
% 1.44/0.60    inference(superposition,[],[f737,f248])).
% 1.44/0.60  thf(f248,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($true = (exists_in_world @ (sK3 @ X3 @ X4 @ X2 @ X5) @ X2)) | ($false = (entry_box @ X5 @ X2)) | ((exists_in_world @ X5 @ X2) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (rel_s4 @ X1 @ X2)) | ($false = (string @ X4 @ X2)) | ($false = (exists_in_world @ X3 @ X2))) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f247])).
% 1.44/0.60  thf(f247,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X3 @ X2)) | ((exists_in_world @ X5 @ X2) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ($true = (~ (entry_box @ X5 @ X2))) | ($false = (string @ X4 @ X2)) | ($false = (rel_s4 @ X1 @ X2)) | ($true = (exists_in_world @ (sK3 @ X3 @ X4 @ X2 @ X5) @ X2))) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f245])).
% 1.44/0.60  thf(f245,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X3 @ X2)) | ($false = (string @ X4 @ X2)) | ($false = (exists_in_world @ X4 @ X2)) | ((exists_in_world @ X5 @ X2) = $false) | ($false = (rel_s4 @ X1 @ X2)) | ($false = ((exists_in_world @ (sK3 @ X3 @ X4 @ X2 @ X5) @ X2) => (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X3 @ (sK3 @ X3 @ X4 @ X2 @ X5) @ Y1 @ Y0)) | (in @ X4 @ X5 @ Y1 @ Y0))))))))))) | ($true = (~ (entry_box @ X5 @ X2)))) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f244])).
% 1.44/0.60  thf(f244,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X3 @ X2)) | ($true = (~ (entry_box @ X5 @ X2))) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (do @ X3 @ Y0 @ Y2 @ Y1)) | (in @ X4 @ X5 @ Y2 @ Y1))))))))))) @ (sK3 @ X3 @ X4 @ X2 @ X5)) = $false) | ((exists_in_world @ X5 @ X2) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (string @ X4 @ X2)) | ($false = (rel_s4 @ X1 @ X2))) )),
% 1.44/0.60    inference(sigma_clausification,[],[f243])).
% 1.44/0.60  thf(f243,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X4 @ X2)) | ((exists_in_world @ X5 @ X2) = $false) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (string @ X4 @ X2)) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (do @ X3 @ Y0 @ Y2 @ Y1)) | (in @ X4 @ X5 @ Y2 @ Y1))))))))))))) | ($false = (rel_s4 @ X1 @ X2)) | ($true = (~ (entry_box @ X5 @ X2)))) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f242])).
% 1.44/0.60  thf(f242,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (((~ (string @ X4 @ X2)) = $true) | ($false = (exists_in_world @ X3 @ X2)) | ((exists_in_world @ X5 @ X2) = $false) | ($true = (~ (entry_box @ X5 @ X2))) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (do @ X3 @ Y0 @ Y2 @ Y1)) | (in @ X4 @ X5 @ Y2 @ Y1))))))))))))) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (rel_s4 @ X1 @ X2))) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f241])).
% 1.44/0.60  thf(f241,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (((exists_in_world @ X5 @ X2) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (rel_s4 @ X1 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | (((~ (string @ X4 @ X2)) | (~ (entry_box @ X5 @ X2))) = $true) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (do @ X3 @ Y0 @ Y2 @ Y1)) | (in @ X4 @ X5 @ Y2 @ Y1)))))))))))))) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f240])).
% 1.44/0.60  thf(f240,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X3 @ X2)) | ($false = (rel_s4 @ X1 @ X2)) | ((exists_in_world @ X5 @ X2) = $false) | ($true = (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (do @ X3 @ Y0 @ Y2 @ Y1)) | (in @ X4 @ X5 @ Y2 @ Y1)))))))))))))) | (((~ (string @ X4 @ X2)) | (~ (entry_box @ X5 @ X2))) = $true) | ($false = (exists_in_world @ X4 @ X2))) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f239])).
% 1.44/0.60  thf(f239,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (((((~ (string @ X4 @ X2)) | (~ (entry_box @ X5 @ X2))) | (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (do @ X3 @ Y0 @ Y2 @ Y1)) | (in @ X4 @ X5 @ Y2 @ Y1)))))))))))))) = $true) | ($false = (exists_in_world @ X4 @ X2)) | ((exists_in_world @ X5 @ X2) = $false) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (rel_s4 @ X1 @ X2))) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f238])).
% 1.44/0.60  thf(f238,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (rel_s4 @ X1 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | (((exists_in_world @ X5 @ X2) => (((~ (string @ X4 @ X2)) | (~ (entry_box @ X5 @ X2))) | (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (do @ X3 @ Y0 @ Y2 @ Y1)) | (in @ X4 @ X5 @ Y2 @ Y1))))))))))))))) = $true) | ($false = (exists_in_world @ X4 @ X2))) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f237])).
% 1.44/0.60  thf(f237,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X4 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (rel_s4 @ X1 @ X2)) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (((~ (string @ X4 @ X2)) | (~ (entry_box @ Y0 @ X2))) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ X2 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (do @ X3 @ Y1 @ Y3 @ Y2)) | (in @ X4 @ Y0 @ Y3 @ Y2)))))))))))))))) @ X5) = $true)) )),
% 1.44/0.60    inference(pi_clausification,[],[f236])).
% 1.44/0.60  thf(f236,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu] : (($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (rel_s4 @ X1 @ X2)) | ($true = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (((~ (string @ X4 @ X2)) | (~ (entry_box @ Y0 @ X2))) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ X2 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (do @ X3 @ Y1 @ Y3 @ Y2)) | (in @ X4 @ Y0 @ Y3 @ Y2))))))))))))))))))) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f235])).
% 1.44/0.60  thf(f235,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu] : (($false = (rel_s4 @ X1 @ X2)) | ($true = ((exists_in_world @ X4 @ X2) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (((~ (string @ X4 @ X2)) | (~ (entry_box @ Y0 @ X2))) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ X2 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (do @ X3 @ Y1 @ Y3 @ Y2)) | (in @ X4 @ Y0 @ Y3 @ Y2))))))))))))))))))) | ($false = (exists_in_world @ X3 @ X2))) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f234])).
% 1.44/0.60  thf(f234,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu] : (($false = (rel_s4 @ X1 @ X2)) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (((~ (string @ Y0 @ X2)) | (~ (entry_box @ Y1 @ X2))) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X2) => (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ X2 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (do @ X3 @ Y2 @ Y4 @ Y3)) | (in @ Y0 @ Y1 @ Y4 @ Y3))))))))))))))))))) @ X4) = $true) | ($false = (exists_in_world @ X3 @ X2))) )),
% 1.44/0.60    inference(pi_clausification,[],[f233])).
% 1.44/0.60  thf(f233,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i] : (($false = (exists_in_world @ X3 @ X2)) | ($false = (rel_s4 @ X1 @ X2)) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (((~ (string @ Y0 @ X2)) | (~ (entry_box @ Y1 @ X2))) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X2) => (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ X2 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (do @ X3 @ Y2 @ Y4 @ Y3)) | (in @ Y0 @ Y1 @ Y4 @ Y3)))))))))))))))))))) = $true)) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f232])).
% 1.44/0.60  thf(f232,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i] : (($false = (rel_s4 @ X1 @ X2)) | (((exists_in_world @ X3 @ X2) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (((~ (string @ Y0 @ X2)) | (~ (entry_box @ Y1 @ X2))) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X2) => (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ X2 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (do @ X3 @ Y2 @ Y4 @ Y3)) | (in @ Y0 @ Y1 @ Y4 @ Y3))))))))))))))))))))) = $true)) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f231])).
% 1.44/0.60  thf(f231,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i] : (((~ (rel_s4 @ X1 @ X2)) = $true) | (((exists_in_world @ X3 @ X2) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (((~ (string @ Y0 @ X2)) | (~ (entry_box @ Y1 @ X2))) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X2) => (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ X2 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (do @ X3 @ Y2 @ Y4 @ Y3)) | (in @ Y0 @ Y1 @ Y4 @ Y3))))))))))))))))))))) = $true)) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f230])).
% 1.44/0.60  thf(f230,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X1 : $i] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X2) => (((~ (string @ Y1 @ X2)) | (~ (entry_box @ Y2 @ X2))) | (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ X2) => (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ X2 @ Y4)) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((~ (do @ Y0 @ Y3 @ Y5 @ Y4)) | (in @ Y1 @ Y2 @ Y5 @ Y4)))))))))))))))))))))) @ X3) = $true) | ((~ (rel_s4 @ X1 @ X2)) = $true)) )),
% 1.44/0.60    inference(pi_clausification,[],[f229])).
% 1.44/0.60  thf(f229,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X2) => (((~ (string @ Y1 @ X2)) | (~ (entry_box @ Y2 @ X2))) | (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ X2) => (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ X2 @ Y4)) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((~ (do @ Y0 @ Y3 @ Y5 @ Y4)) | (in @ Y1 @ Y2 @ Y5 @ Y4))))))))))))))))))))))) = $true) | ((~ (rel_s4 @ X1 @ X2)) = $true)) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f228])).
% 1.44/0.60  thf(f228,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : ((((~ (rel_s4 @ X1 @ X2)) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X2) => (((~ (string @ Y1 @ X2)) | (~ (entry_box @ Y2 @ X2))) | (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ X2) => (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ X2 @ Y4)) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((~ (do @ Y0 @ Y3 @ Y5 @ Y4)) | (in @ Y1 @ Y2 @ Y5 @ Y4)))))))))))))))))))))))) = $true)) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f227])).
% 1.44/0.60  thf(f227,plain,(
% 1.44/0.60    ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y0) => (((~ (string @ Y2 @ Y0)) | (~ (entry_box @ Y3 @ Y0))) | (~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y0) => (~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y0 @ Y5)) | (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((~ (do @ Y1 @ Y4 @ Y6 @ Y5)) | (in @ Y2 @ Y3 @ Y6 @ Y5))))))))))))))))))))))))) @ X2) = $true)) )),
% 1.44/0.60    inference(pi_clausification,[],[f226])).
% 1.44/0.60  thf(f226,plain,(
% 1.44/0.60    ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y0) => (((~ (string @ Y2 @ Y0)) | (~ (entry_box @ Y3 @ Y0))) | (~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y0) => (~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y0 @ Y5)) | (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((~ (do @ Y1 @ Y4 @ Y6 @ Y5)) | (in @ Y2 @ Y3 @ Y6 @ Y5)))))))))))))))))))))))))) = $true)) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f225])).
% 1.44/0.60  thf(f225,plain,(
% 1.44/0.60    ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => (((~ (string @ Y3 @ Y1)) | (~ (entry_box @ Y4 @ Y1))) | (~ (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((~ (do @ Y2 @ Y5 @ Y7 @ Y6)) | (in @ Y3 @ Y4 @ Y7 @ Y6))))))))))))))))))))))))))) @ X1) = $true)) )),
% 1.44/0.60    inference(pi_clausification,[],[f224])).
% 1.44/0.60  thf(f224,plain,(
% 1.44/0.60    ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => (((~ (string @ Y3 @ Y1)) | (~ (entry_box @ Y4 @ Y1))) | (~ (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((~ (do @ Y2 @ Y5 @ Y7 @ Y6)) | (in @ Y3 @ Y4 @ Y7 @ Y6)))))))))))))))))))))))))))))),
% 1.44/0.60    inference(boolean_simplification,[],[f223])).
