%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU488^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n025.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 : Tue May 21 03:49:07 EDT 2024

% Result   : Theorem 1.34s 0.54s
% Output   : Refutation 1.34s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEU488^1 : TPTP v8.2.0. Released v3.6.0.
% 0.07/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n025.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sun May 19 17:17:08 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.15/0.37  This is a TH0_THM_EQU_NAR problem
% 0.15/0.37  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.39  % (23151)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.15/0.39  % (23149)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.39  % (23150)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.39  % (23146)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.39  % (23148)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 theBenchmark for (2999ds/27Mi)
% 0.15/0.39  % (23152)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.39  % (23147)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 theBenchmark for (2999ds/4Mi)
% 0.15/0.39  % (23154)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.39  % (23150)Instruction limit reached!
% 0.15/0.39  % (23150)------------------------------
% 0.15/0.39  % (23150)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39  % (23150)Termination reason: Unknown
% 0.15/0.39  % (23150)Termination phase: shuffling
% 0.15/0.39  
% 0.15/0.39  % (23150)Memory used [KB]: 1023
% 0.15/0.39  % (23150)Time elapsed: 0.003 s
% 0.15/0.39  % (23150)Instructions burned: 2 (million)
% 0.15/0.39  % (23150)------------------------------
% 0.15/0.39  % (23150)------------------------------
% 0.15/0.39  % (23149)Instruction limit reached!
% 0.15/0.39  % (23149)------------------------------
% 0.15/0.39  % (23149)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39  % (23149)Termination reason: Unknown
% 0.15/0.39  % (23149)Termination phase: shuffling
% 0.15/0.39  
% 0.15/0.39  % (23149)Memory used [KB]: 1023
% 0.15/0.39  % (23149)Time elapsed: 0.003 s
% 0.15/0.39  % (23149)Instructions burned: 3 (million)
% 0.15/0.39  % (23149)------------------------------
% 0.15/0.39  % (23149)------------------------------
% 0.15/0.39  % (23154)Instruction limit reached!
% 0.15/0.39  % (23154)------------------------------
% 0.15/0.39  % (23154)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39  % (23154)Termination reason: Unknown
% 0.15/0.39  % (23154)Termination phase: shuffling
% 0.15/0.39  
% 0.15/0.39  % (23154)Memory used [KB]: 1023
% 0.15/0.39  % (23154)Time elapsed: 0.004 s
% 0.15/0.39  % (23154)Instructions burned: 4 (million)
% 0.15/0.39  % (23154)------------------------------
% 0.15/0.39  % (23154)------------------------------
% 0.15/0.39  % (23147)Instruction limit reached!
% 0.15/0.39  % (23147)------------------------------
% 0.15/0.39  % (23147)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39  % (23147)Termination reason: Unknown
% 0.15/0.39  % (23147)Termination phase: Property scanning
% 0.15/0.39  
% 0.15/0.39  % (23147)Memory used [KB]: 1023
% 0.15/0.39  % (23147)Time elapsed: 0.004 s
% 0.15/0.39  % (23147)Instructions burned: 5 (million)
% 0.15/0.39  % (23147)------------------------------
% 0.15/0.39  % (23147)------------------------------
% 0.23/0.39  % (23151)Refutation not found, incomplete strategy
% 0.23/0.39  % (23151)------------------------------
% 0.23/0.39  % (23151)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39  % (23151)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.39  
% 0.23/0.39  
% 0.23/0.39  % (23151)Memory used [KB]: 5628
% 0.23/0.39  % (23151)Time elapsed: 0.008 s
% 0.23/0.39  % (23151)Instructions burned: 9 (million)
% 0.23/0.39  % (23151)------------------------------
% 0.23/0.39  % (23151)------------------------------
% 0.23/0.40  % (23152)Instruction limit reached!
% 0.23/0.40  % (23152)------------------------------
% 0.23/0.40  % (23152)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40  % (23152)Termination reason: Unknown
% 0.23/0.40  % (23152)Termination phase: Saturation
% 0.23/0.40  
% 0.23/0.40  % (23152)Memory used [KB]: 5628
% 0.23/0.40  % (23152)Time elapsed: 0.011 s
% 0.23/0.40  % (23152)Instructions burned: 20 (million)
% 0.23/0.40  % (23152)------------------------------
% 0.23/0.40  % (23152)------------------------------
% 0.23/0.40  % (23148)Instruction limit reached!
% 0.23/0.40  % (23148)------------------------------
% 0.23/0.40  % (23148)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40  % (23148)Termination reason: Unknown
% 0.23/0.40  % (23148)Termination phase: Saturation
% 0.23/0.40  
% 0.23/0.40  % (23148)Memory used [KB]: 5628
% 0.23/0.40  % (23148)Time elapsed: 0.014 s
% 0.23/0.40  % (23148)Instructions burned: 27 (million)
% 0.23/0.40  % (23148)------------------------------
% 0.23/0.40  % (23148)------------------------------
% 0.23/0.40  % (23155)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 theBenchmark for (2999ds/37Mi)
% 0.23/0.40  % (23156)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 theBenchmark for (2999ds/15Mi)
% 0.23/0.40  % (23157)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.23/0.40  % (23158)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 theBenchmark for (2999ds/1041Mi)
% 0.23/0.40  % (23157)Instruction limit reached!
% 0.23/0.40  % (23157)------------------------------
% 0.23/0.40  % (23157)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40  % (23157)Termination reason: Unknown
% 0.23/0.40  % (23157)Termination phase: shuffling
% 0.23/0.40  
% 0.23/0.40  % (23157)Memory used [KB]: 1023
% 0.23/0.40  % (23157)Time elapsed: 0.003 s
% 0.23/0.40  % (23157)Instructions burned: 3 (million)
% 0.23/0.40  % (23157)------------------------------
% 0.23/0.40  % (23157)------------------------------
% 0.23/0.41  % (23159)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.23/0.41  % (23156)Instruction limit reached!
% 0.23/0.41  % (23156)------------------------------
% 0.23/0.41  % (23156)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.41  % (23156)Termination reason: Unknown
% 0.23/0.41  % (23156)Termination phase: Saturation
% 0.23/0.41  
% 0.23/0.41  % (23156)Memory used [KB]: 5628
% 0.23/0.41  % (23156)Time elapsed: 0.009 s
% 0.23/0.41  % (23156)Instructions burned: 16 (million)
% 0.23/0.41  % (23156)------------------------------
% 0.23/0.41  % (23156)------------------------------
% 0.23/0.41  % (23160)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.23/0.41  % (23159)Instruction limit reached!
% 0.23/0.41  % (23159)------------------------------
% 0.23/0.41  % (23159)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.41  % (23159)Termination reason: Unknown
% 0.23/0.41  % (23159)Termination phase: SInE selection
% 0.23/0.41  
% 0.23/0.41  % (23159)Memory used [KB]: 1023
% 0.23/0.41  % (23159)Time elapsed: 0.005 s
% 0.23/0.41  % (23159)Instructions burned: 7 (million)
% 0.23/0.41  % (23159)------------------------------
% 0.23/0.41  % (23159)------------------------------
% 0.23/0.41  % (23161)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 theBenchmark for (2999ds/3Mi)
% 0.23/0.42  % (23161)Instruction limit reached!
% 0.23/0.42  % (23161)------------------------------
% 0.23/0.42  % (23161)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.42  % (23161)Termination reason: Unknown
% 0.23/0.42  % (23161)Termination phase: shuffling
% 0.23/0.42  
% 0.23/0.42  % (23161)Memory used [KB]: 1023
% 0.23/0.42  % (23161)Time elapsed: 0.004 s
% 0.23/0.42  % (23161)Instructions burned: 4 (million)
% 0.23/0.42  % (23161)------------------------------
% 0.23/0.42  % (23161)------------------------------
% 0.23/0.42  % (23160)Instruction limit reached!
% 0.23/0.42  % (23160)------------------------------
% 0.23/0.42  % (23160)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.42  % (23160)Termination reason: Unknown
% 0.23/0.42  % (23160)Termination phase: Saturation
% 0.23/0.42  
% 0.23/0.42  % (23160)Memory used [KB]: 5756
% 0.23/0.42  % (23160)Time elapsed: 0.010 s
% 0.23/0.42  % (23160)Instructions burned: 16 (million)
% 0.23/0.42  % (23160)------------------------------
% 0.23/0.42  % (23160)------------------------------
% 0.23/0.42  % (23162)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 theBenchmark for (2999ds/3Mi)
% 0.23/0.42  % (23155)Instruction limit reached!
