TSTP Solution File: SEU466^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU466^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n032.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 03:49:01 EDT 2024
% Result : Theorem 0.14s 0.35s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : SEU466^1 : TPTP v8.2.0. Released v3.6.0.
% 0.08/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Sun May 19 16:43:37 EDT 2024
% 0.10/0.29 % CPUTime :
% 0.10/0.29 This is a TH0_THM_EQU_NAR problem
% 0.10/0.29 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.30 % (22013)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.10/0.30 % (22015)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)
% 0.10/0.30 % (22018)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)
% 0.10/0.30 % (22020)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)
% 0.10/0.31 % (22020)Instruction limit reached!
% 0.10/0.31 % (22020)------------------------------
% 0.10/0.31 % (22020)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.31 % (22020)Termination reason: Unknown
% 0.10/0.31 % (22020)Termination phase: Property scanning
% 0.10/0.31
% 0.10/0.31 % (22020)Memory used [KB]: 1023
% 0.10/0.31 % (22020)Time elapsed: 0.003 s
% 0.10/0.31 % (22020)Instructions burned: 5 (million)
% 0.10/0.31 % (22020)------------------------------
% 0.10/0.31 % (22020)------------------------------
% 0.10/0.31 % (22014)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)
% 0.10/0.31 % (22017)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)
% 0.10/0.31 % (22018)Refutation not found, incomplete strategy
% 0.10/0.31 % (22018)------------------------------
% 0.10/0.31 % (22018)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.31 % (22018)Termination reason: Refutation not found, incomplete strategy
% 0.10/0.31
% 0.10/0.31
% 0.10/0.31 % (22018)Memory used [KB]: 5628
% 0.10/0.31 % (22018)Time elapsed: 0.004 s
% 0.10/0.31 % (22018)Instructions burned: 7 (million)
% 0.10/0.31 % (22018)------------------------------
% 0.10/0.31 % (22018)------------------------------
% 0.10/0.31 % (22014)Instruction limit reached!
% 0.10/0.31 % (22014)------------------------------
% 0.10/0.31 % (22014)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.31 % (22014)Termination reason: Unknown
% 0.10/0.31 % (22014)Termination phase: Property scanning
% 0.10/0.31
% 0.10/0.31 % (22014)Memory used [KB]: 1023
% 0.10/0.31 % (22014)Time elapsed: 0.004 s
% 0.10/0.31 % (22014)Instructions burned: 6 (million)
% 0.10/0.31 % (22014)------------------------------
% 0.10/0.31 % (22014)------------------------------
% 0.10/0.31 % (22017)Instruction limit reached!
% 0.10/0.31 % (22017)------------------------------
% 0.10/0.31 % (22017)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.31 % (22017)Termination reason: Unknown
% 0.10/0.31 % (22017)Termination phase: shuffling
% 0.10/0.31 % (22019)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.10/0.31
% 0.10/0.31 % (22017)Memory used [KB]: 1023
% 0.10/0.31 % (22017)Time elapsed: 0.003 s
% 0.10/0.31 % (22017)Instructions burned: 4 (million)
% 0.10/0.31 % (22017)------------------------------
% 0.10/0.31 % (22017)------------------------------
% 0.10/0.31 % (22016)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.10/0.31 % (22016)Instruction limit reached!
% 0.10/0.31 % (22016)------------------------------
% 0.10/0.31 % (22016)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.31 % (22016)Termination reason: Unknown
% 0.10/0.31 % (22016)Termination phase: shuffling
% 0.10/0.31
% 0.10/0.31 % (22016)Memory used [KB]: 1023
% 0.10/0.31 % (22016)Time elapsed: 0.003 s
% 0.10/0.31 % (22016)Instructions burned: 3 (million)
% 0.10/0.31 % (22016)------------------------------
% 0.10/0.31 % (22016)------------------------------
% 0.10/0.31 % (22015)Instruction limit reached!