% 1.44/0.60  thf(f223,plain,(
% 1.44/0.60    ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => ((~ (~ ((~ (string @ Y3 @ Y1)) | (~ (entry_box @ Y4 @ Y1))))) | (~ (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((~ (do @ Y2 @ Y5 @ Y7 @ Y6)) | (in @ Y3 @ Y4 @ Y7 @ Y6)))))))))))))))))))))))))))))),
% 1.44/0.60    inference(beta_eta_normalization,[],[f188])).
% 1.44/0.60  thf(f188,plain,(
% 1.44/0.60    (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) @ (^[Y2 : mu]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((Y5 @ Y7) | (Y6 @ Y7))))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y3) @ Y4)))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((Y5 @ Y7) | (Y6 @ Y7))))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y3) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y4)))))) @ (string @ Y1) @ (entry_box @ Y2)) @ ((^[Y3 : mu > $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : mu > $i > $o]: ((^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) @ (^[Y4 : mu]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ (Y3 @ Y4)))))) @ (^[Y3 : mu]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y5 @ Y6)) | (Y4 @ Y6))))))) @ ((^[Y4 : mu > $i > $o]: ((^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) @ (^[Y4 : mu]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: ((Y7 @ Y9) | (Y8 @ Y9))))))) @ ((^[Y7 : $i > $o]: ((^[Y8 : $i]: (~ (Y7 @ Y8))))) @ Y5) @ Y6)))) @ (do @ Y0 @ Y3 @ Y4) @ (in @ Y1 @ Y2 @ Y4)))))))))))))))) = $true)),
% 1.44/0.60    inference(definition_unfolding,[],[f172,f137,f170,f166,f166,f166,f175,f174,f180,f170,f166,f175])).
% 1.44/0.60  thf(f175,plain,(
% 1.44/0.60    (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)))))),
% 1.44/0.60    inference(definition_unfolding,[],[f135,f156,f148])).
% 1.44/0.60  thf(f135,plain,(
% 1.44/0.60    (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 1.44/0.60    inference(cnf_transformation,[],[f80])).
% 1.44/0.60  thf(f80,plain,(
% 1.44/0.60    (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 1.44/0.60    inference(fool_elimination,[],[f79])).
% 1.44/0.60  thf(f79,plain,(
% 1.44/0.60    ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 1.44/0.60    inference(rectify,[],[f9])).
% 1.44/0.60  thf(f9,axiom,(
% 1.44/0.60    ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 1.44/0.60    file('/export/starexec/sandbox/tmp/tmp.7LKmvzLAF1/Vampire---4.8_21131',mimplies)).
% 1.44/0.60  thf(f172,plain,(
% 1.44/0.60    ((mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mforall_ind @ (^[Y2 : mu]: (mimplies @ (mand @ (string @ Y1) @ (entry_box @ Y2)) @ (mexists_ind @ (^[Y3 : mu]: (mbox_s4 @ (mforall_ind @ (^[Y4 : mu]: (mimplies @ (do @ Y0 @ Y3 @ Y4) @ (in @ Y1 @ Y2 @ Y4)))))))))))))))) = $true)),
% 1.44/0.60    inference(cnf_transformation,[],[f119])).
% 1.44/0.60  thf(f119,plain,(
% 1.44/0.60    ((mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mforall_ind @ (^[Y2 : mu]: (mimplies @ (mand @ (string @ Y1) @ (entry_box @ Y2)) @ (mexists_ind @ (^[Y3 : mu]: (mbox_s4 @ (mforall_ind @ (^[Y4 : mu]: (mimplies @ (do @ Y0 @ Y3 @ Y4) @ (in @ Y1 @ Y2 @ Y4)))))))))))))))) = $true)),
% 1.44/0.60    inference(fool_elimination,[],[f118])).
% 1.44/0.60  thf(f118,plain,(
% 1.44/0.60    (mvalid @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mforall_ind @ (^[X1 : mu] : (mforall_ind @ (^[X2 : mu] : (mimplies @ (mand @ (string @ X1) @ (entry_box @ X2)) @ (mexists_ind @ (^[X3 : mu] : (mbox_s4 @ (mforall_ind @ (^[X4 : mu] : (mimplies @ (do @ X0 @ X3 @ X4) @ (in @ X1 @ X2 @ X4))))))))))))))))),
% 1.44/0.60    inference(rectify,[],[f41])).
% 1.44/0.60  thf(f41,axiom,(
% 1.44/0.60    (mvalid @ (mbox_s4 @ (mforall_ind @ (^[X8 : mu] : (mforall_ind @ (^[X11 : mu] : (mforall_ind @ (^[X12 : mu] : (mimplies @ (mand @ (string @ X11) @ (entry_box @ X12)) @ (mexists_ind @ (^[X13 : mu] : (mbox_s4 @ (mforall_ind @ (^[X14 : mu] : (mimplies @ (do @ X8 @ X13 @ X14) @ (in @ X11 @ X12 @ X14))))))))))))))))),
% 1.44/0.60    file('/export/starexec/sandbox/tmp/tmp.7LKmvzLAF1/Vampire---4.8_21131',ax3)).
% 1.44/0.60  thf(f737,plain,(
% 1.44/0.60    ( ! [X2 : mu,X0 : mu,X1 : mu] : (($false = (exists_in_world @ (sK3 @ X1 @ X0 @ sK6 @ X2) @ sK6)) | ($false = (entry_box @ X2 @ sK6)) | ($false = (string @ X0 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (userid @ u @ X0 @ (sK7 @ X0 @ X2))) | ($false = (number @ X2 @ one @ (sK7 @ X0 @ X2))) | ($false = (exists_in_world @ X0 @ sK6)) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (entry_box @ X2 @ (sK7 @ X0 @ X2)))) ) | ~spl1_9),
% 1.44/0.60    inference(avatar_component_clause,[],[f736])).
% 1.44/0.60  thf(f743,plain,(
% 1.44/0.60    spl1_4 | spl1_9),
% 1.44/0.60    inference(avatar_split_clause,[],[f729,f736,f515])).
% 1.44/0.60  thf(f729,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (($false = (entry_box @ X2 @ (sK7 @ X0 @ X2))) | ($false = (userid @ u @ X0 @ (sK7 @ X0 @ X2))) | ($false = (number @ X2 @ one @ (sK7 @ X0 @ X2))) | ($false = (exists_in_world @ X2 @ sK6)) | ((rel_s4 @ X3 @ sK6) = $false) | ($false = (string @ X0 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (entry_box @ X2 @ sK6)) | ($false = (exists_in_world @ (sK3 @ X1 @ X0 @ sK6 @ X2) @ sK6)) | ($false = (exists_in_world @ X0 @ sK6))) )),
% 1.44/0.60    inference(trivial_inequality_removal,[],[f728])).
% 1.44/0.60  thf(f728,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (($false = (exists_in_world @ X0 @ sK6)) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = $true) | ($false = (entry_box @ X2 @ (sK7 @ X0 @ X2))) | ($false = (number @ X2 @ one @ (sK7 @ X0 @ X2))) | ($false = (userid @ u @ X0 @ (sK7 @ X0 @ X2))) | ($false = (exists_in_world @ (sK3 @ X1 @ X0 @ sK6 @ X2) @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ((rel_s4 @ X3 @ sK6) = $false) | ($false = (entry_box @ X2 @ sK6)) | ($false = (string @ X0 @ sK6))) )),
% 1.44/0.60    inference(duplicate_literal_removal,[],[f722])).
% 1.44/0.60  thf(f722,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (($false = (exists_in_world @ (sK3 @ X1 @ X0 @ sK6 @ X2) @ sK6)) | ((rel_s4 @ X3 @ sK6) = $false) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (number @ X2 @ one @ (sK7 @ X0 @ X2))) | ($false = $true) | ($false = (exists_in_world @ X0 @ sK6)) | ($false = (exists_in_world @ X0 @ sK6)) | ($false = (string @ X0 @ sK6)) | ($false = (exists_in_world @ X0 @ sK6)) | ($false = (number @ X2 @ one @ (sK7 @ X0 @ X2))) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (exists_in_world @ (sK3 @ X1 @ X0 @ sK6 @ X2) @ sK6)) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (userid @ u @ X0 @ (sK7 @ X0 @ X2))) | ($false = (userid @ u @ X0 @ (sK7 @ X0 @ X2))) | ($false = (entry_box @ X2 @ sK6)) | ($false = (entry_box @ X2 @ (sK7 @ X0 @ X2))) | ($false = (entry_box @ X2 @ (sK7 @ X0 @ X2))) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6))) )),
% 1.44/0.60    inference(superposition,[],[f336,f717])).
% 1.44/0.60  thf(f717,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X0 : mu,X1 : mu,X4 : $i] : (($false = (rel_s4 @ X2 @ (sK10 @ X0 @ (sK3 @ X1 @ X0 @ X2 @ X3) @ X1 @ X3))) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X3 @ sK6)) | ((exists_in_world @ X0 @ X2) = $false) | ((entry_box @ X3 @ X2) = $false) | ((exists_in_world @ X1 @ X2) = $false) | ($false = (exists_in_world @ X0 @ sK6)) | ($false = (rel_s4 @ X4 @ X2)) | ($false = (exists_in_world @ (sK3 @ X1 @ X0 @ X2 @ X3) @ sK6)) | ($false = (number @ X3 @ one @ (sK7 @ X0 @ X3))) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (entry_box @ X3 @ (sK7 @ X0 @ X3))) | ((userid @ u @ X0 @ (sK7 @ X0 @ X3)) = $false) | ((string @ X0 @ X2) = $false)) )),
% 1.44/0.60    inference(trivial_inequality_removal,[],[f716])).
% 1.44/0.60  thf(f716,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X0 : mu,X1 : mu,X4 : $i] : (($false = $true) | ((entry_box @ X3 @ X2) = $false) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (rel_s4 @ X2 @ (sK10 @ X0 @ (sK3 @ X1 @ X0 @ X2 @ X3) @ X1 @ X3))) | ((userid @ u @ X0 @ (sK7 @ X0 @ X3)) = $false) | ($false = (number @ X3 @ one @ (sK7 @ X0 @ X3))) | ((exists_in_world @ X1 @ sK6) = $false) | ((exists_in_world @ X1 @ X2) = $false) | ($false = (exists_in_world @ X0 @ sK6)) | ((string @ X0 @ X2) = $false) | ($false = (entry_box @ X3 @ (sK7 @ X0 @ X3))) | ((exists_in_world @ X0 @ X2) = $false) | ($false = (exists_in_world @ X3 @ sK6)) | ($false = (exists_in_world @ (sK3 @ X1 @ X0 @ X2 @ X3) @ sK6)) | ($false = (rel_s4 @ X4 @ X2))) )),
% 1.44/0.60    inference(duplicate_literal_removal,[],[f707])).