% 0.23/0.42  % (23155)------------------------------
% 0.23/0.42  % (23155)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.42  % (23155)Termination reason: Unknown
% 0.23/0.42  % (23155)Termination phase: Saturation
% 0.23/0.42  
% 0.23/0.42  % (23155)Memory used [KB]: 5628
% 0.23/0.42  % (23155)Time elapsed: 0.019 s
% 0.23/0.42  % (23155)Instructions burned: 38 (million)
% 0.23/0.42  % (23155)------------------------------
% 0.23/0.42  % (23155)------------------------------
% 0.23/0.42  % (23162)Instruction limit reached!
% 0.23/0.42  % (23162)------------------------------
% 0.23/0.42  % (23162)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.42  % (23162)Termination reason: Unknown
% 0.23/0.42  % (23162)Termination phase: Property scanning
% 0.23/0.42  
% 0.23/0.42  % (23162)Memory used [KB]: 1023
% 0.23/0.42  % (23162)Time elapsed: 0.004 s
% 0.23/0.42  % (23162)Instructions burned: 4 (million)
% 0.23/0.42  % (23162)------------------------------
% 0.23/0.42  % (23162)------------------------------
% 0.23/0.42  % (23163)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.23/0.43  % (23164)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.23/0.43  % (23164)Instruction limit reached!
% 0.23/0.43  % (23164)------------------------------
% 0.23/0.43  % (23164)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.43  % (23164)Termination reason: Unknown
% 0.23/0.43  % (23164)Termination phase: shuffling
% 0.23/0.43  
% 0.23/0.43  % (23164)Memory used [KB]: 1023
% 0.23/0.43  % (23164)Time elapsed: 0.003 s
% 0.23/0.43  % (23164)Instructions burned: 3 (million)
% 0.23/0.43  % (23164)------------------------------
% 0.23/0.43  % (23164)------------------------------
% 0.23/0.43  % (23163)Instruction limit reached!
% 0.23/0.43  % (23163)------------------------------
% 0.23/0.43  % (23163)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.43  % (23163)Termination reason: Unknown
% 0.23/0.43  % (23163)Termination phase: Property scanning
% 0.23/0.43  
% 0.23/0.43  % (23163)Memory used [KB]: 1023
% 0.23/0.43  % (23163)Time elapsed: 0.005 s
% 0.23/0.43  % (23163)Instructions burned: 7 (million)
% 0.23/0.43  % (23163)------------------------------
% 0.23/0.43  % (23163)------------------------------
% 0.23/0.43  % (23165)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.23/0.43  % (23165)Instruction limit reached!
% 0.23/0.43  % (23165)------------------------------
% 0.23/0.43  % (23165)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.43  % (23165)Termination reason: Unknown
% 0.23/0.43  % (23165)Termination phase: Property scanning
% 0.23/0.43  
% 0.23/0.43  % (23165)Memory used [KB]: 1023
% 0.23/0.43  % (23165)Time elapsed: 0.004 s
% 0.23/0.43  % (23165)Instructions burned: 5 (million)
% 0.23/0.43  % (23165)------------------------------
% 0.23/0.43  % (23165)------------------------------
% 0.23/0.43  % (23166)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.23/0.43  % (23167)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.23/0.44  % (23168)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.23/0.44  % (23168)Instruction limit reached!
% 0.23/0.44  % (23168)------------------------------
% 0.23/0.44  % (23168)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.44  % (23168)Termination reason: Unknown
% 0.23/0.44  % (23168)Termination phase: Property scanning
% 0.23/0.44  
% 0.23/0.44  % (23168)Memory used [KB]: 1023
% 0.23/0.44  % (23168)Time elapsed: 0.005 s
% 0.23/0.44  % (23168)Instructions burned: 6 (million)
% 0.23/0.44  % (23168)------------------------------
% 0.23/0.44  % (23168)------------------------------
% 0.23/0.44  % (23169)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 theBenchmark for (2999ds/902Mi)
% 0.23/0.44  % (23170)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 theBenchmark for (2999ds/21Mi)
% 0.23/0.44  % (23167)Refutation not found, incomplete strategy
% 0.23/0.44  % (23167)------------------------------
% 0.23/0.44  % (23167)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.44  % (23167)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.44  
% 0.23/0.44  
% 0.23/0.44  % (23167)Memory used [KB]: 5628
% 0.23/0.44  % (23167)Time elapsed: 0.010 s
% 0.23/0.44  % (23167)Instructions burned: 15 (million)
% 0.23/0.44  % (23167)------------------------------
% 0.23/0.44  % (23167)------------------------------
% 0.23/0.44  % (23166)Instruction limit reached!
% 0.23/0.44  % (23166)------------------------------
% 0.23/0.44  % (23166)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.44  % (23166)Termination reason: Unknown
% 0.23/0.44  % (23166)Termination phase: Saturation
% 0.23/0.44  
% 0.23/0.44  % (23166)Memory used [KB]: 5628
% 0.23/0.44  % (23166)Time elapsed: 0.012 s
% 0.23/0.44  % (23166)Instructions burned: 19 (million)
% 0.23/0.44  % (23166)------------------------------
% 0.23/0.44  % (23166)------------------------------
% 0.23/0.45  % (23169)Refutation not found, incomplete strategy
% 0.23/0.45  % (23169)------------------------------
% 0.23/0.45  % (23169)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.45  % (23169)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.45  
% 0.23/0.45  
% 0.23/0.45  % (23169)Memory used [KB]: 5628
% 0.23/0.45  % (23169)Time elapsed: 0.007 s
% 0.23/0.45  % (23169)Instructions burned: 10 (million)
% 0.23/0.45  % (23169)------------------------------
% 0.23/0.45  % (23169)------------------------------
% 0.23/0.45  % (23171)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.23/0.45  % (23171)Instruction limit reached!
% 0.23/0.45  % (23171)------------------------------
% 0.23/0.45  % (23171)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.45  % (23171)Termination reason: Unknown
% 0.23/0.45  % (23171)Termination phase: Property scanning
% 0.23/0.45  
% 0.23/0.45  % (23171)Memory used [KB]: 1023
% 0.23/0.45  % (23171)Time elapsed: 0.004 s
% 0.23/0.45  % (23171)Instructions burned: 5 (million)
% 0.23/0.45  % (23171)------------------------------
% 0.23/0.45  % (23171)------------------------------
% 0.23/0.45  % (23172)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 theBenchmark for (2999ds/6Mi)
% 0.23/0.45  % (23170)Instruction limit reached!
% 0.23/0.45  % (23170)------------------------------
% 0.23/0.45  % (23170)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.45  % (23170)Termination reason: Unknown
% 0.23/0.45  % (23170)Termination phase: Saturation
% 0.23/0.45  
% 0.23/0.45  % (23170)Memory used [KB]: 5628
% 0.23/0.45  % (23170)Time elapsed: 0.013 s
% 0.23/0.45  % (23170)Instructions burned: 22 (million)
% 0.23/0.45  % (23170)------------------------------
% 0.23/0.45  % (23170)------------------------------
% 0.23/0.46  % (23172)Instruction limit reached!
% 0.23/0.46  % (23172)------------------------------
% 0.23/0.46  % (23172)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.46  % (23172)Termination reason: Unknown
% 0.23/0.46  % (23172)Termination phase: SInE selection
% 0.23/0.46  
% 0.23/0.46  % (23172)Memory used [KB]: 1023
% 0.23/0.46  % (23172)Time elapsed: 0.005 s
% 0.23/0.46  % (23172)Instructions burned: 6 (million)
% 0.23/0.46  % (23172)------------------------------
% 0.23/0.46  % (23172)------------------------------
% 0.23/0.46  % (23173)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.23/0.46  % (23174)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 theBenchmark for (2999ds/779Mi)
% 0.23/0.46  % (23175)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 theBenchmark for (2999ds/19Mi)
% 0.23/0.46  % (23176)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2999ds/879Mi)
% 0.23/0.47  % (23175)Refutation not found, incomplete strategy
% 0.23/0.47  % (23175)------------------------------
% 0.23/0.47  % (23175)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.47  % (23175)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.47  
% 0.23/0.47  
% 0.23/0.47  % (23175)Memory used [KB]: 5628
% 0.23/0.47  % (23175)Time elapsed: 0.007 s
% 0.23/0.47  % (23175)Instructions burned: 10 (million)
% 0.23/0.47  % (23175)------------------------------
% 0.23/0.47  % (23175)------------------------------
% 0.23/0.47  % (23177)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.23/0.47  % (23178)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.23/0.47  % (23178)Instruction limit reached!
% 0.23/0.47  % (23178)------------------------------
% 0.23/0.47  % (23178)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.47  % (23178)Termination reason: Unknown
% 0.23/0.47  % (23178)Termination phase: shuffling
% 0.23/0.47  
% 0.23/0.47  % (23178)Memory used [KB]: 1023
% 0.23/0.47  % (23178)Time elapsed: 0.004 s
% 0.23/0.47  % (23178)Instructions burned: 4 (million)
% 0.23/0.47  % (23178)------------------------------
% 0.23/0.47  % (23178)------------------------------
% 0.23/0.48  % (23146)Instruction limit reached!