% 0.10/0.31 % (22015)------------------------------
% 0.10/0.31 % (22015)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.31 % (22015)Termination reason: Unknown
% 0.10/0.31 % (22015)Termination phase: Saturation
% 0.10/0.31
% 0.10/0.31 % (22015)Memory used [KB]: 5756
% 0.10/0.31 % (22015)Time elapsed: 0.010 s
% 0.10/0.31 % (22015)Instructions burned: 29 (million)
% 0.10/0.31 % (22015)------------------------------
% 0.10/0.31 % (22015)------------------------------
% 0.14/0.31 % (22021)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)
% 0.14/0.32 % (22019)Instruction limit reached!
% 0.14/0.32 % (22019)------------------------------
% 0.14/0.32 % (22019)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (22019)Termination reason: Unknown
% 0.14/0.32 % (22019)Termination phase: Saturation
% 0.14/0.32
% 0.14/0.32 % (22019)Memory used [KB]: 5628
% 0.14/0.32 % (22019)Time elapsed: 0.009 s
% 0.14/0.32 % (22019)Instructions burned: 18 (million)
% 0.14/0.32 % (22019)------------------------------
% 0.14/0.32 % (22019)------------------------------
% 0.14/0.32 % (22022)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)
% 0.14/0.32 % (22023)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)
% 0.14/0.32 % (22024)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)
% 0.14/0.32 % (22023)Instruction limit reached!
% 0.14/0.32 % (22023)------------------------------
% 0.14/0.32 % (22023)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (22023)Termination reason: Unknown
% 0.14/0.32 % (22023)Termination phase: shuffling
% 0.14/0.32
% 0.14/0.32 % (22023)Memory used [KB]: 1023
% 0.14/0.32 % (22023)Time elapsed: 0.003 s
% 0.14/0.32 % (22023)Instructions burned: 4 (million)
% 0.14/0.32 % (22023)------------------------------
% 0.14/0.32 % (22023)------------------------------
% 0.14/0.32 % (22026)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.32 % (22022)Instruction limit reached!
% 0.14/0.32 % (22022)------------------------------
% 0.14/0.32 % (22022)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (22022)Termination reason: Unknown
% 0.14/0.32 % (22022)Termination phase: Saturation
% 0.14/0.32
% 0.14/0.32 % (22022)Memory used [KB]: 5756
% 0.14/0.32 % (22022)Time elapsed: 0.006 s
% 0.14/0.32 % (22022)Instructions burned: 16 (million)
% 0.14/0.32 % (22022)------------------------------
% 0.14/0.32 % (22022)------------------------------
% 0.14/0.32 % (22025)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.33 % (22021)Instruction limit reached!
% 0.14/0.33 % (22021)------------------------------
% 0.14/0.33 % (22021)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.33 % (22021)Termination reason: Unknown
% 0.14/0.33 % (22021)Termination phase: Saturation
% 0.14/0.33
% 0.14/0.33 % (22021)Memory used [KB]: 5756
% 0.14/0.33 % (22021)Time elapsed: 0.013 s
% 0.14/0.33 % (22021)Instructions burned: 40 (million)
% 0.14/0.33 % (22021)------------------------------
% 0.14/0.33 % (22021)------------------------------
% 0.14/0.33 % (22026)Instruction limit reached!
% 0.14/0.33 % (22026)------------------------------
% 0.14/0.33 % (22026)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.33 % (22026)Termination reason: Unknown
% 0.14/0.33 % (22026)Termination phase: Saturation
% 0.14/0.33
% 0.14/0.33 % (22026)Memory used [KB]: 5884
% 0.14/0.33 % (22026)Time elapsed: 0.007 s
% 0.14/0.33 % (22026)Instructions burned: 17 (million)
% 0.14/0.33 % (22026)------------------------------
% 0.14/0.33 % (22026)------------------------------
% 0.14/0.33 % (22025)Instruction limit reached!