% 1.44/0.60  thf(f707,plain,(
% 1.44/0.60    ( ! [X2 : $i,X3 : mu,X0 : mu,X1 : mu,X4 : $i] : (((exists_in_world @ X1 @ X2) = $false) | ($false = (exists_in_world @ X0 @ sK6)) | ($false = (rel_s4 @ X4 @ X2)) | ($false = (exists_in_world @ (sK3 @ X1 @ X0 @ X2 @ X3) @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (entry_box @ X3 @ (sK7 @ X0 @ X3))) | ((userid @ u @ X0 @ (sK7 @ X0 @ X3)) = $false) | ((string @ X0 @ X2) = $false) | ($false = (number @ X3 @ one @ (sK7 @ X0 @ X3))) | ($false = $true) | ($false = (exists_in_world @ X0 @ sK6)) | ($false = (entry_box @ X3 @ (sK7 @ X0 @ X3))) | ($false = (exists_in_world @ X3 @ X2)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (number @ X3 @ one @ (sK7 @ X0 @ X3))) | ($false = (exists_in_world @ X3 @ sK6)) | ((entry_box @ X3 @ X2) = $false) | ($false = (exists_in_world @ (sK3 @ X1 @ X0 @ X2 @ X3) @ sK6)) | ($false = (rel_s4 @ X2 @ (sK10 @ X0 @ (sK3 @ X1 @ X0 @ X2 @ X3) @ X1 @ X3))) | ((exists_in_world @ X0 @ X2) = $false) | ((userid @ u @ X0 @ (sK7 @ X0 @ X3)) = $false) | ($false = (exists_in_world @ X3 @ sK6))) )),
% 1.44/0.60    inference(superposition,[],[f705,f341])).
% 1.44/0.60  thf(f341,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($true = (exists_in_world @ (sK11 @ X1 @ X3 @ X4 @ X2) @ (sK10 @ X1 @ X3 @ X4 @ X2))) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (entry_box @ X2 @ (sK7 @ X1 @ X2))) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X3 @ sK6)) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2)))) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f339])).
% 1.44/0.60  thf(f339,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X3 @ sK6)) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | ($false = ((exists_in_world @ (sK11 @ X1 @ X3 @ X4 @ X2) @ (sK10 @ X1 @ X3 @ X4 @ X2)) => ((~ (do @ X4 @ X3 @ (sK11 @ X1 @ X3 @ X4 @ X2) @ (sK10 @ X1 @ X3 @ X4 @ X2))) | (in @ X1 @ X2 @ (sK11 @ X1 @ X3 @ X4 @ X2) @ (sK10 @ X1 @ X3 @ X4 @ X2))))) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (entry_box @ X2 @ (sK7 @ X1 @ X2))) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2)))) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f338])).
% 1.44/0.60  thf(f338,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((~ (entry_box @ X2 @ (sK7 @ X1 @ X2))) = $true) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = ((exists_in_world @ (sK11 @ X1 @ X3 @ X4 @ X2) @ (sK10 @ X1 @ X3 @ X4 @ X2)) => ((~ (do @ X4 @ X3 @ (sK11 @ X1 @ X3 @ X4 @ X2) @ (sK10 @ X1 @ X3 @ X4 @ X2))) | (in @ X1 @ X2 @ (sK11 @ X1 @ X3 @ X4 @ X2) @ (sK10 @ X1 @ X3 @ X4 @ X2))))) | ($false = (exists_in_world @ X3 @ sK6)) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X4 @ sK6) = $false)) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f337])).
% 1.44/0.60  thf(f337,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ X4 @ sK6) = $false) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ($false = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ (sK10 @ X1 @ X3 @ X4 @ X2)) => ((~ (do @ X4 @ X3 @ Y0 @ (sK10 @ X1 @ X3 @ X4 @ X2))) | (in @ X1 @ X2 @ Y0 @ (sK10 @ X1 @ X3 @ X4 @ X2))))) @ (sK11 @ X1 @ X3 @ X4 @ X2))) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | ((~ (entry_box @ X2 @ (sK7 @ X1 @ X2))) = $true) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X3 @ sK6)) | ($false = (exists_in_world @ X2 @ sK6))) )),
% 1.44/0.60    inference(sigma_clausification,[],[f333])).
% 1.44/0.60  thf(f333,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ X1 @ sK6) = $false) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ (sK10 @ X1 @ X3 @ X4 @ X2)) => ((~ (do @ X4 @ X3 @ Y0 @ (sK10 @ X1 @ X3 @ X4 @ X2))) | (in @ X1 @ X2 @ Y0 @ (sK10 @ X1 @ X3 @ X4 @ X2))))))) | ($false = (exists_in_world @ X2 @ sK6)) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X3 @ sK6)) | ((~ (entry_box @ X2 @ (sK7 @ X1 @ X2))) = $true)) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f332])).
% 1.44/0.60  thf(f332,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : ((((~ (rel_s4 @ sK6 @ (sK10 @ X1 @ X3 @ X4 @ X2))) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ (sK10 @ X1 @ X3 @ X4 @ X2)) => ((~ (do @ X4 @ X3 @ Y0 @ (sK10 @ X1 @ X3 @ X4 @ X2))) | (in @ X1 @ X2 @ Y0 @ (sK10 @ X1 @ X3 @ X4 @ X2))))))) = $false) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((~ (entry_box @ X2 @ (sK7 @ X1 @ X2))) = $true) | ($false = (exists_in_world @ X3 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X4 @ sK6) = $false)) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f331])).
% 1.44/0.60  thf(f331,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X2 @ sK6)) | ((~ (entry_box @ X2 @ (sK7 @ X1 @ X2))) = $true) | ($false = (exists_in_world @ X3 @ sK6)) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | (((^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0))))))) @ (sK10 @ X1 @ X3 @ X4 @ X2)) = $false) | ((exists_in_world @ X4 @ sK6) = $false) | ((exists_in_world @ X1 @ sK6) = $false)) )),
% 1.44/0.60    inference(sigma_clausification,[],[f330])).
% 1.44/0.60  thf(f330,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0)))))))) = $false) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (exists_in_world @ X3 @ sK6)) | ((~ (entry_box @ X2 @ (sK7 @ X1 @ X2))) = $true)) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f329])).
% 1.44/0.60  thf(f329,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ X4 @ sK6) = $false) | ((~ (number @ X2 @ one @ (sK7 @ X1 @ X2))) = $true) | ($false = (exists_in_world @ X3 @ sK6)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0)))))))) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((~ (entry_box @ X2 @ (sK7 @ X1 @ X2))) = $true)) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f328])).
% 1.44/0.60  thf(f328,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0))))))))) = $true) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((~ (entry_box @ X2 @ (sK7 @ X1 @ X2))) = $true) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X3 @ sK6)) | ((~ (number @ X2 @ one @ (sK7 @ X1 @ X2))) = $true)) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f327])).
% 1.44/0.60  thf(f327,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ($true = ((~ (entry_box @ X2 @ (sK7 @ X1 @ X2))) | (~ (number @ X2 @ one @ (sK7 @ X1 @ X2))))) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X3 @ sK6)) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0))))))))) = $true)) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f326])).
% 1.44/0.60  thf(f326,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ X4 @ sK6) = $false) | ($true = (~ (userid @ u @ X1 @ (sK7 @ X1 @ X2)))) | ($false = (exists_in_world @ X3 @ sK6)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0))))))))) = $true) | ($true = ((~ (entry_box @ X2 @ (sK7 @ X1 @ X2))) | (~ (number @ X2 @ one @ (sK7 @ X1 @ X2))))) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false)) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f325])).
% 1.44/0.60  thf(f325,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X2 @ sK6)) | ($true = ((~ (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((~ (entry_box @ X2 @ (sK7 @ X1 @ X2))) | (~ (number @ X2 @ one @ (sK7 @ X1 @ X2)))))) | ((exists_in_world @ X1 @ sK6) = $false) | ((exists_in_world @ X4 @ sK6) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0))))))))) = $true) | ($false = (exists_in_world @ X3 @ sK6))) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f309])).
% 1.44/0.60  thf(f309,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (~ ((~ (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((~ (entry_box @ X2 @ (sK7 @ X1 @ X2))) | (~ (number @ X2 @ one @ (sK7 @ X1 @ X2))))))) | ((exists_in_world @ X1 @ sK6) = $false) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X3 @ sK6)) | ($false = (exists_in_world @ X2 @ sK6)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0))))))))) = $true)) )),
% 1.44/0.60    inference(binary_proxy_clausification,[],[f308])).
% 1.44/0.60  thf(f308,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X2 @ sK6)) | ($false = (exists_in_world @ X3 @ sK6)) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = ((~ (rel_s4 @ sK6 @ (sK7 @ X1 @ X2))) | (~ ((~ (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((~ (entry_box @ X2 @ (sK7 @ X1 @ X2))) | (~ (number @ X2 @ one @ (sK7 @ X1 @ X2)))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0))))))))) = $true) | ((exists_in_world @ X1 @ sK6) = $false)) )),
% 1.44/0.60    inference(beta_eta_normalization,[],[f307])).
% 1.44/0.60  thf(f307,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ X1 @ sK6) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0))))))))) = $true) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X3 @ sK6)) | (((^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (~ ((~ (userid @ u @ X1 @ Y0)) | ((~ (entry_box @ X2 @ Y0)) | (~ (number @ X2 @ one @ Y0))))))) @ (sK7 @ X1 @ X2)) = $false) | ($false = (exists_in_world @ X2 @ sK6))) )),
% 1.44/0.60    inference(sigma_clausification,[],[f306])).
% 1.44/0.60  thf(f306,plain,(
% 1.44/0.60    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (~ ((~ (userid @ u @ X1 @ Y0)) | ((~ (entry_box @ X2 @ Y0)) | (~ (number @ X2 @ one @ Y0))))))))) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0))))))))) = $true) | ($false = (exists_in_world @ X3 @ sK6)) | ((exists_in_world @ X4 @ sK6) = $false)) )),
% 1.44/0.60    inference(not_proxy_clausification,[],[f305])).
% 1.44/0.61  thf(f305,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X2 @ sK6)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (~ ((~ (userid @ u @ X1 @ Y0)) | ((~ (entry_box @ X2 @ Y0)) | (~ (number @ X2 @ one @ Y0)))))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0))))))))) = $true) | ($false = (exists_in_world @ X3 @ sK6)) | ((exists_in_world @ X4 @ sK6) = $false) | ((exists_in_world @ X1 @ sK6) = $false)) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f304])).
% 1.44/0.61  thf(f304,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (~ ((~ (userid @ u @ X1 @ Y0)) | ((~ (entry_box @ X2 @ Y0)) | (~ (number @ X2 @ one @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0)))))))))) = $true) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X3 @ sK6))) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f303])).
% 1.44/0.61  thf(f303,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | (((exists_in_world @ X4 @ sK6) => ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (~ ((~ (userid @ u @ X1 @ Y0)) | ((~ (entry_box @ X2 @ Y0)) | (~ (number @ X2 @ one @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0))))))))))) = $true) | ($false = (exists_in_world @ X3 @ sK6))) )),
% 1.44/0.61    inference(beta_eta_normalization,[],[f302])).
% 1.44/0.61  thf(f302,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | (~ ((~ (userid @ u @ X1 @ Y1)) | ((~ (entry_box @ X2 @ Y1)) | (~ (number @ X2 @ one @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (do @ Y0 @ X3 @ Y2 @ Y1)) | (in @ X1 @ X2 @ Y2 @ Y1)))))))))))) @ X4)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (exists_in_world @ X3 @ sK6))) )),
% 1.44/0.61    inference(pi_clausification,[],[f301])).