% 0.23/0.48  % (23146)------------------------------
% 0.23/0.48  % (23146)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.48  % (23146)Termination reason: Unknown
% 0.23/0.48  % (23146)Termination phase: Saturation
% 0.23/0.48  
% 0.23/0.48  % (23146)Memory used [KB]: 6524
% 0.23/0.48  % (23146)Time elapsed: 0.090 s
% 0.23/0.48  % (23146)Instructions burned: 183 (million)
% 0.23/0.48  % (23146)------------------------------
% 0.23/0.48  % (23146)------------------------------
% 0.23/0.48  % (23177)Instruction limit reached!
% 0.23/0.48  % (23177)------------------------------
% 0.23/0.48  % (23177)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.48  % (23177)Termination reason: Unknown
% 0.23/0.48  % (23177)Termination phase: Saturation
% 0.23/0.48  
% 0.23/0.48  % (23177)Memory used [KB]: 5628
% 0.23/0.48  % (23177)Time elapsed: 0.010 s
% 0.23/0.48  % (23177)Instructions burned: 18 (million)
% 0.23/0.48  % (23177)------------------------------
% 0.23/0.48  % (23177)------------------------------
% 0.23/0.48  % (23179)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.23/0.49  % (23180)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2999ds/127Mi)
% 0.23/0.49  % (23181)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.23/0.49  % (23182)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 theBenchmark for (2999ds/3Mi)
% 0.23/0.49  % (23182)Instruction limit reached!
% 0.23/0.49  % (23182)------------------------------
% 0.23/0.49  % (23182)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.49  % (23182)Termination reason: Unknown
% 0.23/0.49  % (23182)Termination phase: shuffling
% 0.23/0.49  
% 0.23/0.49  % (23182)Memory used [KB]: 1023
% 0.23/0.49  % (23182)Time elapsed: 0.003 s
% 0.23/0.49  % (23182)Instructions burned: 4 (million)
% 0.23/0.49  % (23182)------------------------------
% 0.23/0.49  % (23182)------------------------------
% 0.23/0.50  % (23179)Instruction limit reached!
% 0.23/0.50  % (23179)------------------------------
% 0.23/0.50  % (23179)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.50  % (23179)Termination reason: Unknown
% 0.23/0.50  % (23179)Termination phase: Saturation
% 0.23/0.50  
% 0.23/0.50  % (23179)Memory used [KB]: 5628
% 0.23/0.50  % (23179)Time elapsed: 0.016 s
% 0.23/0.50  % (23179)Instructions burned: 31 (million)
% 0.23/0.50  % (23179)------------------------------
% 0.23/0.50  % (23179)------------------------------
% 0.23/0.51  % (23183)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 theBenchmark for (2998ds/20Mi)
% 0.23/0.51  % (23184)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 theBenchmark for (2998ds/86Mi)
% 0.23/0.51  % (23183)Refutation not found, incomplete strategy
% 0.23/0.51  % (23183)------------------------------
% 0.23/0.51  % (23183)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.51  % (23183)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.51  
% 0.23/0.51  
% 0.23/0.51  % (23183)Memory used [KB]: 5628
% 0.23/0.51  % (23183)Time elapsed: 0.008 s
% 0.23/0.51  % (23183)Instructions burned: 11 (million)
% 0.23/0.51  % (23183)------------------------------
% 0.23/0.51  % (23183)------------------------------
% 0.23/0.52  % (23158)First to succeed.
% 1.34/0.53  % (23185)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 theBenchmark for (2998ds/107Mi)
% 1.34/0.54  % (23158)Refutation found. Thanks to Tanya!
% 1.34/0.54  % SZS status Theorem for theBenchmark
% 1.34/0.54  % SZS output start Proof for theBenchmark
% 1.34/0.54  thf(func_def_0, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_2, type, inv: ($i > $i > $o) > $i > $i > $o).
% 1.34/0.54  thf(func_def_3, type, idem: (($i > $i > $o) > $i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_4, type, infl: (($i > $i > $o) > $i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_5, type, mono: (($i > $i > $o) > $i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_6, type, refl: ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_7, type, irrefl: ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_8, type, rc: ($i > $i > $o) > $i > $i > $o).
% 1.34/0.54  thf(func_def_9, type, symm: ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_10, type, antisymm: ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_11, type, asymm: ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_12, type, sc: ($i > $i > $o) > $i > $i > $o).
% 1.34/0.54  thf(func_def_13, type, trans: ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_14, type, tc: ($i > $i > $o) > $i > $i > $o).
% 1.34/0.54  thf(func_def_15, type, trc: ($i > $i > $o) > $i > $i > $o).
% 1.34/0.54  thf(func_def_16, type, trsc: ($i > $i > $o) > $i > $i > $o).
% 1.34/0.54  thf(func_def_17, type, po: ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_18, type, so: ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_19, type, total: ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_20, type, term: ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_21, type, ind: ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_22, type, innf: ($i > $i > $o) > $i > $o).
% 1.34/0.54  thf(func_def_23, type, nfof: ($i > $i > $o) > $i > $i > $o).
% 1.34/0.54  thf(func_def_24, type, norm: ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_25, type, join: ($i > $i > $o) > $i > $i > $o).
% 1.34/0.54  thf(func_def_26, type, lconfl: ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_27, type, sconfl: ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_28, type, confl: ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_29, type, cr: ($i > $i > $o) > $o).
% 1.34/0.54  thf(func_def_50, type, ph1: !>[X0: $tType]:(X0)).
% 1.34/0.54  thf(func_def_51, type, sK2: $i > $i > $o).
% 1.34/0.54  thf(func_def_56, type, sK7: $i > $i > $o).
% 1.34/0.54  thf(func_def_57, type, sK8: $i > $i > $o).
% 1.34/0.54  thf(f631,plain,(
% 1.34/0.54    $false),
% 1.34/0.54    inference(avatar_sat_refutation,[],[f176,f393,f630])).
% 1.34/0.54  thf(f630,plain,(
% 1.34/0.54    ~spl0_1),
% 1.34/0.54    inference(avatar_contradiction_clause,[],[f629])).
% 1.34/0.54  thf(f629,plain,(
% 1.34/0.54    $false | ~spl0_1),
% 1.34/0.54    inference(trivial_inequality_removal,[],[f628])).
% 1.34/0.54  thf(f628,plain,(
% 1.34/0.54    ($true = $false) | ~spl0_1),
% 1.34/0.54    inference(forward_demodulation,[],[f622,f505])).
% 1.34/0.54  thf(f505,plain,(
% 1.34/0.54    ((sK7 @ sK4 @ sK3) = $false) | ~spl0_1),
% 1.34/0.54    inference(boolean_simplification,[],[f504])).
% 1.34/0.54  thf(f504,plain,(
% 1.34/0.54    ($false = ($true => (sK7 @ sK4 @ sK3))) | ~spl0_1),
% 1.34/0.54    inference(backward_demodulation,[],[f491,f503])).
% 1.34/0.54  thf(f503,plain,(
% 1.34/0.54    (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK7 @ Y0 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK7 @ Y2 @ Y0) & (sK7 @ Y0 @ Y1)) => (sK7 @ Y2 @ Y1))))))))) = $true) | ~spl0_1),
% 1.34/0.54    inference(binary_proxy_clausification,[],[f491])).
% 1.34/0.54  thf(f491,plain,(
% 1.34/0.54    ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK7 @ Y0 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK7 @ Y2 @ Y0) & (sK7 @ Y0 @ Y1)) => (sK7 @ Y2 @ Y1))))))))) => (sK7 @ sK4 @ sK3))) | ~spl0_1),
% 1.34/0.54    inference(beta_eta_normalization,[],[f472])).
% 1.34/0.54  thf(f472,plain,(
% 1.34/0.54    ($false = ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK3))) @ sK7)) | ~spl0_1),
% 1.34/0.54    inference(sigma_clausification,[],[f421])).
% 1.34/0.54  thf(f421,plain,(
% 1.34/0.54    ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK3))))) | ~spl0_1),
% 1.34/0.54    inference(binary_proxy_clausification,[],[f402])).
% 1.34/0.54  thf(f402,plain,(
% 1.34/0.54    ($false = ((sK4 = sK3) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK3)))))) | ~spl0_1),
% 1.34/0.54    inference(boolean_simplification,[],[f401])).
% 1.34/0.54  thf(f401,plain,(
% 1.34/0.54    ($false = (((sK4 = sK3) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK3))))) & $true)) | ~spl0_1),
% 1.34/0.54    inference(boolean_simplification,[],[f398])).
% 1.34/0.54  thf(f398,plain,(
% 1.34/0.54    ($false = (((sK4 = sK3) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK3))))) & ($true | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK5))))))) | ~spl0_1),
% 1.34/0.54    inference(superposition,[],[f196,f172])).