% 0.14/0.33 % (22025)------------------------------
% 0.14/0.33 % (22025)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.33 % (22025)Termination reason: Unknown
% 0.14/0.33 % (22025)Termination phase: Property scanning
% 0.14/0.33
% 0.14/0.33 % (22025)Memory used [KB]: 1023
% 0.14/0.33 % (22025)Time elapsed: 0.005 s
% 0.14/0.33 % (22027)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)
% 0.14/0.33 % (22025)Instructions burned: 7 (million)
% 0.14/0.33 % (22025)------------------------------
% 0.14/0.33 % (22025)------------------------------
% 0.14/0.33 % (22027)Instruction limit reached!
% 0.14/0.33 % (22027)------------------------------
% 0.14/0.33 % (22027)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.33 % (22027)Termination reason: Unknown
% 0.14/0.33 % (22027)Termination phase: shuffling
% 0.14/0.33
% 0.14/0.33 % (22027)Memory used [KB]: 1023
% 0.14/0.33 % (22027)Time elapsed: 0.003 s
% 0.14/0.33 % (22027)Instructions burned: 3 (million)
% 0.14/0.33 % (22027)------------------------------
% 0.14/0.33 % (22027)------------------------------
% 0.14/0.33 % (22029)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)
% 0.14/0.33 % (22028)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)
% 0.14/0.33 % (22028)Instruction limit reached!
% 0.14/0.33 % (22028)------------------------------
% 0.14/0.33 % (22028)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.33 % (22028)Termination reason: Unknown
% 0.14/0.33 % (22028)Termination phase: Property scanning
% 0.14/0.33
% 0.14/0.33 % (22028)Memory used [KB]: 1023
% 0.14/0.33 % (22028)Time elapsed: 0.003 s
% 0.14/0.33 % (22028)Instructions burned: 5 (million)
% 0.14/0.33 % (22028)------------------------------
% 0.14/0.33 % (22028)------------------------------
% 0.14/0.33 % (22029)Instruction limit reached!
% 0.14/0.33 % (22029)------------------------------
% 0.14/0.33 % (22029)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.33 % (22029)Termination reason: Unknown
% 0.14/0.33 % (22029)Termination phase: Property scanning
% 0.14/0.33
% 0.14/0.33 % (22029)Memory used [KB]: 1023
% 0.14/0.33 % (22029)Time elapsed: 0.003 s
% 0.14/0.33 % (22029)Instructions burned: 7 (million)
% 0.14/0.33 % (22029)------------------------------
% 0.14/0.33 % (22029)------------------------------
% 0.14/0.33 % (22030)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)
% 0.14/0.34 % (22031)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.34 % (22030)Instruction limit reached!
% 0.14/0.34 % (22030)------------------------------
% 0.14/0.34 % (22030)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.34 % (22030)Termination reason: Unknown
% 0.14/0.34 % (22030)Termination phase: shuffling
% 0.14/0.34
% 0.14/0.34 % (22030)Memory used [KB]: 1023
% 0.14/0.34 % (22030)Time elapsed: 0.002 s
% 0.14/0.34 % (22030)Instructions burned: 4 (million)
% 0.14/0.34 % (22030)------------------------------
% 0.14/0.34 % (22030)------------------------------
% 0.14/0.34 % (22031)Instruction limit reached!
% 0.14/0.34 % (22031)------------------------------
% 0.14/0.34 % (22031)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.34 % (22031)Termination reason: Unknown
% 0.14/0.34 % (22031)Termination phase: shuffling
% 0.14/0.34
% 0.14/0.34 % (22031)Memory used [KB]: 1023
% 0.14/0.34 % (22031)Time elapsed: 0.003 s
% 0.14/0.34 % (22031)Instructions burned: 6 (million)
% 0.14/0.34 % (22031)------------------------------
% 0.14/0.34 % (22031)------------------------------
% 0.14/0.34 % (22033)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.14/0.34 % (22032)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)
% 0.14/0.34 % (22035)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)
% 0.14/0.34 % (22034)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.14/0.34 % (22034)Instruction limit reached!