% 1.44/0.61  thf(f301,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu] : (($false = (exists_in_world @ X3 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ($true = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | (~ ((~ (userid @ u @ X1 @ Y1)) | ((~ (entry_box @ X2 @ Y1)) | (~ (number @ X2 @ one @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (do @ Y0 @ X3 @ Y2 @ Y1)) | (in @ X1 @ X2 @ Y2 @ Y1)))))))))))))) | ($false = (exists_in_world @ X2 @ sK6))) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f300])).
% 1.44/0.61  thf(f300,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu] : (((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ($true = ((exists_in_world @ X3 @ sK6) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | (~ ((~ (userid @ u @ X1 @ Y1)) | ((~ (entry_box @ X2 @ Y1)) | (~ (number @ X2 @ one @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (do @ Y0 @ X3 @ Y2 @ Y1)) | (in @ X1 @ X2 @ Y2 @ Y1)))))))))))))))) )),
% 1.44/0.61    inference(beta_eta_normalization,[],[f299])).
% 1.44/0.61  thf(f299,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK6) => ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ sK6 @ Y2)) | (~ ((~ (userid @ u @ X1 @ Y2)) | ((~ (entry_box @ X2 @ Y2)) | (~ (number @ X2 @ one @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ sK6 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (do @ Y1 @ Y0 @ Y3 @ Y2)) | (in @ X1 @ X2 @ Y3 @ Y2))))))))))))))) @ X3) = $true) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false)) )),
% 1.44/0.61    inference(pi_clausification,[],[f298])).
% 1.44/0.61  thf(f298,plain,(
% 1.44/0.61    ( ! [X2 : mu,X1 : mu] : (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK6) => ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ sK6 @ Y2)) | (~ ((~ (userid @ u @ X1 @ Y2)) | ((~ (entry_box @ X2 @ Y2)) | (~ (number @ X2 @ one @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ sK6 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (do @ Y1 @ Y0 @ Y3 @ Y2)) | (in @ X1 @ X2 @ Y3 @ Y2)))))))))))))))) = $true) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6))) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f297])).
% 1.44/0.61  thf(f297,plain,(
% 1.44/0.61    ( ! [X2 : mu,X1 : mu] : (($true = ((exists_in_world @ X2 @ sK6) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK6) => ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ sK6 @ Y2)) | (~ ((~ (userid @ u @ X1 @ Y2)) | ((~ (entry_box @ X2 @ Y2)) | (~ (number @ X2 @ one @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ sK6 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ (do @ Y1 @ Y0 @ Y3 @ Y2)) | (in @ X1 @ X2 @ Y3 @ Y2)))))))))))))))))) | ((exists_in_world @ X1 @ sK6) = $false)) )),
% 1.44/0.61    inference(beta_eta_normalization,[],[f296])).
% 1.44/0.61  thf(f296,plain,(
% 1.44/0.61    ( ! [X2 : mu,X1 : mu] : (((exists_in_world @ X1 @ sK6) = $false) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK6) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK6) => ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ sK6 @ Y3)) | (~ ((~ (userid @ u @ X1 @ Y3)) | ((~ (entry_box @ Y0 @ Y3)) | (~ (number @ Y0 @ one @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ sK6 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (do @ Y2 @ Y1 @ Y4 @ Y3)) | (in @ X1 @ Y0 @ Y4 @ Y3)))))))))))))))))) @ X2) = $true)) )),
% 1.44/0.61    inference(pi_clausification,[],[f295])).
% 1.44/0.61  thf(f295,plain,(
% 1.44/0.61    ( ! [X1 : mu] : (($true = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK6) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK6) => ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ sK6 @ Y3)) | (~ ((~ (userid @ u @ X1 @ Y3)) | ((~ (entry_box @ Y0 @ Y3)) | (~ (number @ Y0 @ one @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ sK6 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (do @ Y2 @ Y1 @ Y4 @ Y3)) | (in @ X1 @ Y0 @ Y4 @ Y3)))))))))))))))))))) | ((exists_in_world @ X1 @ sK6) = $false)) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f294])).
% 1.44/0.61  thf(f294,plain,(
% 1.44/0.61    ( ! [X1 : mu] : ((((exists_in_world @ X1 @ sK6) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK6) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK6) => ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ sK6 @ Y3)) | (~ ((~ (userid @ u @ X1 @ Y3)) | ((~ (entry_box @ Y0 @ Y3)) | (~ (number @ Y0 @ one @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ sK6 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((~ (do @ Y2 @ Y1 @ Y4 @ Y3)) | (in @ X1 @ Y0 @ Y4 @ Y3)))))))))))))))))))) = $true)) )),
% 1.44/0.61    inference(beta_eta_normalization,[],[f293])).
% 1.44/0.61  thf(f293,plain,(
% 1.44/0.61    ( ! [X1 : mu] : (($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK6) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK6) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ sK6) => ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ sK6 @ Y4)) | (~ ((~ (userid @ u @ Y0 @ Y4)) | ((~ (entry_box @ Y1 @ Y4)) | (~ (number @ Y1 @ one @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ sK6 @ Y4)) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((~ (do @ Y3 @ Y2 @ Y5 @ Y4)) | (in @ Y0 @ Y1 @ Y5 @ Y4))))))))))))))))))))) @ X1))) )),
% 1.44/0.61    inference(pi_clausification,[],[f292])).
% 1.44/0.61  thf(f292,plain,(
% 1.44/0.61    ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK6) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK6) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ sK6) => ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ sK6 @ Y4)) | (~ ((~ (userid @ u @ Y0 @ Y4)) | ((~ (entry_box @ Y1 @ Y4)) | (~ (number @ Y1 @ one @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ sK6 @ Y4)) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((~ (do @ Y3 @ Y2 @ Y5 @ Y4)) | (in @ Y0 @ Y1 @ Y5 @ Y4)))))))))))))))))))))) = $true)),
% 1.44/0.61    inference(not_proxy_clausification,[],[f289])).
% 1.44/0.61  thf(f289,plain,(
% 1.44/0.61    ((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK6) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK6) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ sK6) => ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ sK6 @ Y4)) | (~ ((~ (userid @ u @ Y0 @ Y4)) | ((~ (entry_box @ Y1 @ Y4)) | (~ (number @ Y1 @ one @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ sK6 @ Y4)) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((~ (do @ Y3 @ Y2 @ Y5 @ Y4)) | (in @ Y0 @ Y1 @ Y5 @ Y4))))))))))))))))))))))) = $false)),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f288])).
% 1.44/0.61  thf(f288,plain,(
% 1.44/0.61    ($false = ((~ (rel_s4 @ sK5 @ sK6)) | (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK6) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK6) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ sK6) => ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ sK6 @ Y4)) | (~ ((~ (userid @ u @ Y0 @ Y4)) | ((~ (entry_box @ Y1 @ Y4)) | (~ (number @ Y1 @ one @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ sK6 @ Y4)) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((~ (do @ Y3 @ Y2 @ Y5 @ Y4)) | (in @ Y0 @ Y1 @ Y5 @ Y4)))))))))))))))))))))))))),
% 1.44/0.61    inference(beta_eta_normalization,[],[f287])).
% 1.44/0.61  thf(f287,plain,(
% 1.44/0.61    ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y0) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y0) => ((~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y0 @ Y5)) | (~ ((~ (userid @ u @ Y1 @ Y5)) | ((~ (entry_box @ Y2 @ Y5)) | (~ (number @ Y2 @ one @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y0 @ Y5)) | (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((~ (do @ Y4 @ Y3 @ Y6 @ Y5)) | (in @ Y1 @ Y2 @ Y6 @ Y5))))))))))))))))))))))))) @ sK6))),
% 1.44/0.61    inference(sigma_clausification,[],[f286])).
% 1.44/0.61  thf(f286,plain,(
% 1.44/0.61    ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y0) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y0) => ((~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y0 @ Y5)) | (~ ((~ (userid @ u @ Y1 @ Y5)) | ((~ (entry_box @ Y2 @ Y5)) | (~ (number @ Y2 @ one @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y0 @ Y5)) | (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((~ (do @ Y4 @ Y3 @ Y6 @ Y5)) | (in @ Y1 @ Y2 @ Y6 @ Y5)))))))))))))))))))))))))))),
% 1.44/0.61    inference(beta_eta_normalization,[],[f285])).
% 1.44/0.61  thf(f285,plain,(
% 1.44/0.61    ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => ((~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (~ ((~ (userid @ u @ Y2 @ Y6)) | ((~ (entry_box @ Y3 @ Y6)) | (~ (number @ Y3 @ one @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((~ (do @ Y5 @ Y4 @ Y7 @ Y6)) | (in @ Y2 @ Y3 @ Y7 @ Y6))))))))))))))))))))))))))) @ sK5))),
% 1.44/0.61    inference(sigma_clausification,[],[f284])).
% 1.44/0.61  thf(f284,plain,(
% 1.44/0.61    ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => ((~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (~ ((~ (userid @ u @ Y2 @ Y6)) | ((~ (entry_box @ Y3 @ Y6)) | (~ (number @ Y3 @ one @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((~ (do @ Y5 @ Y4 @ Y7 @ Y6)) | (in @ Y2 @ Y3 @ Y7 @ Y6)))))))))))))))))))))))))))) != $true)),
% 1.44/0.61    inference(boolean_simplification,[],[f283])).
% 1.44/0.61  thf(f283,plain,(
% 1.44/0.61    ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => ((~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (~ ((~ (userid @ u @ Y2 @ Y6)) | (~ (~ ((~ (entry_box @ Y3 @ Y6)) | (~ (number @ Y3 @ one @ Y6))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((~ (do @ Y5 @ Y4 @ Y7 @ Y6)) | (in @ Y2 @ Y3 @ Y7 @ Y6)))))))))))))))))))))))))))) != $true)),
% 1.44/0.61    inference(boolean_simplification,[],[f282])).
% 1.44/0.61  thf(f282,plain,(
% 1.44/0.61    ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => (~ (~ ((~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (~ ((~ (userid @ u @ Y2 @ Y6)) | (~ (~ ((~ (entry_box @ Y3 @ Y6)) | (~ (number @ Y3 @ one @ Y6))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((~ (do @ Y5 @ Y4 @ Y7 @ Y6)) | (in @ Y2 @ Y3 @ Y7 @ Y6)))))))))))))))))))))))))))))) != $true)),
% 1.44/0.61    inference(boolean_simplification,[],[f281])).
% 1.44/0.61  thf(f281,plain,(
% 1.44/0.61    ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => (~ (~ (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => (~ (~ ((~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (~ ((~ (userid @ u @ Y2 @ Y6)) | (~ (~ ((~ (entry_box @ Y3 @ Y6)) | (~ (number @ Y3 @ one @ Y6))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((~ (do @ Y5 @ Y4 @ Y7 @ Y6)) | (in @ Y2 @ Y3 @ Y7 @ Y6)))))))))))))))))))))))))))))))))),
% 1.44/0.61    inference(boolean_simplification,[],[f280])).
% 1.44/0.61  thf(f280,plain,(
% 1.44/0.61    ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (~ (~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => (~ (~ (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => (~ (~ ((~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (~ ((~ (userid @ u @ Y2 @ Y6)) | (~ (~ ((~ (entry_box @ Y3 @ Y6)) | (~ (number @ Y3 @ one @ Y6))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((~ (do @ Y5 @ Y4 @ Y7 @ Y6)) | (in @ Y2 @ Y3 @ Y7 @ Y6)))))))))))))))))))))))))))))))))))),
% 1.44/0.61    inference(boolean_simplification,[],[f279])).