% 1.34/0.54  thf(f172,plain,(
% 1.34/0.54    ((sK4 = sK5) = $true) | ~spl0_1),
% 1.34/0.54    inference(avatar_component_clause,[],[f171])).
% 1.34/0.54  thf(f171,plain,(
% 1.34/0.54    spl0_1 <=> ((sK4 = sK5) = $true)),
% 1.34/0.54    introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 1.34/0.54  thf(f196,plain,(
% 1.34/0.54    ( ! [X0 : $i] : (($false = (((X0 = sK3) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ X0 @ sK3))))) & ((X0 = sK5) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ X0 @ sK5)))))))) )),
% 1.34/0.54    inference(not_proxy_clausification,[],[f193])).
% 1.34/0.54  thf(f193,plain,(
% 1.34/0.54    ( ! [X0 : $i] : (($true = (~ (((X0 = sK3) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ X0 @ sK3))))) & ((X0 = sK5) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ X0 @ sK5))))))))) )),
% 1.34/0.54    inference(boolean_simplification,[],[f192])).
% 1.34/0.54  thf(f192,plain,(
% 1.34/0.54    ( ! [X0 : $i] : ((((((X0 = sK3) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ X0 @ sK3))))) & ((X0 = sK5) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ X0 @ sK5)))))) => $false) = $true)) )),
% 1.34/0.54    inference(superposition,[],[f180,f155])).
% 1.34/0.54  thf(f155,plain,(
% 1.34/0.54    ($false = (?? @ $i @ (^[Y0 : $i]: (((sK5 = Y0) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK5 @ Y0))))) & ((sK3 = Y0) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK3 @ Y0)))))))))),
% 1.34/0.54    inference(binary_proxy_clausification,[],[f154])).
% 1.34/0.54  thf(f154,plain,(
% 1.34/0.54    ($false = (((sK2 @ sK4 @ sK3) & ((sK4 = sK5) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK5)))))) => (?? @ $i @ (^[Y0 : $i]: (((sK5 = Y0) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK5 @ Y0))))) & ((sK3 = Y0) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK3 @ Y0))))))))))),
% 1.34/0.54    inference(beta_eta_normalization,[],[f153])).
% 1.34/0.54  thf(f153,plain,(
% 1.34/0.54    (((^[Y0 : $i]: (((sK2 @ sK4 @ sK3) & ((sK4 = Y0) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK4 @ Y0)))))) => (?? @ $i @ (^[Y1 : $i]: (((Y0 = Y1) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1))))) & ((sK3 = Y1) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ sK3 @ Y1)))))))))) @ sK5) = $false)),
% 1.34/0.54    inference(sigma_clausification,[],[f152])).
% 1.34/0.54  thf(f152,plain,(
% 1.34/0.54    ((!! @ $i @ (^[Y0 : $i]: (((sK2 @ sK4 @ sK3) & ((sK4 = Y0) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ sK4 @ Y0)))))) => (?? @ $i @ (^[Y1 : $i]: (((Y0 = Y1) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1))))) & ((sK3 = Y1) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ sK3 @ Y1))))))))))) = $false)),
% 1.34/0.54    inference(beta_eta_normalization,[],[f151])).
% 1.34/0.54  thf(f151,plain,(
% 1.34/0.54    ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0 @ sK3) & ((Y0 = Y1) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))))) => (?? @ $i @ (^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2))))) & ((sK3 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ sK3 @ Y2)))))))))))) @ sK4))),
% 1.34/0.54    inference(sigma_clausification,[],[f150])).
% 1.34/0.54  thf(f150,plain,(
% 1.34/0.54    ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0 @ sK3) & ((Y0 = Y1) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1)))))) => (?? @ $i @ (^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2))))) & ((sK3 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ sK3 @ Y2))))))))))))) = $false)),
% 1.34/0.54    inference(beta_eta_normalization,[],[f149])).
% 1.34/0.54  thf(f149,plain,(
% 1.34/0.54    ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2)))))) => (?? @ $i @ (^[Y3 : $i]: (((Y2 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y2 @ Y3))))) & ((Y0 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y0 @ Y3)))))))))))))) @ sK3))),
% 1.34/0.54    inference(sigma_clausification,[],[f143])).
% 1.34/0.54  thf(f143,plain,(
% 1.34/0.54    ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2)))))) => (?? @ $i @ (^[Y3 : $i]: (((Y2 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y2 @ Y3))))) & ((Y0 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y0 @ Y3))))))))))))))))),
% 1.34/0.54    inference(binary_proxy_clausification,[],[f142])).
% 1.34/0.54  thf(f142,plain,(
% 1.34/0.54    ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((Y0 = Y1) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y1))))) & ((Y0 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y2)))))) => (?? @ $i @ (^[Y3 : $i]: (((Y2 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y2 @ Y3))))) & ((Y1 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y1 @ Y3))))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2)))))) => (?? @ $i @ (^[Y3 : $i]: (((Y2 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y2 @ Y3))))) & ((Y0 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y0 @ Y3)))))))))))))))))),
% 1.34/0.54    inference(beta_eta_normalization,[],[f141])).
% 1.34/0.54  thf(f141,plain,(
% 1.34/0.54    ($false = ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y1 @ Y2))))) & ((Y1 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y1 @ Y3)))))) => (?? @ $i @ (^[Y4 : $i]: (((Y3 = Y4) | (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y0 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y3 @ Y4))))) & ((Y2 = Y4) | (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y0 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y2 @ Y4))))))))))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & ((Y2 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y2 @ Y3)))))) => (?? @ $i @ (^[Y4 : $i]: (((Y3 = Y4) | (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y0 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y3 @ Y4))))) & ((Y1 = Y4) | (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y0 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y1 @ Y4))))))))))))))))) @ sK2))),
% 1.34/0.54    inference(sigma_clausification,[],[f138])).
% 1.34/0.54  thf(f138,plain,(
% 1.34/0.54    ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y1 @ Y2))))) & ((Y1 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y1 @ Y3)))))) => (?? @ $i @ (^[Y4 : $i]: (((Y3 = Y4) | (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y0 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y3 @ Y4))))) & ((Y2 = Y4) | (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y0 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y2 @ Y4))))))))))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & ((Y2 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y2 @ Y3)))))) => (?? @ $i @ (^[Y4 : $i]: (((Y3 = Y4) | (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y0 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y3 @ Y4))))) & ((Y1 = Y4) | (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y0 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y1 @ Y4)))))))))))))))))))),
% 1.34/0.54    inference(not_proxy_clausification,[],[f137])).
% 1.34/0.54  thf(f137,plain,(
% 1.34/0.54    ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y1 @ Y2))))) & ((Y1 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y1 @ Y3)))))) => (?? @ $i @ (^[Y4 : $i]: (((Y3 = Y4) | (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y0 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y3 @ Y4))))) & ((Y2 = Y4) | (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y0 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y2 @ Y4))))))))))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & ((Y2 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y2 @ Y3)))))) => (?? @ $i @ (^[Y4 : $i]: (((Y3 = Y4) | (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y0 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y3 @ Y4))))) & ((Y1 = Y4) | (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y0 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y1 @ Y4))))))))))))))))))) = $true)),
% 1.34/0.54    inference(beta_eta_normalization,[],[f136])).