% 0.14/0.34 % (22034)------------------------------
% 0.14/0.34 % (22034)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.34 % (22034)Termination reason: Unknown
% 0.14/0.34 % (22034)Termination phase: Property scanning
% 0.14/0.34
% 0.14/0.34 % (22034)Memory used [KB]: 1023
% 0.14/0.34 % (22034)Time elapsed: 0.004 s
% 0.14/0.34 % (22034)Instructions burned: 7 (million)
% 0.14/0.34 % (22034)------------------------------
% 0.14/0.34 % (22034)------------------------------
% 0.14/0.34 % (22036)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)
% 0.14/0.34 % (22035)Refutation not found, incomplete strategy
% 0.14/0.34 % (22035)------------------------------
% 0.14/0.34 % (22035)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.34 % (22035)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.34
% 0.14/0.34
% 0.14/0.34 % (22035)Memory used [KB]: 5628
% 0.14/0.34 % (22035)Time elapsed: 0.005 s
% 0.14/0.34 % (22035)Instructions burned: 9 (million)
% 0.14/0.34 % (22035)------------------------------
% 0.14/0.34 % (22035)------------------------------
% 0.14/0.35 % (22024)First to succeed.
% 0.14/0.35 % (22037)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.14/0.35 % (22037)Instruction limit reached!
% 0.14/0.35 % (22037)------------------------------
% 0.14/0.35 % (22037)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (22037)Termination reason: Unknown
% 0.14/0.35 % (22037)Termination phase: Property scanning
% 0.14/0.35
% 0.14/0.35 % (22037)Memory used [KB]: 1023
% 0.14/0.35 % (22037)Time elapsed: 0.003 s
% 0.14/0.35 % (22037)Instructions burned: 7 (million)
% 0.14/0.35 % (22037)------------------------------
% 0.14/0.35 % (22037)------------------------------
% 0.14/0.35 % (22032)Instruction limit reached!
% 0.14/0.35 % (22032)------------------------------
% 0.14/0.35 % (22032)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (22032)Termination reason: Unknown
% 0.14/0.35 % (22032)Termination phase: Saturation
% 0.14/0.35
% 0.14/0.35 % (22032)Memory used [KB]: 5628
% 0.14/0.35 % (22032)Time elapsed: 0.011 s
% 0.14/0.35 % (22032)Instructions burned: 19 (million)
% 0.14/0.35 % (22032)------------------------------
% 0.14/0.35 % (22032)------------------------------
% 0.14/0.35 % (22024)Refutation found. Thanks to Tanya!
% 0.14/0.35 % SZS status Theorem for theBenchmark
% 0.14/0.35 % SZS output start Proof for theBenchmark
% 0.14/0.35 thf(func_def_0, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_2, type, inv: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.35 thf(func_def_3, type, idem: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_4, type, infl: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_5, type, mono: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_6, type, refl: ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_7, type, irrefl: ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_8, type, rc: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.35 thf(func_def_9, type, symm: ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_10, type, antisymm: ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_11, type, asymm: ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_12, type, sc: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.35 thf(func_def_13, type, trans: ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_14, type, tc: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.35 thf(func_def_15, type, trc: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.35 thf(func_def_16, type, trsc: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.35 thf(func_def_17, type, po: ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_18, type, so: ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_19, type, total: ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_20, type, term: ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_21, type, ind: ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_22, type, innf: ($i > $i > $o) > $i > $o).
% 0.14/0.35 thf(func_def_23, type, nfof: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.35 thf(func_def_24, type, norm: ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_25, type, join: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.35 thf(func_def_26, type, lconfl: ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_27, type, sconfl: ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_28, type, confl: ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_29, type, cr: ($i > $i > $o) > $o).
% 0.14/0.35 thf(func_def_50, type, ph1: !>[X0: $tType]:(X0)).
% 0.14/0.35 thf(func_def_51, type, sK2: $i > $i > $o).
% 0.14/0.35 thf(func_def_54, type, sK5: $i > $i > $o).
% 0.14/0.35 thf(func_def_57, type, sK8: $i > $i > $o).
% 0.14/0.35 thf(f342,plain,(
% 0.14/0.35 $false),
% 0.14/0.35 inference(avatar_sat_refutation,[],[f156,f163,f281,f284,f289,f341])).