% 1.44/0.61  thf(f279,plain,(
% 1.44/0.61    ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (~ (~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => (~ (~ (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => (~ (~ ((~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (~ ((~ (userid @ u @ Y2 @ Y6)) | (~ (~ ((~ (entry_box @ Y3 @ Y6)) | (~ (number @ Y3 @ one @ Y6))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((~ (do @ Y5 @ Y4 @ Y7 @ Y6)) | (in @ Y2 @ Y3 @ Y7 @ Y6)))))))))))))))))))))))))))))))))))) != $true)),
% 1.44/0.61    inference(beta_eta_normalization,[],[f186])).
% 1.44/0.61  thf(f186,plain,(
% 1.44/0.61    (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) @ (^[Y2 : mu]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ (Y1 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : mu > $i > $o]: ((^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) @ (^[Y3 : mu]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ (Y2 @ Y3)))))) @ (^[Y2 : mu]: ((^[Y3 : mu > $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : mu > $i > $o]: ((^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) @ (^[Y4 : mu]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ (Y3 @ Y4)))))) @ (^[Y3 : mu]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y5)))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y5 @ Y6)) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y5)))))) @ (userid @ u @ Y0) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y5)))))) @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y5 @ Y6)) | (Y4 @ Y6))))))) @ ((^[Y4 : mu > $i > $o]: ((^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) @ (^[Y4 : mu]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: ((Y7 @ Y9) | (Y8 @ Y9))))))) @ ((^[Y7 : $i > $o]: ((^[Y8 : $i]: (~ (Y7 @ Y8))))) @ Y5) @ Y6)))) @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4)))))))))))))))) != $true)),
% 1.44/0.61    inference(definition_unfolding,[],[f162,f137,f170,f180,f180,f180,f180,f174,f170,f174,f174,f170,f166,f175])).
% 1.44/0.61  thf(f162,plain,(
% 1.44/0.61    ((mvalid @ (mbox_s4 @ (mexists_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mexists_ind @ (^[Y2 : mu]: (mexists_ind @ (^[Y3 : mu]: (mand @ (mbox_s4 @ (mand @ (userid @ u @ Y0) @ (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ (mbox_s4 @ (mforall_ind @ (^[Y4 : mu]: (mimplies @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4)))))))))))))))) != $true)),
% 1.44/0.61    inference(cnf_transformation,[],[f126])).
% 1.44/0.61  thf(f126,plain,(
% 1.44/0.61    ((mvalid @ (mbox_s4 @ (mexists_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mexists_ind @ (^[Y2 : mu]: (mexists_ind @ (^[Y3 : mu]: (mand @ (mbox_s4 @ (mand @ (userid @ u @ Y0) @ (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ (mbox_s4 @ (mforall_ind @ (^[Y4 : mu]: (mimplies @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4)))))))))))))))) != $true)),
% 1.44/0.61    inference(flattening,[],[f70])).
% 1.44/0.61  thf(f70,plain,(
% 1.44/0.61    ~((mvalid @ (mbox_s4 @ (mexists_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mexists_ind @ (^[Y2 : mu]: (mexists_ind @ (^[Y3 : mu]: (mand @ (mbox_s4 @ (mand @ (userid @ u @ Y0) @ (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ (mbox_s4 @ (mforall_ind @ (^[Y4 : mu]: (mimplies @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4)))))))))))))))) = $true)),
% 1.44/0.61    inference(fool_elimination,[],[f69])).
% 1.44/0.61  thf(f69,plain,(
% 1.44/0.61    ~(mvalid @ (mbox_s4 @ (mexists_ind @ (^[X0 : mu] : (mexists_ind @ (^[X1 : mu] : (mexists_ind @ (^[X2 : mu] : (mexists_ind @ (^[X3 : mu] : (mand @ (mbox_s4 @ (mand @ (userid @ u @ X0) @ (mand @ (entry_box @ X1) @ (number @ X1 @ one)))) @ (mbox_s4 @ (mforall_ind @ (^[X4 : mu] : (mimplies @ (do @ X3 @ X2 @ X4) @ (in @ X0 @ X1 @ X4))))))))))))))))),
% 1.44/0.61    inference(rectify,[],[f43])).
% 1.44/0.61  thf(f43,negated_conjecture,(
% 1.44/0.61    ~(mvalid @ (mbox_s4 @ (mexists_ind @ (^[X11 : mu] : (mexists_ind @ (^[X12 : mu] : (mexists_ind @ (^[X13 : mu] : (mexists_ind @ (^[X8 : mu] : (mand @ (mbox_s4 @ (mand @ (userid @ u @ X11) @ (mand @ (entry_box @ X12) @ (number @ X12 @ one)))) @ (mbox_s4 @ (mforall_ind @ (^[X14 : mu] : (mimplies @ (do @ X8 @ X13 @ X14) @ (in @ X11 @ X12 @ X14))))))))))))))))),
% 1.44/0.61    inference(negated_conjecture,[],[f42])).
% 1.44/0.61  thf(f42,conjecture,(
% 1.44/0.61    (mvalid @ (mbox_s4 @ (mexists_ind @ (^[X11 : mu] : (mexists_ind @ (^[X12 : mu] : (mexists_ind @ (^[X13 : mu] : (mexists_ind @ (^[X8 : mu] : (mand @ (mbox_s4 @ (mand @ (userid @ u @ X11) @ (mand @ (entry_box @ X12) @ (number @ X12 @ one)))) @ (mbox_s4 @ (mforall_ind @ (^[X14 : mu] : (mimplies @ (do @ X8 @ X13 @ X14) @ (in @ X11 @ X12 @ X14))))))))))))))))),
% 1.44/0.61    file('/export/starexec/sandbox/tmp/tmp.7LKmvzLAF1/Vampire---4.8_21131',con)).
% 1.44/0.61  thf(f705,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu,X4 : $i] : (((exists_in_world @ (sK11 @ X0 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X2 @ X1) @ (sK10 @ X0 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X2 @ X1)) = $false) | ($false = (rel_s4 @ X3 @ (sK10 @ X0 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X2 @ X1))) | ((string @ X0 @ X3) = $false) | ((exists_in_world @ X1 @ X3) = $false) | ((entry_box @ X1 @ X3) = $false) | ((entry_box @ X1 @ (sK7 @ X0 @ X1)) = $false) | ((exists_in_world @ X1 @ sK6) = $false) | ((rel_s4 @ X4 @ X3) = $false) | ($false = (exists_in_world @ X0 @ X3)) | ($false = (userid @ u @ X0 @ (sK7 @ X0 @ X1))) | ($false = (number @ X1 @ one @ (sK7 @ X0 @ X1))) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ (sK3 @ X2 @ X0 @ X3 @ X1) @ sK6) = $false) | ($false = (exists_in_world @ X2 @ X3)) | ($false = (exists_in_world @ X0 @ sK6))) )),
% 1.44/0.61    inference(trivial_inequality_removal,[],[f704])).
% 1.44/0.61  thf(f704,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu,X4 : $i] : (($false = (userid @ u @ X0 @ (sK7 @ X0 @ X1))) | ((entry_box @ X1 @ X3) = $false) | ((rel_s4 @ X4 @ X3) = $false) | ((string @ X0 @ X3) = $false) | ((exists_in_world @ X1 @ sK6) = $false) | ((exists_in_world @ (sK3 @ X2 @ X0 @ X3 @ X1) @ sK6) = $false) | ($false = (exists_in_world @ X2 @ X3)) | ((entry_box @ X1 @ (sK7 @ X0 @ X1)) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (number @ X1 @ one @ (sK7 @ X0 @ X1))) | ($false = $true) | ((exists_in_world @ (sK11 @ X0 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X2 @ X1) @ (sK10 @ X0 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X2 @ X1)) = $false) | ($false = (exists_in_world @ X0 @ sK6)) | ((exists_in_world @ X1 @ X3) = $false) | ($false = (exists_in_world @ X0 @ X3)) | ($false = (rel_s4 @ X3 @ (sK10 @ X0 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X2 @ X1)))) )),
% 1.44/0.61    inference(duplicate_literal_removal,[],[f700])).
% 1.44/0.61  thf(f700,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu,X4 : $i] : (($false = (rel_s4 @ X3 @ (sK10 @ X0 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X2 @ X1))) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (exists_in_world @ X2 @ X3)) | ((exists_in_world @ (sK3 @ X2 @ X0 @ X3 @ X1) @ sK6) = $false) | ((rel_s4 @ X4 @ X3) = $false) | ($false = (exists_in_world @ X0 @ X3)) | ((exists_in_world @ X1 @ X3) = $false) | ((string @ X0 @ X3) = $false) | ($false = (exists_in_world @ X0 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (number @ X1 @ one @ (sK7 @ X0 @ X1))) | ($false = (exists_in_world @ X2 @ sK6)) | ((entry_box @ X1 @ (sK7 @ X0 @ X1)) = $false) | ((entry_box @ X1 @ X3) = $false) | ((entry_box @ X1 @ (sK7 @ X0 @ X1)) = $false) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = $true) | ($false = (exists_in_world @ X0 @ sK6)) | ($false = (number @ X1 @ one @ (sK7 @ X0 @ X1))) | ($false = (userid @ u @ X0 @ (sK7 @ X0 @ X1))) | ($false = (userid @ u @ X0 @ (sK7 @ X0 @ X1))) | ((exists_in_world @ (sK11 @ X0 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X2 @ X1) @ (sK10 @ X0 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X2 @ X1)) = $false) | ((exists_in_world @ (sK3 @ X2 @ X0 @ X3 @ X1) @ sK6) = $false)) )),
% 1.44/0.61    inference(superposition,[],[f467,f342])).
% 1.44/0.61  thf(f342,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (in @ X1 @ X2 @ (sK11 @ X1 @ X3 @ X4 @ X2) @ (sK10 @ X1 @ X3 @ X4 @ X2))) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X4 @ sK6) = $false) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X3 @ sK6)) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | ($false = (entry_box @ X2 @ (sK7 @ X1 @ X2))) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2)))) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f340])).
% 1.44/0.61  thf(f340,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ X4 @ sK6) = $false) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | (((~ (do @ X4 @ X3 @ (sK11 @ X1 @ X3 @ X4 @ X2) @ (sK10 @ X1 @ X3 @ X4 @ X2))) | (in @ X1 @ X2 @ (sK11 @ X1 @ X3 @ X4 @ X2) @ (sK10 @ X1 @ X3 @ X4 @ X2))) = $false) | ($false = (exists_in_world @ X3 @ sK6)) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (entry_box @ X2 @ (sK7 @ X1 @ X2))) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((exists_in_world @ X1 @ sK6) = $false)) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f339])).