% 1.34/0.54  thf(f136,plain,(
% 1.34/0.54    ($true = (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((^[Y5 : $i > $i > $o]: ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((Y7 = Y8) | (Y6 @ Y7 @ Y8))))))) @ ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (!! @ ($i > $i > $o) @ (^[Y9 : $i > $i > $o]: ((((^[Y10 : $i > $i > $o]: ((^[Y11 : $i > $i > $o]: (!! @ $i @ (^[Y12 : $i]: (!! @ $i @ (^[Y13 : $i]: ((Y10 @ Y12 @ Y13) => (Y11 @ Y12 @ Y13))))))))) @ Y6 @ Y9) & ((^[Y10 : $i > $i > $o]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: (!! @ $i @ (^[Y13 : $i]: (((Y10 @ Y13 @ Y11) & (Y10 @ Y11 @ Y12)) => (Y10 @ Y13 @ Y12))))))))) @ Y9)) => (Y9 @ Y7 @ Y8))))))))) @ Y5))) @ Y1 @ Y2 @ Y3) & ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((Y7 = Y8) | (Y6 @ Y7 @ Y8))))))) @ ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (!! @ ($i > $i > $o) @ (^[Y9 : $i > $i > $o]: ((((^[Y10 : $i > $i > $o]: ((^[Y11 : $i > $i > $o]: (!! @ $i @ (^[Y12 : $i]: (!! @ $i @ (^[Y13 : $i]: ((Y10 @ Y12 @ Y13) => (Y11 @ Y12 @ Y13))))))))) @ Y6 @ Y9) & ((^[Y10 : $i > $i > $o]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: (!! @ $i @ (^[Y13 : $i]: (((Y10 @ Y13 @ Y11) & (Y10 @ Y11 @ Y12)) => (Y10 @ Y13 @ Y12))))))))) @ Y9)) => (Y9 @ Y7 @ Y8))))))))) @ Y5))) @ Y1 @ Y2 @ Y4)) => ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (?? @ $i @ (^[Y8 : $i]: (((^[Y9 : $i > $i > $o]: ((^[Y10 : $i > $i > $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: ((Y11 = Y12) | (Y10 @ Y11 @ Y12))))))) @ ((^[Y10 : $i > $i > $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((((^[Y14 : $i > $i > $o]: ((^[Y15 : $i > $i > $o]: (!! @ $i @ (^[Y16 : $i]: (!! @ $i @ (^[Y17 : $i]: ((Y14 @ Y16 @ Y17) => (Y15 @ Y16 @ Y17))))))))) @ Y10 @ Y13) & ((^[Y14 : $i > $i > $o]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: (!! @ $i @ (^[Y17 : $i]: (((Y14 @ Y17 @ Y15) & (Y14 @ Y15 @ Y16)) => (Y14 @ Y17 @ Y16))))))))) @ Y13)) => (Y13 @ Y11 @ Y12))))))))) @ Y9))) @ Y5 @ Y7 @ Y8) & ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i > $i > $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: ((Y11 = Y12) | (Y10 @ Y11 @ Y12))))))) @ ((^[Y10 : $i > $i > $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((((^[Y14 : $i > $i > $o]: ((^[Y15 : $i > $i > $o]: (!! @ $i @ (^[Y16 : $i]: (!! @ $i @ (^[Y17 : $i]: ((Y14 @ Y16 @ Y17) => (Y15 @ Y16 @ Y17))))))))) @ Y10 @ Y13) & ((^[Y14 : $i > $i > $o]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: (!! @ $i @ (^[Y17 : $i]: (((Y14 @ Y17 @ Y15) & (Y14 @ Y15 @ Y16)) => (Y14 @ Y17 @ Y16))))))))) @ Y13)) => (Y13 @ Y11 @ Y12))))))))) @ Y9))) @ Y5 @ Y6 @ Y8))))))))) @ Y1 @ Y3 @ Y4))))))))) @ Y0) => ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) & ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((Y7 = Y8) | (Y6 @ Y7 @ Y8))))))) @ ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (!! @ ($i > $i > $o) @ (^[Y9 : $i > $i > $o]: ((((^[Y10 : $i > $i > $o]: ((^[Y11 : $i > $i > $o]: (!! @ $i @ (^[Y12 : $i]: (!! @ $i @ (^[Y13 : $i]: ((Y10 @ Y12 @ Y13) => (Y11 @ Y12 @ Y13))))))))) @ Y6 @ Y9) & ((^[Y10 : $i > $i > $o]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: (!! @ $i @ (^[Y13 : $i]: (((Y10 @ Y13 @ Y11) & (Y10 @ Y11 @ Y12)) => (Y10 @ Y13 @ Y12))))))))) @ Y9)) => (Y9 @ Y7 @ Y8))))))))) @ Y5))) @ Y1 @ Y3 @ Y4)) => ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (?? @ $i @ (^[Y8 : $i]: (((^[Y9 : $i > $i > $o]: ((^[Y10 : $i > $i > $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: ((Y11 = Y12) | (Y10 @ Y11 @ Y12))))))) @ ((^[Y10 : $i > $i > $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((((^[Y14 : $i > $i > $o]: ((^[Y15 : $i > $i > $o]: (!! @ $i @ (^[Y16 : $i]: (!! @ $i @ (^[Y17 : $i]: ((Y14 @ Y16 @ Y17) => (Y15 @ Y16 @ Y17))))))))) @ Y10 @ Y13) & ((^[Y14 : $i > $i > $o]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: (!! @ $i @ (^[Y17 : $i]: (((Y14 @ Y17 @ Y15) & (Y14 @ Y15 @ Y16)) => (Y14 @ Y17 @ Y16))))))))) @ Y13)) => (Y13 @ Y11 @ Y12))))))))) @ Y9))) @ Y5 @ Y7 @ Y8) & ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i > $i > $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: ((Y11 = Y12) | (Y10 @ Y11 @ Y12))))))) @ ((^[Y10 : $i > $i > $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((((^[Y14 : $i > $i > $o]: ((^[Y15 : $i > $i > $o]: (!! @ $i @ (^[Y16 : $i]: (!! @ $i @ (^[Y17 : $i]: ((Y14 @ Y16 @ Y17) => (Y15 @ Y16 @ Y17))))))))) @ Y10 @ Y13) & ((^[Y14 : $i > $i > $o]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: (!! @ $i @ (^[Y17 : $i]: (((Y14 @ Y17 @ Y15) & (Y14 @ Y15 @ Y16)) => (Y14 @ Y17 @ Y16))))))))) @ Y13)) => (Y13 @ Y11 @ Y12))))))))) @ Y9))) @ Y5 @ Y6 @ Y8))))))))) @ Y1 @ Y2 @ Y4))))))))) @ Y0))))))),
% 1.34/0.54    inference(definition_unfolding,[],[f112,f134,f133])).
% 1.34/0.54  thf(f133,plain,(
% 1.34/0.54    (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((Y6 = Y7) | (Y5 @ Y6 @ Y7))))))) @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (!! @ ($i > $i > $o) @ (^[Y8 : $i > $i > $o]: ((((^[Y9 : $i > $i > $o]: ((^[Y10 : $i > $i > $o]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: ((Y9 @ Y11 @ Y12) => (Y10 @ Y11 @ Y12))))))))) @ Y5 @ Y8) & ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: (((Y9 @ Y12 @ Y10) & (Y9 @ Y10 @ Y11)) => (Y9 @ Y12 @ Y11))))))))) @ Y8)) => (Y8 @ Y6 @ Y7))))))))) @ Y4))) @ Y0 @ Y2 @ Y3)) => ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((^[Y8 : $i > $i > $o]: ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((Y10 = Y11) | (Y9 @ Y10 @ Y11))))))) @ ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (!! @ ($i > $i > $o) @ (^[Y12 : $i > $i > $o]: ((((^[Y13 : $i > $i > $o]: ((^[Y14 : $i > $i > $o]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: ((Y13 @ Y15 @ Y16) => (Y14 @ Y15 @ Y16))))))))) @ Y9 @ Y12) & ((^[Y13 : $i > $i > $o]: (!! @ $i @ (^[Y14 : $i]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: (((Y13 @ Y16 @ Y14) & (Y13 @ Y14 @ Y15)) => (Y13 @ Y16 @ Y15))))))))) @ Y12)) => (Y12 @ Y10 @ Y11))))))))) @ Y8))) @ Y4 @ Y6 @ Y7) & ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((Y10 = Y11) | (Y9 @ Y10 @ Y11))))))) @ ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (!! @ ($i > $i > $o) @ (^[Y12 : $i > $i > $o]: ((((^[Y13 : $i > $i > $o]: ((^[Y14 : $i > $i > $o]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: ((Y13 @ Y15 @ Y16) => (Y14 @ Y15 @ Y16))))))))) @ Y9 @ Y12) & ((^[Y13 : $i > $i > $o]: (!! @ $i @ (^[Y14 : $i]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: (((Y13 @ Y16 @ Y14) & (Y13 @ Y14 @ Y15)) => (Y13 @ Y16 @ Y15))))))))) @ Y12)) => (Y12 @ Y10 @ Y11))))))))) @ Y8))) @ Y4 @ Y5 @ Y7))))))))) @ Y0 @ Y1 @ Y3))))))))))),
% 1.34/0.54    inference(definition_unfolding,[],[f100,f124,f131])).
% 1.34/0.54  thf(f131,plain,(
% 1.34/0.54    (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((Y6 = Y7) | (Y5 @ Y6 @ Y7))))))) @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (!! @ ($i > $i > $o) @ (^[Y8 : $i > $i > $o]: ((((^[Y9 : $i > $i > $o]: ((^[Y10 : $i > $i > $o]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: ((Y9 @ Y11 @ Y12) => (Y10 @ Y11 @ Y12))))))))) @ Y5 @ Y8) & ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: (((Y9 @ Y12 @ Y10) & (Y9 @ Y10 @ Y11)) => (Y9 @ Y12 @ Y11))))))))) @ Y8)) => (Y8 @ Y6 @ Y7))))))))) @ Y4))) @ Y0 @ Y2 @ Y3) & ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((Y6 = Y7) | (Y5 @ Y6 @ Y7))))))) @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (!! @ ($i > $i > $o) @ (^[Y8 : $i > $i > $o]: ((((^[Y9 : $i > $i > $o]: ((^[Y10 : $i > $i > $o]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: ((Y9 @ Y11 @ Y12) => (Y10 @ Y11 @ Y12))))))))) @ Y5 @ Y8) & ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: (((Y9 @ Y12 @ Y10) & (Y9 @ Y10 @ Y11)) => (Y9 @ Y12 @ Y11))))))))) @ Y8)) => (Y8 @ Y6 @ Y7))))))))) @ Y4))) @ Y0 @ Y1 @ Y3))))))))))),
% 1.34/0.54    inference(definition_unfolding,[],[f104,f124,f124])).