% 0.14/0.35 thf(f341,plain,(
% 0.14/0.35 ~spl0_1 | ~spl0_4),
% 0.14/0.35 inference(avatar_contradiction_clause,[],[f340])).
% 0.14/0.35 thf(f340,plain,(
% 0.14/0.35 $false | (~spl0_1 | ~spl0_4)),
% 0.14/0.35 inference(trivial_inequality_removal,[],[f339])).
% 0.14/0.35 thf(f339,plain,(
% 0.14/0.35 ($false = $true) | (~spl0_1 | ~spl0_4)),
% 0.14/0.35 inference(forward_demodulation,[],[f333,f298])).
% 0.14/0.35 thf(f298,plain,(
% 0.14/0.35 ($false = (sK8 @ sK3 @ sK4)) | ~spl0_4),
% 0.14/0.35 inference(binary_proxy_clausification,[],[f297])).
% 0.14/0.35 thf(f297,plain,(
% 0.14/0.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK8 @ Y0 @ Y2) & (sK8 @ Y2 @ Y1)) => (sK8 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) => (sK8 @ Y0 @ Y1))))))) => (sK8 @ sK3 @ sK4)) = $false) | ~spl0_4),
% 0.14/0.35 inference(beta_eta_normalization,[],[f296])).
% 0.14/0.35 thf(f296,plain,(
% 0.14/0.35 (((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4))) @ sK8) = $false) | ~spl0_4),
% 0.14/0.35 inference(sigma_clausification,[],[f162])).
% 0.14/0.35 thf(f162,plain,(
% 0.14/0.35 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4)))) = $false) | ~spl0_4),
% 0.14/0.35 inference(avatar_component_clause,[],[f161])).
% 0.14/0.35 thf(f161,plain,(
% 0.14/0.35 spl0_4 <=> ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4)))) = $false)),
% 0.14/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.14/0.35 thf(f333,plain,(
% 0.14/0.35 ($true = (sK8 @ sK3 @ sK4)) | (~spl0_1 | ~spl0_4)),
% 0.14/0.35 inference(boolean_simplification,[],[f332])).
% 0.14/0.35 thf(f332,plain,(
% 0.14/0.35 (($true => (sK8 @ sK3 @ sK4)) = $true) | (~spl0_1 | ~spl0_4)),
% 0.14/0.35 inference(superposition,[],[f325,f152])).
% 0.14/0.35 thf(f152,plain,(
% 0.14/0.35 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4)))) = $true) | ~spl0_1),
% 0.14/0.35 inference(avatar_component_clause,[],[f151])).
% 0.14/0.35 thf(f151,plain,(
% 0.14/0.35 spl0_1 <=> ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4)))) = $true)),
% 0.14/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.14/0.35 thf(f325,plain,(
% 0.14/0.35 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ X1 @ X2)))) => (sK8 @ X1 @ X2)))) ) | ~spl0_4),
% 0.14/0.35 inference(beta_eta_normalization,[],[f324])).
% 0.14/0.35 thf(f324,plain,(
% 0.14/0.35 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ X1 @ Y0)))) => (sK8 @ X1 @ Y0))) @ X2) = $true)) ) | ~spl0_4),
% 0.14/0.35 inference(pi_clausification,[],[f321])).
% 0.14/0.35 thf(f321,plain,(
% 0.14/0.35 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ X1 @ Y0)))) => (sK8 @ X1 @ Y0)))) = $true)) ) | ~spl0_4),
% 0.14/0.35 inference(beta_eta_normalization,[],[f320])).
% 0.14/0.35 thf(f320,plain,(
% 0.14/0.35 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) => (sK8 @ Y0 @ Y1))))) @ X1) = $true)) ) | ~spl0_4),
% 0.14/0.35 inference(pi_clausification,[],[f313])).
% 0.14/0.35 thf(f313,plain,(
% 0.14/0.35 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) => (sK8 @ Y0 @ Y1)))))) = $true) | ~spl0_4),
% 0.14/0.35 inference(boolean_simplification,[],[f312])).