% 1.44/0.61  thf(f467,plain,(
% 1.44/0.61    ( ! [X2 : $i,X3 : mu,X0 : mu,X1 : mu,X6 : $i,X4 : mu,X5 : mu] : (((in @ X1 @ X3 @ (sK11 @ X4 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X0 @ X5) @ (sK10 @ X4 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X0 @ X5)) = $true) | ($false = (exists_in_world @ X3 @ X2)) | ((entry_box @ X3 @ X2) = $false) | ($false = (exists_in_world @ X0 @ sK6)) | ((rel_s4 @ X6 @ X2) = $false) | ((string @ X1 @ X2) = $false) | ($false = (exists_in_world @ (sK11 @ X4 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X0 @ X5) @ (sK10 @ X4 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X0 @ X5))) | ((exists_in_world @ X0 @ X2) = $false) | ((number @ X5 @ one @ (sK7 @ X4 @ X5)) = $false) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X5 @ sK6)) | ((exists_in_world @ X1 @ X2) = $false) | ((rel_s4 @ X2 @ (sK10 @ X4 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X0 @ X5)) = $false) | ($false = (exists_in_world @ (sK3 @ X0 @ X1 @ X2 @ X3) @ sK6)) | ($false = (entry_box @ X5 @ (sK7 @ X4 @ X5))) | ($false = (userid @ u @ X4 @ (sK7 @ X4 @ X5)))) )),
% 1.44/0.61    inference(trivial_inequality_removal,[],[f464])).
% 1.44/0.61  thf(f464,plain,(
% 1.44/0.61    ( ! [X2 : $i,X3 : mu,X0 : mu,X1 : mu,X6 : $i,X4 : mu,X5 : mu] : (((in @ X1 @ X3 @ (sK11 @ X4 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X0 @ X5) @ (sK10 @ X4 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X0 @ X5)) = $true) | ((string @ X1 @ X2) = $false) | ($false = (exists_in_world @ (sK3 @ X0 @ X1 @ X2 @ X3) @ sK6)) | ((exists_in_world @ X4 @ sK6) = $false) | ((rel_s4 @ X2 @ (sK10 @ X4 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X0 @ X5)) = $false) | ((number @ X5 @ one @ (sK7 @ X4 @ X5)) = $false) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ X5 @ sK6)) | ((exists_in_world @ X1 @ X2) = $false) | ((exists_in_world @ X0 @ X2) = $false) | ($false = (exists_in_world @ (sK11 @ X4 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X0 @ X5) @ (sK10 @ X4 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X0 @ X5))) | ($false = $true) | ((rel_s4 @ X6 @ X2) = $false) | ($false = (userid @ u @ X4 @ (sK7 @ X4 @ X5))) | ($false = (entry_box @ X5 @ (sK7 @ X4 @ X5))) | ($false = (exists_in_world @ X0 @ sK6)) | ((entry_box @ X3 @ X2) = $false)) )),
% 1.44/0.61    inference(superposition,[],[f344,f259])).
% 1.44/0.61  thf(f259,plain,(
% 1.44/0.61    ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X7 : mu,X4 : mu,X5 : mu] : (($false = (do @ X3 @ (sK3 @ X3 @ X4 @ X2 @ X5) @ X7 @ X6)) | ($false = (rel_s4 @ X1 @ X2)) | ((in @ X4 @ X5 @ X7 @ X6) = $true) | ($false = (string @ X4 @ X2)) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ X2 @ X6) = $false) | ((exists_in_world @ X7 @ X6) = $false) | ($false = (entry_box @ X5 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ((exists_in_world @ X5 @ X2) = $false)) )),
% 1.44/0.61    inference(not_proxy_clausification,[],[f258])).
% 1.44/0.61  thf(f258,plain,(
% 1.44/0.61    ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X7 : mu,X4 : mu,X5 : mu] : (((rel_s4 @ X2 @ X6) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (rel_s4 @ X1 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (entry_box @ X5 @ X2)) | ((exists_in_world @ X7 @ X6) = $false) | ($false = (string @ X4 @ X2)) | ((in @ X4 @ X5 @ X7 @ X6) = $true) | ((exists_in_world @ X5 @ X2) = $false) | ((~ (do @ X3 @ (sK3 @ X3 @ X4 @ X2 @ X5) @ X7 @ X6)) = $true)) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f257])).
% 1.44/0.61  thf(f257,plain,(
% 1.44/0.61    ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X7 : mu,X4 : mu,X5 : mu] : (((exists_in_world @ X7 @ X6) = $false) | ($false = (entry_box @ X5 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ($true = ((~ (do @ X3 @ (sK3 @ X3 @ X4 @ X2 @ X5) @ X7 @ X6)) | (in @ X4 @ X5 @ X7 @ X6))) | ($false = (exists_in_world @ X4 @ X2)) | ((exists_in_world @ X5 @ X2) = $false) | ((rel_s4 @ X2 @ X6) = $false) | ($false = (string @ X4 @ X2)) | ($false = (rel_s4 @ X1 @ X2))) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f256])).
% 1.44/0.61  thf(f256,plain,(
% 1.44/0.61    ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X7 : mu,X4 : mu,X5 : mu] : ((((exists_in_world @ X7 @ X6) => ((~ (do @ X3 @ (sK3 @ X3 @ X4 @ X2 @ X5) @ X7 @ X6)) | (in @ X4 @ X5 @ X7 @ X6))) = $true) | ($false = (string @ X4 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ((rel_s4 @ X2 @ X6) = $false) | ((exists_in_world @ X5 @ X2) = $false) | ($false = (rel_s4 @ X1 @ X2)) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (entry_box @ X5 @ X2))) )),
% 1.44/0.61    inference(beta_eta_normalization,[],[f255])).
% 1.44/0.61  thf(f255,plain,(
% 1.44/0.61    ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X7 : mu,X4 : mu,X5 : mu] : (($false = (entry_box @ X5 @ X2)) | ($false = (rel_s4 @ X1 @ X2)) | ((exists_in_world @ X5 @ X2) = $false) | ($false = (string @ X4 @ X2)) | ((rel_s4 @ X2 @ X6) = $false) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ X6) => ((~ (do @ X3 @ (sK3 @ X3 @ X4 @ X2 @ X5) @ Y0 @ X6)) | (in @ X4 @ X5 @ Y0 @ X6)))) @ X7) = $true) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ X4 @ X2))) )),
% 1.44/0.61    inference(pi_clausification,[],[f254])).
% 1.44/0.61  thf(f254,plain,(
% 1.44/0.61    ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X4 : mu,X5 : mu] : (($false = (entry_box @ X5 @ X2)) | ($false = (rel_s4 @ X1 @ X2)) | ($true = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X6) => ((~ (do @ X3 @ (sK3 @ X3 @ X4 @ X2 @ X5) @ Y0 @ X6)) | (in @ X4 @ X5 @ Y0 @ X6)))))) | ((rel_s4 @ X2 @ X6) = $false) | ($false = (string @ X4 @ X2)) | ((exists_in_world @ X5 @ X2) = $false) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ X4 @ X2))) )),
% 1.44/0.61    inference(not_proxy_clausification,[],[f253])).
% 1.44/0.61  thf(f253,plain,(
% 1.44/0.61    ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (entry_box @ X5 @ X2)) | ($true = (~ (rel_s4 @ X2 @ X6))) | ($false = (string @ X4 @ X2)) | ($true = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X6) => ((~ (do @ X3 @ (sK3 @ X3 @ X4 @ X2 @ X5) @ Y0 @ X6)) | (in @ X4 @ X5 @ Y0 @ X6)))))) | ($false = (rel_s4 @ X1 @ X2)) | ((exists_in_world @ X5 @ X2) = $false)) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f252])).
% 1.44/0.61  thf(f252,plain,(
% 1.44/0.61    ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X3 @ X2)) | ($false = (entry_box @ X5 @ X2)) | ($true = ((~ (rel_s4 @ X2 @ X6)) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X6) => ((~ (do @ X3 @ (sK3 @ X3 @ X4 @ X2 @ X5) @ Y0 @ X6)) | (in @ X4 @ X5 @ Y0 @ X6))))))) | ($false = (rel_s4 @ X1 @ X2)) | ((exists_in_world @ X5 @ X2) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (string @ X4 @ X2))) )),
% 1.44/0.61    inference(beta_eta_normalization,[],[f251])).
% 1.44/0.61  thf(f251,plain,(
% 1.44/0.61    ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X4 : mu,X5 : mu] : (($false = (rel_s4 @ X1 @ X2)) | ($false = (string @ X4 @ X2)) | ($true = ((^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X3 @ (sK3 @ X3 @ X4 @ X2 @ X5) @ Y1 @ Y0)) | (in @ X4 @ X5 @ Y1 @ Y0))))))) @ X6)) | ((exists_in_world @ X5 @ X2) = $false) | ($false = (entry_box @ X5 @ X2)) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (exists_in_world @ X3 @ X2))) )),
% 1.44/0.61    inference(pi_clausification,[],[f250])).
% 1.44/0.61  thf(f250,plain,(
% 1.44/0.61    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X3 @ (sK3 @ X3 @ X4 @ X2 @ X5) @ Y1 @ Y0)) | (in @ X4 @ X5 @ Y1 @ Y0))))))))) | ($false = (rel_s4 @ X1 @ X2)) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (entry_box @ X5 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ((exists_in_world @ X5 @ X2) = $false) | ($false = (string @ X4 @ X2))) )),
% 1.44/0.61    inference(not_proxy_clausification,[],[f249])).
% 1.44/0.61  thf(f249,plain,(
% 1.44/0.61    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (rel_s4 @ X1 @ X2)) | ($false = (entry_box @ X5 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (string @ X4 @ X2)) | ($false = (exists_in_world @ X4 @ X2)) | ((exists_in_world @ X5 @ X2) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X3 @ (sK3 @ X3 @ X4 @ X2 @ X5) @ Y1 @ Y0)) | (in @ X4 @ X5 @ Y1 @ Y0))))))))))) )),
% 1.44/0.61    inference(not_proxy_clausification,[],[f246])).
% 1.44/0.61  thf(f246,plain,(
% 1.44/0.61    ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (rel_s4 @ X1 @ X2)) | ($false = (string @ X4 @ X2)) | ((exists_in_world @ X5 @ X2) = $false) | ($true = (~ (entry_box @ X5 @ X2))) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X3 @ (sK3 @ X3 @ X4 @ X2 @ X5) @ Y1 @ Y0)) | (in @ X4 @ X5 @ Y1 @ Y0))))))))))) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f245])).
% 1.44/0.61  thf(f344,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((do @ X4 @ X3 @ (sK11 @ X1 @ X3 @ X4 @ X2) @ (sK10 @ X1 @ X3 @ X4 @ X2)) = $true) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X4 @ sK6) = $false) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (entry_box @ X2 @ (sK7 @ X1 @ X2))) | ($false = (exists_in_world @ X3 @ sK6)) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false)) )),
% 1.44/0.61    inference(not_proxy_clausification,[],[f343])).
% 1.44/0.61  thf(f343,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X2 @ sK6)) | ($false = (exists_in_world @ X3 @ sK6)) | ((~ (do @ X4 @ X3 @ (sK11 @ X1 @ X3 @ X4 @ X2) @ (sK10 @ X1 @ X3 @ X4 @ X2))) = $false) | ($false = (entry_box @ X2 @ (sK7 @ X1 @ X2))) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((exists_in_world @ X1 @ sK6) = $false) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false)) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f340])).