% 1.34/0.54  thf(f104,plain,(
% 1.34/0.54    (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((trc @ Y0 @ Y2 @ Y3) & (trc @ Y0 @ Y1 @ Y3))))))))))),
% 1.34/0.54    inference(cnf_transformation,[],[f62])).
% 1.34/0.54  thf(f62,plain,(
% 1.34/0.54    (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((trc @ Y0 @ Y2 @ Y3) & (trc @ Y0 @ Y1 @ Y3))))))))))),
% 1.34/0.54    inference(fool_elimination,[],[f61])).
% 1.34/0.54  thf(f61,plain,(
% 1.34/0.54    (join = (^[X0 : $i > $i > $o, X1 : $i, X2 : $i] : (? [X3] : ((trc @ X0 @ X1 @ X3) & (trc @ X0 @ X2 @ X3)))))),
% 1.34/0.54    inference(rectify,[],[f25])).
% 1.34/0.54  thf(f25,axiom,(
% 1.34/0.54    (join = (^[X0 : $i > $i > $o, X2 : $i, X3 : $i] : (? [X5] : ((trc @ X0 @ X2 @ X5) & (trc @ X0 @ X3 @ X5)))))),
% 1.34/0.54    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',joinable)).
% 1.34/0.54  thf(f124,plain,(
% 1.34/0.54    (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y2 = Y3) | (Y1 @ Y2 @ Y3))))))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((((^[Y5 : $i > $i > $o]: ((^[Y6 : $i > $i > $o]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y5 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))))) @ Y1 @ Y4) & ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) @ Y4)) => (Y4 @ Y2 @ Y3))))))))) @ Y0))))),
% 1.34/0.54    inference(definition_unfolding,[],[f116,f101,f123])).
% 1.34/0.54  thf(f123,plain,(
% 1.34/0.54    (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))))) @ Y0 @ Y3) & ((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 1.34/0.54    inference(definition_unfolding,[],[f97,f103,f94])).
% 1.34/0.54  thf(f94,plain,(
% 1.34/0.54    (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))))),
% 1.34/0.54    inference(cnf_transformation,[],[f36])).
% 1.34/0.54  thf(f36,plain,(
% 1.34/0.54    (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))))),
% 1.34/0.54    inference(fool_elimination,[],[f35])).
% 1.34/0.54  thf(f35,plain,(
% 1.34/0.54    ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X3 @ X2) & (X0 @ X1 @ X3)) => (X0 @ X1 @ X2)))) = trans)),
% 1.34/0.54    inference(rectify,[],[f13])).
% 1.34/0.54  thf(f13,axiom,(
% 1.34/0.54    ((^[X0 : $i > $i > $o] : (! [X2,X5,X3] : (((X0 @ X3 @ X5) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X5)))) = trans)),
% 1.34/0.54    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive)).
% 1.34/0.54  thf(f103,plain,(
% 1.34/0.54    (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 1.34/0.54    inference(cnf_transformation,[],[f88])).
% 1.34/0.54  thf(f88,plain,(
% 1.34/0.54    (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 1.34/0.54    inference(fool_elimination,[],[f87])).
% 1.34/0.54  thf(f87,plain,(
% 1.34/0.54    (subrel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X3 @ X2) => (X1 @ X3 @ X2)))))),
% 1.34/0.54    inference(rectify,[],[f1])).
% 1.34/0.54  thf(f1,axiom,(
% 1.34/0.54    (subrel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X3,X2] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))))),
% 1.34/0.54    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subrel)).
% 1.34/0.54  thf(f97,plain,(
% 1.34/0.54    (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((subrel @ Y0 @ Y3) & (trans @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 1.34/0.54    inference(cnf_transformation,[],[f86])).
% 1.34/0.54  thf(f86,plain,(
% 1.34/0.54    (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((subrel @ Y0 @ Y3) & (trans @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 1.34/0.54    inference(fool_elimination,[],[f85])).
% 1.34/0.54  thf(f85,plain,(
% 1.34/0.54    ((^[X0 : $i > $i > $o, X1 : $i, X2 : $i] : (! [X3 : $i > $i > $o] : (((trans @ X3) & (subrel @ X0 @ X3)) => (X3 @ X1 @ X2)))) = tc)),
% 1.34/0.54    inference(rectify,[],[f14])).
% 1.34/0.54  thf(f14,axiom,(
% 1.34/0.54    ((^[X0 : $i > $i > $o, X2 : $i, X3 : $i] : (! [X1 : $i > $i > $o] : (((trans @ X1) & (subrel @ X0 @ X1)) => (X1 @ X2 @ X3)))) = tc)),
% 1.34/0.54    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_closure)).
% 1.34/0.54  thf(f101,plain,(
% 1.34/0.54    (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))))),
% 1.34/0.54    inference(cnf_transformation,[],[f44])).
% 1.34/0.54  thf(f44,plain,(
% 1.34/0.54    (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))))),
% 1.34/0.54    inference(fool_elimination,[],[f43])).
% 1.34/0.54  thf(f43,plain,(
% 1.34/0.54    (rc = (^[X0 : $i > $i > $o, X1 : $i, X2 : $i] : ((X0 @ X1 @ X2) | (X1 = X2))))),
% 1.34/0.54    inference(rectify,[],[f8])).
% 1.34/0.54  thf(f8,axiom,(
% 1.34/0.54    (rc = (^[X0 : $i > $i > $o, X2 : $i, X3 : $i] : ((X0 @ X2 @ X3) | (X2 = X3))))),
% 1.34/0.54    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexive_closure)).
% 1.34/0.54  thf(f116,plain,(
% 1.34/0.54    (trc = (^[Y0 : $i > $i > $o]: (rc @ (tc @ Y0))))),
% 1.34/0.54    inference(cnf_transformation,[],[f76])).
% 1.34/0.54  thf(f76,plain,(
% 1.34/0.54    (trc = (^[Y0 : $i > $i > $o]: (rc @ (tc @ Y0))))),
% 1.34/0.54    inference(fool_elimination,[],[f15])).
% 1.34/0.54  thf(f15,axiom,(
% 1.34/0.54    ((^[X0 : $i > $i > $o] : (rc @ (tc @ X0))) = trc)),
% 1.34/0.54    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_reflexive_closure)).
% 1.34/0.54  thf(f100,plain,(
% 1.34/0.54    (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (trc @ Y0 @ Y2 @ Y3)) => (join @ Y0 @ Y1 @ Y3))))))))))),
% 1.34/0.54    inference(cnf_transformation,[],[f69])).
% 1.34/0.54  thf(f69,plain,(
% 1.34/0.54    (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (trc @ Y0 @ Y2 @ Y3)) => (join @ Y0 @ Y1 @ Y3))))))))))),
% 1.34/0.54    inference(fool_elimination,[],[f68])).
% 1.34/0.54  thf(f68,plain,(
% 1.34/0.54    (sconfl = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((trc @ X0 @ X2 @ X1) & (X0 @ X2 @ X3)) => (join @ X0 @ X3 @ X1)))))),
% 1.34/0.54    inference(rectify,[],[f27])).
% 1.34/0.54  thf(f27,axiom,(
% 1.34/0.54    (sconfl = (^[X0 : $i > $i > $o] : (! [X3,X2,X5] : (((trc @ X0 @ X2 @ X3) & (X0 @ X2 @ X5)) => (join @ X0 @ X5 @ X3)))))),
% 1.34/0.54    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',semi_confluent)).