% 0.14/0.35 thf(f312,plain,(
% 0.14/0.35 (($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) => (sK8 @ Y0 @ Y1))))))) = $true) | ~spl0_4),
% 0.14/0.35 inference(backward_demodulation,[],[f299,f310])).
% 0.14/0.35 thf(f310,plain,(
% 0.14/0.35 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK8 @ Y0 @ Y2) & (sK8 @ Y2 @ Y1)) => (sK8 @ Y0 @ Y1)))))))) = $true) | ~spl0_4),
% 0.14/0.35 inference(binary_proxy_clausification,[],[f299])).
% 0.14/0.35 thf(f299,plain,(
% 0.14/0.35 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK8 @ Y0 @ Y2) & (sK8 @ Y2 @ Y1)) => (sK8 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) => (sK8 @ Y0 @ Y1))))))) = $true) | ~spl0_4),
% 0.14/0.35 inference(binary_proxy_clausification,[],[f297])).
% 0.14/0.35 thf(f289,plain,(
% 0.14/0.35 ~spl0_2 | ~spl0_4),
% 0.14/0.35 inference(avatar_contradiction_clause,[],[f288])).
% 0.14/0.35 thf(f288,plain,(
% 0.14/0.35 $false | (~spl0_2 | ~spl0_4)),
% 0.14/0.35 inference(trivial_inequality_removal,[],[f287])).
% 0.14/0.35 thf(f287,plain,(
% 0.14/0.35 ($false = $true) | (~spl0_2 | ~spl0_4)),
% 0.14/0.35 inference(forward_demodulation,[],[f155,f162])).
% 0.14/0.35 thf(f155,plain,(
% 0.14/0.35 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4)))) = $true) | ~spl0_2),
% 0.14/0.35 inference(avatar_component_clause,[],[f154])).
% 0.14/0.35 thf(f154,plain,(
% 0.14/0.35 spl0_2 <=> ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4)))) = $true)),
% 0.14/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.14/0.35 thf(f284,plain,(
% 0.14/0.35 ~spl0_1 | ~spl0_3),
% 0.14/0.35 inference(avatar_contradiction_clause,[],[f283])).
% 0.14/0.35 thf(f283,plain,(
% 0.14/0.35 $false | (~spl0_1 | ~spl0_3)),
% 0.14/0.35 inference(trivial_inequality_removal,[],[f282])).
% 0.14/0.35 thf(f282,plain,(
% 0.14/0.35 ($false = $true) | (~spl0_1 | ~spl0_3)),
% 0.14/0.35 inference(forward_demodulation,[],[f152,f159])).
% 0.14/0.35 thf(f159,plain,(
% 0.14/0.35 ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4))))) | ~spl0_3),
% 0.14/0.35 inference(avatar_component_clause,[],[f158])).
% 0.14/0.35 thf(f158,plain,(
% 0.14/0.35 spl0_3 <=> ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4)))))),
% 0.14/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.14/0.35 thf(f281,plain,(
% 0.14/0.35 ~spl0_2 | ~spl0_3),
% 0.14/0.35 inference(avatar_contradiction_clause,[],[f280])).
% 0.14/0.35 thf(f280,plain,(
% 0.14/0.35 $false | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(trivial_inequality_removal,[],[f279])).
% 0.14/0.35 thf(f279,plain,(
% 0.14/0.35 ($false = $true) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(forward_demodulation,[],[f278,f218])).
% 0.14/0.35 thf(f218,plain,(
% 0.14/0.35 ((sK5 @ sK6 @ sK7) = $false) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(boolean_simplification,[],[f217])).
% 0.14/0.35 thf(f217,plain,(
% 0.14/0.35 (($true => (sK5 @ sK6 @ sK7)) = $false) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(backward_demodulation,[],[f212,f216])).
% 0.14/0.35 thf(f216,plain,(
% 0.14/0.35 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK6 @ sK7)))) = $true) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(binary_proxy_clausification,[],[f212])).
% 0.14/0.35 thf(f212,plain,(
% 0.14/0.35 (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK6 @ sK7)))) => (sK5 @ sK6 @ sK7)) = $false) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(beta_eta_normalization,[],[f211])).