% 1.44/0.61  thf(f336,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((rel_s4 @ sK6 @ (sK10 @ X1 @ X3 @ X4 @ X2)) = $true) | ($false = (exists_in_world @ X3 @ sK6)) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ((exists_in_world @ X1 @ sK6) = $false) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | ($false = (entry_box @ X2 @ (sK7 @ X1 @ X2))) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6))) )),
% 1.44/0.61    inference(not_proxy_clausification,[],[f335])).
% 1.44/0.61  thf(f335,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X3 @ sK6)) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ((exists_in_world @ X4 @ sK6) = $false) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false) | ($false = (~ (rel_s4 @ sK6 @ (sK10 @ X1 @ X3 @ X4 @ X2)))) | ($false = (entry_box @ X2 @ (sK7 @ X1 @ X2)))) )),
% 1.44/0.61    inference(not_proxy_clausification,[],[f334])).
% 1.44/0.61  thf(f334,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((~ (entry_box @ X2 @ (sK7 @ X1 @ X2))) = $true) | ($false = (userid @ u @ X1 @ (sK7 @ X1 @ X2))) | ($false = (exists_in_world @ X3 @ sK6)) | ($false = (~ (rel_s4 @ sK6 @ (sK10 @ X1 @ X3 @ X4 @ X2)))) | ((exists_in_world @ X1 @ sK6) = $false) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ((number @ X2 @ one @ (sK7 @ X1 @ X2)) = $false)) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f332])).
% 1.44/0.61  thf(f554,plain,(
% 1.44/0.61    ~spl1_4),
% 1.44/0.61    inference(avatar_contradiction_clause,[],[f553])).
% 1.44/0.61  thf(f553,plain,(
% 1.44/0.61    $false | ~spl1_4),
% 1.44/0.61    inference(trivial_inequality_removal,[],[f551])).
% 1.44/0.61  thf(f551,plain,(
% 1.44/0.61    ($false = $true) | ~spl1_4),
% 1.44/0.61    inference(backward_demodulation,[],[f291,f516])).
% 1.44/0.61  thf(f516,plain,(
% 1.44/0.61    ( ! [X3 : $i] : (((rel_s4 @ X3 @ sK6) = $false)) ) | ~spl1_4),
% 1.44/0.61    inference(avatar_component_clause,[],[f515])).
% 1.44/0.61  thf(f291,plain,(
% 1.44/0.61    ($true = (rel_s4 @ sK5 @ sK6))),
% 1.44/0.61    inference(not_proxy_clausification,[],[f290])).
% 1.44/0.61  thf(f290,plain,(
% 1.44/0.61    ($false = (~ (rel_s4 @ sK5 @ sK6)))),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f288])).
% 1.44/0.61  thf(f550,plain,(
% 1.44/0.61    spl1_4 | spl1_6 | spl1_5 | ~spl1_3),
% 1.44/0.61    inference(avatar_split_clause,[],[f537,f512,f544,f547,f515])).
% 1.44/0.61  thf(f512,plain,(
% 1.44/0.61    spl1_3 <=> ! [X2 : mu,X0 : mu,X1 : mu] : (((exists_in_world @ (sK3 @ X0 @ X1 @ sK6 @ X2) @ sK6) = $false) | ($false = (entry_box @ X2 @ sK6)) | ($false = (exists_in_world @ X0 @ sK6)) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true) | ((exists_in_world @ X1 @ sK6) = $false) | ((string @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)))),
% 1.44/0.61    introduced(avatar_definition,[new_symbols(naming,[spl1_3])])).
% 1.44/0.61  thf(f537,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (((string @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ((rel_s4 @ X3 @ sK6) = $false) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (entry_box @ X2 @ sK6)) | ($false = (exists_in_world @ X0 @ sK6)) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true)) ) | ~spl1_3),
% 1.44/0.61    inference(trivial_inequality_removal,[],[f536])).
% 1.44/0.61  thf(f536,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (exists_in_world @ X0 @ sK6)) | ((string @ X1 @ sK6) = $false) | ($false = (entry_box @ X2 @ sK6)) | ($false = $true) | ((rel_s4 @ X3 @ sK6) = $false) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true)) ) | ~spl1_3),
% 1.44/0.61    inference(duplicate_literal_removal,[],[f533])).
% 1.44/0.61  thf(f533,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (($false = (exists_in_world @ X0 @ sK6)) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (entry_box @ X2 @ sK6)) | ($false = $true) | ($false = (exists_in_world @ X0 @ sK6)) | ((rel_s4 @ X3 @ sK6) = $false) | ((string @ X1 @ sK6) = $false) | ((string @ X1 @ sK6) = $false) | ($false = (entry_box @ X2 @ sK6))) ) | ~spl1_3),
% 1.44/0.61    inference(superposition,[],[f513,f248])).
% 1.44/0.61  thf(f513,plain,(
% 1.44/0.61    ( ! [X2 : mu,X0 : mu,X1 : mu] : (((exists_in_world @ (sK3 @ X0 @ X1 @ sK6 @ X2) @ sK6) = $false) | ((string @ X1 @ sK6) = $false) | ($false = (entry_box @ X2 @ sK6)) | ($false = (exists_in_world @ X0 @ sK6)) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true)) ) | ~spl1_3),
% 1.44/0.61    inference(avatar_component_clause,[],[f512])).
% 1.44/0.61  thf(f519,plain,(
% 1.44/0.61    spl1_3 | spl1_4),
% 1.44/0.61    inference(avatar_split_clause,[],[f497,f515,f512])).
% 1.44/0.61  thf(f497,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (((string @ X1 @ sK6) = $false) | ((rel_s4 @ X3 @ sK6) = $false) | ($false = (exists_in_world @ X0 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ((exists_in_world @ (sK3 @ X0 @ X1 @ sK6 @ X2) @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (entry_box @ X2 @ sK6)) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true)) )),
% 1.44/0.61    inference(trivial_inequality_removal,[],[f496])).
% 1.44/0.61  thf(f496,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (((string @ X1 @ sK6) = $false) | ($false = $true) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true) | ($false = (entry_box @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ((exists_in_world @ (sK3 @ X0 @ X1 @ sK6 @ X2) @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (exists_in_world @ X0 @ sK6)) | ((rel_s4 @ X3 @ sK6) = $false)) )),
% 1.44/0.61    inference(duplicate_literal_removal,[],[f491])).
% 1.44/0.61  thf(f491,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true) | ((string @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X0 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (exists_in_world @ X0 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X0 @ sK6)) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = $true) | ((exists_in_world @ (sK3 @ X0 @ X1 @ sK6 @ X2) @ sK6) = $false) | ($false = (entry_box @ X2 @ sK6)) | ((exists_in_world @ (sK3 @ X0 @ X1 @ sK6 @ X2) @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ((rel_s4 @ X3 @ sK6) = $false)) )),
% 1.44/0.61    inference(superposition,[],[f317,f485])).
% 1.44/0.61  thf(f485,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu,X4 : $i] : (($false = (rel_s4 @ X3 @ (sK8 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X0 @ X2 @ X1))) | ((exists_in_world @ X1 @ X3) = $false) | ($false = (exists_in_world @ X0 @ X3)) | ((string @ X0 @ X3) = $false) | ((rel_s4 @ X4 @ X3) = $false) | ((entry_box @ X1 @ X3) = $false) | ($true = (rel_s4 @ sK6 @ (sK7 @ X0 @ X1))) | ($false = (exists_in_world @ X2 @ X3)) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ (sK3 @ X2 @ X0 @ X3 @ X1) @ sK6) = $false) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X0 @ sK6))) )),
% 1.44/0.61    inference(trivial_inequality_removal,[],[f484])).
% 1.44/0.61  thf(f484,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu,X4 : $i] : (((rel_s4 @ X4 @ X3) = $false) | ($false = (rel_s4 @ X3 @ (sK8 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X0 @ X2 @ X1))) | ($false = $true) | ((entry_box @ X1 @ X3) = $false) | ($false = (exists_in_world @ X2 @ X3)) | ((string @ X0 @ X3) = $false) | ((exists_in_world @ (sK3 @ X2 @ X0 @ X3 @ X1) @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (exists_in_world @ X0 @ X3)) | ((exists_in_world @ X1 @ sK6) = $false) | ((exists_in_world @ X1 @ X3) = $false) | ($false = (exists_in_world @ X0 @ sK6)) | ($true = (rel_s4 @ sK6 @ (sK7 @ X0 @ X1)))) )),
% 1.44/0.61    inference(duplicate_literal_removal,[],[f478])).
% 1.44/0.61  thf(f478,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu,X4 : $i] : (((exists_in_world @ (sK3 @ X2 @ X0 @ X3 @ X1) @ sK6) = $false) | ((string @ X0 @ X3) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = $true) | ($false = (exists_in_world @ X2 @ sK6)) | ($true = (rel_s4 @ sK6 @ (sK7 @ X0 @ X1))) | ($false = (exists_in_world @ X0 @ sK6)) | ($false = (exists_in_world @ X0 @ X3)) | ($false = (rel_s4 @ X3 @ (sK8 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X0 @ X2 @ X1))) | ((exists_in_world @ X1 @ sK6) = $false) | ((exists_in_world @ X1 @ X3) = $false) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ X3)) | ($false = (exists_in_world @ X0 @ sK6)) | ((entry_box @ X1 @ X3) = $false) | ((exists_in_world @ (sK3 @ X2 @ X0 @ X3 @ X1) @ sK6) = $false) | ($true = (rel_s4 @ sK6 @ (sK7 @ X0 @ X1))) | ((rel_s4 @ X4 @ X3) = $false)) )),
% 1.44/0.61    inference(superposition,[],[f321,f474])).
% 1.44/0.61  thf(f474,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu,X4 : $i] : (($false = (exists_in_world @ (sK9 @ X0 @ X1 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X2) @ (sK8 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X0 @ X2 @ X1))) | ($false = (exists_in_world @ X0 @ sK6)) | ($false = (exists_in_world @ X2 @ sK6)) | ((string @ X0 @ X3) = $false) | ((entry_box @ X1 @ X3) = $false) | ($false = (exists_in_world @ X2 @ X3)) | ((exists_in_world @ X1 @ sK6) = $false) | ((rel_s4 @ X4 @ X3) = $false) | ((exists_in_world @ X1 @ X3) = $false) | ($false = (exists_in_world @ X0 @ X3)) | ($false = (rel_s4 @ X3 @ (sK8 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X0 @ X2 @ X1))) | ($true = (rel_s4 @ sK6 @ (sK7 @ X0 @ X1))) | ((exists_in_world @ (sK3 @ X2 @ X0 @ X3 @ X1) @ sK6) = $false)) )),
% 1.44/0.61    inference(trivial_inequality_removal,[],[f473])).
% 1.44/0.61  thf(f473,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu,X4 : $i] : (($true = (rel_s4 @ sK6 @ (sK7 @ X0 @ X1))) | ((rel_s4 @ X4 @ X3) = $false) | ($false = (exists_in_world @ (sK9 @ X0 @ X1 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X2) @ (sK8 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X0 @ X2 @ X1))) | ($false = (rel_s4 @ X3 @ (sK8 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X0 @ X2 @ X1))) | ($false = $true) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (exists_in_world @ X2 @ X3)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X0 @ X3)) | ($false = (exists_in_world @ X0 @ sK6)) | ((exists_in_world @ X1 @ X3) = $false) | ((string @ X0 @ X3) = $false) | ((exists_in_world @ (sK3 @ X2 @ X0 @ X3 @ X1) @ sK6) = $false) | ((entry_box @ X1 @ X3) = $false)) )),
% 1.44/0.61    inference(duplicate_literal_removal,[],[f470])).