% 1.34/0.54  thf(f134,plain,(
% 1.34/0.54    (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((Y6 = Y7) | (Y5 @ Y6 @ Y7))))))) @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (!! @ ($i > $i > $o) @ (^[Y8 : $i > $i > $o]: ((((^[Y9 : $i > $i > $o]: ((^[Y10 : $i > $i > $o]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: ((Y9 @ Y11 @ Y12) => (Y10 @ Y11 @ Y12))))))))) @ Y5 @ Y8) & ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: (((Y9 @ Y12 @ Y10) & (Y9 @ Y10 @ Y11)) => (Y9 @ Y12 @ Y11))))))))) @ Y8)) => (Y8 @ Y6 @ Y7))))))))) @ Y4))) @ Y0 @ Y1 @ Y2) & ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((Y6 = Y7) | (Y5 @ Y6 @ Y7))))))) @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (!! @ ($i > $i > $o) @ (^[Y8 : $i > $i > $o]: ((((^[Y9 : $i > $i > $o]: ((^[Y10 : $i > $i > $o]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: ((Y9 @ Y11 @ Y12) => (Y10 @ Y11 @ Y12))))))))) @ Y5 @ Y8) & ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: (((Y9 @ Y12 @ Y10) & (Y9 @ Y10 @ Y11)) => (Y9 @ Y12 @ Y11))))))))) @ Y8)) => (Y8 @ Y6 @ Y7))))))))) @ Y4))) @ Y0 @ Y1 @ Y3)) => ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((^[Y8 : $i > $i > $o]: ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((Y10 = Y11) | (Y9 @ Y10 @ Y11))))))) @ ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (!! @ ($i > $i > $o) @ (^[Y12 : $i > $i > $o]: ((((^[Y13 : $i > $i > $o]: ((^[Y14 : $i > $i > $o]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: ((Y13 @ Y15 @ Y16) => (Y14 @ Y15 @ Y16))))))))) @ Y9 @ Y12) & ((^[Y13 : $i > $i > $o]: (!! @ $i @ (^[Y14 : $i]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: (((Y13 @ Y16 @ Y14) & (Y13 @ Y14 @ Y15)) => (Y13 @ Y16 @ Y15))))))))) @ Y12)) => (Y12 @ Y10 @ Y11))))))))) @ Y8))) @ Y4 @ Y6 @ Y7) & ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((Y10 = Y11) | (Y9 @ Y10 @ Y11))))))) @ ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (!! @ ($i > $i > $o) @ (^[Y12 : $i > $i > $o]: ((((^[Y13 : $i > $i > $o]: ((^[Y14 : $i > $i > $o]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: ((Y13 @ Y15 @ Y16) => (Y14 @ Y15 @ Y16))))))))) @ Y9 @ Y12) & ((^[Y13 : $i > $i > $o]: (!! @ $i @ (^[Y14 : $i]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: (((Y13 @ Y16 @ Y14) & (Y13 @ Y14 @ Y15)) => (Y13 @ Y16 @ Y15))))))))) @ Y12)) => (Y12 @ Y10 @ Y11))))))))) @ Y8))) @ Y4 @ Y5 @ Y7))))))))) @ Y0 @ Y2 @ Y3))))))))))),
% 1.34/0.54    inference(definition_unfolding,[],[f107,f124,f124,f131])).
% 1.34/0.54  thf(f107,plain,(
% 1.34/0.54    (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((trc @ Y0 @ Y1 @ Y2) & (trc @ Y0 @ Y1 @ Y3)) => (join @ Y0 @ Y2 @ Y3))))))))))),
% 1.34/0.54    inference(cnf_transformation,[],[f54])).
% 1.34/0.54  thf(f54,plain,(
% 1.34/0.54    (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((trc @ Y0 @ Y1 @ Y2) & (trc @ Y0 @ Y1 @ Y3)) => (join @ Y0 @ Y2 @ Y3))))))))))),
% 1.34/0.54    inference(fool_elimination,[],[f53])).
% 1.34/0.54  thf(f53,plain,(
% 1.34/0.54    (confl = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((trc @ X0 @ X3 @ X1) & (trc @ X0 @ X3 @ X2)) => (join @ X0 @ X2 @ X1)))))),
% 1.34/0.54    inference(rectify,[],[f28])).
% 1.34/0.54  thf(f28,axiom,(
% 1.34/0.54    (confl = (^[X0 : $i > $i > $o] : (! [X3,X5,X2] : (((trc @ X0 @ X2 @ X3) & (trc @ X0 @ X2 @ X5)) => (join @ X0 @ X5 @ X3)))))),
% 1.34/0.54    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',confluent)).
% 1.34/0.54  thf(f112,plain,(
% 1.34/0.54    ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((confl @ Y0) => (sconfl @ Y0))))) = $true)),
% 1.34/0.54    inference(cnf_transformation,[],[f52])).
% 1.34/0.54  thf(f52,plain,(
% 1.34/0.54    ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((confl @ Y0) => (sconfl @ Y0))))) = $true)),
% 1.34/0.54    inference(fool_elimination,[],[f51])).
% 1.34/0.54  thf(f51,plain,(
% 1.34/0.54    ~! [X0 : $i > $i > $o] : ((confl @ X0) => (sconfl @ X0))),
% 1.34/0.54    inference(rectify,[],[f31])).
% 1.34/0.54  thf(f31,negated_conjecture,(
% 1.34/0.54    ~! [X0 : $i > $i > $o] : ((confl @ X0) => (sconfl @ X0))),
% 1.34/0.54    inference(negated_conjecture,[],[f30])).
% 1.34/0.54  thf(f30,conjecture,(
% 1.34/0.54    ! [X0 : $i > $i > $o] : ((confl @ X0) => (sconfl @ X0))),
% 1.34/0.54    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',confluence_implies_semi_confluence)).
% 1.34/0.54  thf(f180,plain,(
% 1.34/0.54    ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((((X1 = X2) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ X1 @ X2))))) & ((X1 = X3) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ X1 @ X3)))))) => (?? @ $i @ (^[Y0 : $i]: (((X3 = Y0) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ X3 @ Y0))))) & ((X2 = Y0) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ X2 @ Y0))))))))))) )),
% 1.34/0.54    inference(beta_eta_normalization,[],[f179])).
% 1.34/0.54  thf(f179,plain,(
% 1.34/0.54    ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((((X1 = X2) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ X1 @ X2))))) & ((X1 = Y0) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ X1 @ Y0)))))) => (?? @ $i @ (^[Y1 : $i]: (((Y0 = Y1) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1))))) & ((X2 = Y1) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ X2 @ Y1)))))))))) @ X3) = $true)) )),
% 1.34/0.54    inference(pi_clausification,[],[f168])).
% 1.34/0.54  thf(f168,plain,(
% 1.34/0.54    ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((((X1 = X2) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ X1 @ X2))))) & ((X1 = Y0) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ X1 @ Y0)))))) => (?? @ $i @ (^[Y1 : $i]: (((Y0 = Y1) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y0 @ Y1))))) & ((X2 = Y1) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ X2 @ Y1))))))))))))) )),
% 1.34/0.54    inference(beta_eta_normalization,[],[f167])).
% 1.34/0.54  thf(f167,plain,(
% 1.34/0.54    ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((X1 = Y0) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ X1 @ Y0))))) & ((X1 = Y1) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ X1 @ Y1)))))) => (?? @ $i @ (^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2))))) & ((Y0 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y2)))))))))))) @ X2))) )),
% 1.34/0.54    inference(pi_clausification,[],[f166])).
% 1.34/0.54  thf(f166,plain,(
% 1.34/0.54    ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((X1 = Y0) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ X1 @ Y0))))) & ((X1 = Y1) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ X1 @ Y1)))))) => (?? @ $i @ (^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y1 @ Y2))))) & ((Y0 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y2))))))))))))))) )),
% 1.34/0.54    inference(beta_eta_normalization,[],[f165])).
% 1.34/0.54  thf(f165,plain,(
% 1.34/0.54    ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((Y0 = Y1) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y1))))) & ((Y0 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y2)))))) => (?? @ $i @ (^[Y3 : $i]: (((Y2 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y2 @ Y3))))) & ((Y1 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y1 @ Y3)))))))))))))) @ X1))) )),
% 1.34/0.54    inference(pi_clausification,[],[f144])).
% 1.34/0.54  thf(f144,plain,(
% 1.34/0.54    ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((Y0 = Y1) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y1))))) & ((Y0 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y0 @ Y2)))))) => (?? @ $i @ (^[Y3 : $i]: (((Y2 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y2 @ Y3))))) & ((Y1 = Y3) | (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y1 @ Y3))))))))))))))))),
% 1.34/0.54    inference(binary_proxy_clausification,[],[f142])).
% 1.34/0.54  thf(f622,plain,(
% 1.34/0.54    ((sK7 @ sK4 @ sK3) = $true) | ~spl0_1),
% 1.34/0.54    inference(boolean_simplification,[],[f621])).
% 1.34/0.54  thf(f621,plain,(
% 1.34/0.54    ($true = ($true => (sK7 @ sK4 @ sK3))) | ~spl0_1),
% 1.34/0.54    inference(superposition,[],[f609,f162])).
% 1.34/0.54  thf(f162,plain,(
% 1.34/0.54    ($true = (sK2 @ sK4 @ sK3))),
% 1.34/0.54    inference(binary_proxy_clausification,[],[f156])).
% 1.34/0.54  thf(f156,plain,(
% 1.34/0.54    ($true = ((sK2 @ sK4 @ sK3) & ((sK4 = sK5) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK5)))))))),
% 1.34/0.54    inference(binary_proxy_clausification,[],[f154])).
% 1.34/0.54  thf(f609,plain,(
% 1.34/0.54    ( ! [X2 : $i,X1 : $i] : (($true = ((sK2 @ X1 @ X2) => (sK7 @ X1 @ X2)))) ) | ~spl0_1),
% 1.34/0.54    inference(beta_eta_normalization,[],[f608])).