% 1.44/0.61  thf(f470,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu,X4 : $i] : (($false = (exists_in_world @ (sK9 @ X0 @ X1 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X2) @ (sK8 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X0 @ X2 @ X1))) | ($false = (exists_in_world @ X0 @ X3)) | ((exists_in_world @ (sK3 @ X2 @ X0 @ X3 @ X1) @ sK6) = $false) | ((exists_in_world @ X1 @ X3) = $false) | ($false = (exists_in_world @ X2 @ X3)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X0 @ sK6)) | ((exists_in_world @ (sK3 @ X2 @ X0 @ X3 @ X1) @ sK6) = $false) | ((exists_in_world @ X1 @ sK6) = $false) | ($true = (rel_s4 @ sK6 @ (sK7 @ X0 @ X1))) | ($true = (rel_s4 @ sK6 @ (sK7 @ X0 @ X1))) | ($false = $true) | ((string @ X0 @ X3) = $false) | ((rel_s4 @ X4 @ X3) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ((entry_box @ X1 @ X3) = $false) | ($false = (exists_in_world @ X0 @ sK6)) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (rel_s4 @ X3 @ (sK8 @ (sK3 @ X2 @ X0 @ X3 @ X1) @ X0 @ X2 @ X1)))) )),
% 1.44/0.61    inference(superposition,[],[f322,f459])).
% 1.44/0.61  thf(f459,plain,(
% 1.44/0.61    ( ! [X2 : $i,X3 : mu,X0 : mu,X1 : mu,X6 : $i,X4 : mu,X5 : mu] : (($true = (in @ X1 @ X3 @ (sK9 @ X4 @ X5 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X0) @ (sK8 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X4 @ X0 @ X5))) | ((entry_box @ X3 @ X2) = $false) | ((exists_in_world @ X0 @ X2) = $false) | ((exists_in_world @ (sK9 @ X4 @ X5 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X0) @ (sK8 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X4 @ X0 @ X5)) = $false) | ((string @ X1 @ X2) = $false) | ((rel_s4 @ X6 @ X2) = $false) | ($false = (exists_in_world @ X0 @ sK6)) | ($false = (exists_in_world @ (sK3 @ X0 @ X1 @ X2 @ X3) @ sK6)) | ((exists_in_world @ X1 @ X2) = $false) | ($false = (exists_in_world @ X3 @ X2)) | ((rel_s4 @ sK6 @ (sK7 @ X4 @ X5)) = $true) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X5 @ sK6)) | ((rel_s4 @ X2 @ (sK8 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X4 @ X0 @ X5)) = $false)) )),
% 1.44/0.61    inference(trivial_inequality_removal,[],[f456])).
% 1.44/0.61  thf(f456,plain,(
% 1.44/0.61    ( ! [X2 : $i,X3 : mu,X0 : mu,X1 : mu,X6 : $i,X4 : mu,X5 : mu] : (((exists_in_world @ X1 @ X2) = $false) | ((exists_in_world @ X4 @ sK6) = $false) | ((entry_box @ X3 @ X2) = $false) | ((rel_s4 @ sK6 @ (sK7 @ X4 @ X5)) = $true) | ($false = $true) | ($false = (exists_in_world @ (sK3 @ X0 @ X1 @ X2 @ X3) @ sK6)) | ((rel_s4 @ X6 @ X2) = $false) | ($false = (exists_in_world @ X3 @ X2)) | ((exists_in_world @ (sK9 @ X4 @ X5 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X0) @ (sK8 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X4 @ X0 @ X5)) = $false) | ($false = (exists_in_world @ X5 @ sK6)) | ((exists_in_world @ X0 @ X2) = $false) | ($false = (exists_in_world @ X0 @ sK6)) | ((rel_s4 @ X2 @ (sK8 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X4 @ X0 @ X5)) = $false) | ($true = (in @ X1 @ X3 @ (sK9 @ X4 @ X5 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X0) @ (sK8 @ (sK3 @ X0 @ X1 @ X2 @ X3) @ X4 @ X0 @ X5))) | ((string @ X1 @ X2) = $false)) )),
% 1.44/0.61    inference(superposition,[],[f324,f259])).
% 1.44/0.61  thf(f324,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((do @ X4 @ X3 @ (sK9 @ X1 @ X2 @ X3 @ X4) @ (sK8 @ X3 @ X1 @ X4 @ X2)) = $true) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true) | ((exists_in_world @ X1 @ sK6) = $false) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (exists_in_world @ X3 @ sK6))) )),
% 1.44/0.61    inference(not_proxy_clausification,[],[f323])).
% 1.44/0.61  thf(f323,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true) | ($false = (~ (do @ X4 @ X3 @ (sK9 @ X1 @ X2 @ X3 @ X4) @ (sK8 @ X3 @ X1 @ X4 @ X2)))) | ($false = (exists_in_world @ X3 @ sK6))) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f320])).
% 1.44/0.61  thf(f320,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = ((~ (do @ X4 @ X3 @ (sK9 @ X1 @ X2 @ X3 @ X4) @ (sK8 @ X3 @ X1 @ X4 @ X2))) | (in @ X1 @ X2 @ (sK9 @ X1 @ X2 @ X3 @ X4) @ (sK8 @ X3 @ X1 @ X4 @ X2)))) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X3 @ sK6)) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true)) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f319])).
% 1.44/0.61  thf(f319,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (exists_in_world @ X3 @ sK6)) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true) | ($false = ((exists_in_world @ (sK9 @ X1 @ X2 @ X3 @ X4) @ (sK8 @ X3 @ X1 @ X4 @ X2)) => ((~ (do @ X4 @ X3 @ (sK9 @ X1 @ X2 @ X3 @ X4) @ (sK8 @ X3 @ X1 @ X4 @ X2))) | (in @ X1 @ X2 @ (sK9 @ X1 @ X2 @ X3 @ X4) @ (sK8 @ X3 @ X1 @ X4 @ X2))))) | ((exists_in_world @ X1 @ sK6) = $false)) )),
% 1.44/0.61    inference(beta_eta_normalization,[],[f318])).
% 1.44/0.61  thf(f318,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true) | ($false = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ (sK8 @ X3 @ X1 @ X4 @ X2)) => ((~ (do @ X4 @ X3 @ Y0 @ (sK8 @ X3 @ X1 @ X4 @ X2))) | (in @ X1 @ X2 @ Y0 @ (sK8 @ X3 @ X1 @ X4 @ X2))))) @ (sK9 @ X1 @ X2 @ X3 @ X4))) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X3 @ sK6))) )),
% 1.44/0.61    inference(sigma_clausification,[],[f315])).
% 1.44/0.61  thf(f315,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X3 @ sK6)) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X4 @ sK6) = $false) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ (sK8 @ X3 @ X1 @ X4 @ X2)) => ((~ (do @ X4 @ X3 @ Y0 @ (sK8 @ X3 @ X1 @ X4 @ X2))) | (in @ X1 @ X2 @ Y0 @ (sK8 @ X3 @ X1 @ X4 @ X2)))))))) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f314])).
% 1.44/0.61  thf(f314,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = ((~ (rel_s4 @ sK6 @ (sK8 @ X3 @ X1 @ X4 @ X2))) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ (sK8 @ X3 @ X1 @ X4 @ X2)) => ((~ (do @ X4 @ X3 @ Y0 @ (sK8 @ X3 @ X1 @ X4 @ X2))) | (in @ X1 @ X2 @ Y0 @ (sK8 @ X3 @ X1 @ X4 @ X2)))))))) | ($false = (exists_in_world @ X3 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6))) )),
% 1.44/0.61    inference(beta_eta_normalization,[],[f313])).
% 1.44/0.61  thf(f313,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ X1 @ sK6) = $false) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X3 @ sK6)) | (((^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0))))))) @ (sK8 @ X3 @ X1 @ X4 @ X2)) = $false) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X2 @ sK6))) )),
% 1.44/0.61    inference(sigma_clausification,[],[f312])).
% 1.44/0.61  thf(f312,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0)))))))) = $false) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X3 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X2 @ sK6))) )),
% 1.44/0.61    inference(not_proxy_clausification,[],[f311])).
% 1.44/0.61  thf(f311,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X3 @ sK6)) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (~ (rel_s4 @ sK6 @ (sK7 @ X1 @ X2)))) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0)))))))) = $false)) )),
% 1.44/0.61    inference(not_proxy_clausification,[],[f310])).
% 1.44/0.61  thf(f310,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (do @ X4 @ X3 @ Y1 @ Y0)) | (in @ X1 @ X2 @ Y1 @ Y0))))))))) = $true) | ((exists_in_world @ X4 @ sK6) = $false) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (~ (rel_s4 @ sK6 @ (sK7 @ X1 @ X2)))) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (exists_in_world @ X3 @ sK6))) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f308])).
% 1.44/0.61  thf(f322,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (in @ X1 @ X2 @ (sK9 @ X1 @ X2 @ X3 @ X4) @ (sK8 @ X3 @ X1 @ X4 @ X2))) | ($false = (exists_in_world @ X3 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true)) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f320])).
% 1.44/0.61  thf(f321,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ (sK9 @ X1 @ X2 @ X3 @ X4) @ (sK8 @ X3 @ X1 @ X4 @ X2)) = $true) | ($false = (exists_in_world @ X2 @ sK6)) | ($false = (exists_in_world @ X3 @ sK6)) | ((exists_in_world @ X1 @ sK6) = $false) | ((exists_in_world @ X4 @ sK6) = $false) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true)) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f319])).
% 1.44/0.61  thf(f317,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((rel_s4 @ sK6 @ (sK8 @ X3 @ X1 @ X4 @ X2)) = $true) | ((exists_in_world @ X1 @ sK6) = $false) | ($false = (exists_in_world @ X2 @ sK6)) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X3 @ sK6)) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true)) )),
% 1.44/0.61    inference(not_proxy_clausification,[],[f316])).
% 1.44/0.61  thf(f316,plain,(
% 1.44/0.61    ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ X1 @ sK6) = $false) | ((exists_in_world @ X4 @ sK6) = $false) | ($false = (exists_in_world @ X3 @ sK6)) | ($false = (~ (rel_s4 @ sK6 @ (sK8 @ X3 @ X1 @ X4 @ X2)))) | ((rel_s4 @ sK6 @ (sK7 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X2 @ sK6))) )),
% 1.44/0.61    inference(binary_proxy_clausification,[],[f314])).
% 1.44/0.61  % SZS output end Proof for Vampire---4
% 1.44/0.61  % (21408)------------------------------
% 1.44/0.61  % (21408)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.44/0.61  % (21408)Termination reason: Refutation
% 1.44/0.61  
% 1.44/0.61  % (21408)Memory used [KB]: 6908
% 1.44/0.61  % (21408)Time elapsed: 0.135 s
% 1.44/0.61  % (21408)Instructions burned: 290 (million)
% 1.44/0.61  % (21408)------------------------------
% 1.44/0.61  % (21408)------------------------------
% 1.44/0.61  % (21372)Success in time 0.229 s
% 1.44/0.61  % Vampire---4.8 exiting
%------------------------------------------------------------------------------