% 1.34/0.54  thf(f608,plain,(
% 1.34/0.54    ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((sK2 @ X1 @ Y0) => (sK7 @ X1 @ Y0))) @ X2))) ) | ~spl0_1),
% 1.34/0.54    inference(pi_clausification,[],[f568])).
% 1.34/0.54  thf(f568,plain,(
% 1.34/0.54    ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK2 @ X1 @ Y0) => (sK7 @ X1 @ Y0)))))) ) | ~spl0_1),
% 1.34/0.54    inference(beta_eta_normalization,[],[f567])).
% 1.34/0.54  thf(f567,plain,(
% 1.34/0.54    ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK7 @ Y0 @ Y1))))) @ X1))) ) | ~spl0_1),
% 1.34/0.54    inference(pi_clausification,[],[f509])).
% 1.34/0.54  thf(f509,plain,(
% 1.34/0.54    ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK7 @ Y0 @ Y1))))))) | ~spl0_1),
% 1.34/0.54    inference(boolean_simplification,[],[f508])).
% 1.34/0.54  thf(f508,plain,(
% 1.34/0.54    ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK7 @ Y0 @ Y1)))))) & $true)) | ~spl0_1),
% 1.34/0.54    inference(backward_demodulation,[],[f503,f506])).
% 1.34/0.54  thf(f506,plain,(
% 1.34/0.54    ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK7 @ Y2 @ Y0) & (sK7 @ Y0 @ Y1)) => (sK7 @ Y2 @ Y1))))))))) | ~spl0_1),
% 1.34/0.54    inference(binary_proxy_clausification,[],[f503])).
% 1.34/0.54  thf(f393,plain,(
% 1.34/0.54    ~spl0_2),
% 1.34/0.54    inference(avatar_contradiction_clause,[],[f392])).
% 1.34/0.54  thf(f392,plain,(
% 1.34/0.54    $false | ~spl0_2),
% 1.34/0.54    inference(trivial_inequality_removal,[],[f391])).
% 1.34/0.54  thf(f391,plain,(
% 1.34/0.54    ($true = $false) | ~spl0_2),
% 1.34/0.54    inference(boolean_simplification,[],[f390])).
% 1.34/0.54  thf(f390,plain,(
% 1.34/0.54    ($true = (~ $true)) | ~spl0_2),
% 1.34/0.54    inference(forward_demodulation,[],[f384,f162])).
% 1.34/0.54  thf(f384,plain,(
% 1.34/0.54    ((~ (sK2 @ sK4 @ sK3)) = $true) | ~spl0_2),
% 1.34/0.54    inference(boolean_simplification,[],[f381])).
% 1.34/0.54  thf(f381,plain,(
% 1.34/0.54    (((sK2 @ sK4 @ sK3) => $false) = $true) | ~spl0_2),
% 1.34/0.54    inference(superposition,[],[f373,f320])).
% 1.34/0.54  thf(f320,plain,(
% 1.34/0.54    ((sK7 @ sK4 @ sK3) = $false) | ~spl0_2),
% 1.34/0.54    inference(boolean_simplification,[],[f319])).
% 1.34/0.54  thf(f319,plain,(
% 1.34/0.54    ($false = ($true => (sK7 @ sK4 @ sK3))) | ~spl0_2),
% 1.34/0.54    inference(backward_demodulation,[],[f275,f318])).
% 1.34/0.54  thf(f318,plain,(
% 1.34/0.54    (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK7 @ Y0 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK7 @ Y2 @ Y0) & (sK7 @ Y0 @ Y1)) => (sK7 @ Y2 @ Y1))))))))) = $true) | ~spl0_2),
% 1.34/0.54    inference(binary_proxy_clausification,[],[f275])).
% 1.34/0.54  thf(f275,plain,(
% 1.34/0.54    ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK7 @ Y0 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK7 @ Y2 @ Y0) & (sK7 @ Y0 @ Y1)) => (sK7 @ Y2 @ Y1))))))))) => (sK7 @ sK4 @ sK3))) | ~spl0_2),
% 1.34/0.54    inference(beta_eta_normalization,[],[f264])).
% 1.34/0.54  thf(f264,plain,(
% 1.34/0.54    ($false = ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK3))) @ sK7)) | ~spl0_2),
% 1.34/0.54    inference(sigma_clausification,[],[f211])).
% 1.34/0.54  thf(f211,plain,(
% 1.34/0.54    ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK3))))) | ~spl0_2),
% 1.34/0.54    inference(binary_proxy_clausification,[],[f202])).
% 1.34/0.54  thf(f202,plain,(
% 1.34/0.54    ($false = ((sK4 = sK3) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK3)))))) | ~spl0_2),
% 1.34/0.54    inference(not_proxy_clausification,[],[f199])).
% 1.34/0.54  thf(f199,plain,(
% 1.34/0.54    ($true = (~ ((sK4 = sK3) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK3))))))) | ~spl0_2),
% 1.34/0.54    inference(boolean_simplification,[],[f198])).
% 1.34/0.54  thf(f198,plain,(
% 1.34/0.54    ($true = (~ (((sK4 = sK3) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK3))))) & $true))) | ~spl0_2),
% 1.34/0.54    inference(boolean_simplification,[],[f197])).
% 1.34/0.54  thf(f197,plain,(
% 1.34/0.54    ($true = (~ (((sK4 = sK3) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK3))))) & ((sK4 = sK5) | $true)))) | ~spl0_2),
% 1.34/0.54    inference(superposition,[],[f193,f175])).
% 1.34/0.54  thf(f175,plain,(
% 1.34/0.54    ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK5))))) | ~spl0_2),
% 1.34/0.54    inference(avatar_component_clause,[],[f174])).
% 1.34/0.54  thf(f174,plain,(
% 1.34/0.54    spl0_2 <=> ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK5)))))),
% 1.34/0.54    introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 1.34/0.54  thf(f373,plain,(
% 1.34/0.54    ( ! [X2 : $i,X1 : $i] : (($true = ((sK2 @ X1 @ X2) => (sK7 @ X1 @ X2)))) ) | ~spl0_2),
% 1.34/0.54    inference(beta_eta_normalization,[],[f372])).
% 1.34/0.54  thf(f372,plain,(
% 1.34/0.54    ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((sK2 @ X1 @ Y0) => (sK7 @ X1 @ Y0))) @ X2))) ) | ~spl0_2),
% 1.34/0.54    inference(pi_clausification,[],[f367])).
% 1.34/0.54  thf(f367,plain,(
% 1.34/0.54    ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK2 @ X1 @ Y0) => (sK7 @ X1 @ Y0)))))) ) | ~spl0_2),
% 1.34/0.54    inference(beta_eta_normalization,[],[f365])).
% 1.34/0.54  thf(f365,plain,(
% 1.34/0.54    ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK7 @ Y0 @ Y1))))) @ X1))) ) | ~spl0_2),
% 1.34/0.54    inference(pi_clausification,[],[f322])).
% 1.34/0.54  thf(f322,plain,(
% 1.34/0.54    ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK7 @ Y0 @ Y1))))))) | ~spl0_2),
% 1.34/0.54    inference(binary_proxy_clausification,[],[f318])).
% 1.34/0.54  thf(f176,plain,(
% 1.34/0.54    spl0_1 | spl0_2),
% 1.34/0.54    inference(avatar_split_clause,[],[f169,f174,f171])).
% 1.34/0.54  thf(f169,plain,(
% 1.34/0.54    ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK5))))) | ((sK4 = sK5) = $true)),
% 1.34/0.54    inference(binary_proxy_clausification,[],[f164])).
% 1.34/0.54  thf(f164,plain,(
% 1.34/0.54    (((sK4 = sK5) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK5))))) = $true)),
% 1.34/0.54    inference(boolean_simplification,[],[f163])).
% 1.34/0.54  thf(f163,plain,(
% 1.34/0.54    (($true & ((sK4 = sK5) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK4 @ sK5)))))) = $true)),
% 1.34/0.54    inference(backward_demodulation,[],[f156,f162])).
% 1.34/0.54  % SZS output end Proof for theBenchmark
% 1.34/0.54  % (23158)------------------------------
% 1.34/0.54  % (23158)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.34/0.54  % (23158)Termination reason: Refutation
% 1.34/0.54  
% 1.34/0.54  % (23158)Memory used [KB]: 6652
% 1.34/0.54  % (23158)Time elapsed: 0.136 s
% 1.34/0.54  % (23158)Instructions burned: 254 (million)
% 1.34/0.54  % (23158)------------------------------
% 1.34/0.54  % (23158)------------------------------
% 1.34/0.54  % (23145)Success in time 0.161 s
% 1.34/0.54  % Vampire---4.8 exiting
%------------------------------------------------------------------------------