% 0.14/0.35 thf(f211,plain,(
% 0.14/0.35 ($false = ((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK6 @ Y0)))) => (sK5 @ sK6 @ Y0))) @ sK7)) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(sigma_clausification,[],[f204])).
% 0.14/0.35 thf(f204,plain,(
% 0.14/0.35 ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK6 @ Y0)))) => (sK5 @ sK6 @ Y0)))) = $false) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(beta_eta_normalization,[],[f200])).
% 0.14/0.35 thf(f200,plain,(
% 0.14/0.35 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) => (sK5 @ Y0 @ Y1))))) @ sK6) = $false) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(sigma_clausification,[],[f193])).
% 0.14/0.35 thf(f193,plain,(
% 0.14/0.35 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) => (sK5 @ Y0 @ Y1))))))) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(not_proxy_clausification,[],[f184])).
% 0.14/0.35 thf(f184,plain,(
% 0.14/0.35 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) => (sK5 @ Y0 @ Y1))))))) = $true) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(boolean_simplification,[],[f183])).
% 0.14/0.35 thf(f183,plain,(
% 0.14/0.35 ((~ ($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) => (sK5 @ Y0 @ Y1)))))))) = $true) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(forward_demodulation,[],[f182,f173])).
% 0.14/0.35 thf(f173,plain,(
% 0.14/0.35 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK5 @ Y0 @ Y2) & (sK5 @ Y2 @ Y1)) => (sK5 @ Y0 @ Y1)))))))) = $true) | ~spl0_3),
% 0.14/0.35 inference(binary_proxy_clausification,[],[f169])).
% 0.14/0.35 thf(f169,plain,(
% 0.14/0.35 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK5 @ Y0 @ Y2) & (sK5 @ Y2 @ Y1)) => (sK5 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK5 @ Y0 @ Y1))))))) = $true) | ~spl0_3),
% 0.14/0.35 inference(binary_proxy_clausification,[],[f167])).
% 0.14/0.35 thf(f167,plain,(
% 0.14/0.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK5 @ Y0 @ Y2) & (sK5 @ Y2 @ Y1)) => (sK5 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK5 @ Y0 @ Y1))))))) => (sK5 @ sK3 @ sK4)) = $false) | ~spl0_3),
% 0.14/0.35 inference(beta_eta_normalization,[],[f166])).
% 0.14/0.35 thf(f166,plain,(
% 0.14/0.35 (((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4))) @ sK5) = $false) | ~spl0_3),
% 0.14/0.35 inference(sigma_clausification,[],[f159])).
% 0.14/0.35 thf(f182,plain,(
% 0.14/0.35 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK5 @ Y0 @ Y2) & (sK5 @ Y2 @ Y1)) => (sK5 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) => (sK5 @ Y0 @ Y1)))))))) = $true) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(boolean_simplification,[],[f181])).
% 0.14/0.35 thf(f181,plain,(
% 0.14/0.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK5 @ Y0 @ Y2) & (sK5 @ Y2 @ Y1)) => (sK5 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) => (sK5 @ Y0 @ Y1))))))) => $false) = $true) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(superposition,[],[f177,f171])).
% 0.14/0.35 thf(f171,plain,(
% 0.14/0.35 ($false = (sK5 @ sK3 @ sK4)) | ~spl0_3),
% 0.14/0.35 inference(boolean_simplification,[],[f170])).
% 0.14/0.35 thf(f170,plain,(
% 0.14/0.35 (($true => (sK5 @ sK3 @ sK4)) = $false) | ~spl0_3),
% 0.14/0.35 inference(backward_demodulation,[],[f167,f169])).
% 0.14/0.35 thf(f177,plain,(
% 0.14/0.35 ( ! [X1 : $i > $i > $o] : (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X1 @ Y0 @ Y2) & (X1 @ Y2 @ Y1)) => (X1 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) => (X1 @ Y0 @ Y1))))))) => (X1 @ sK3 @ sK4)) = $true)) ) | ~spl0_2),
% 0.14/0.35 inference(beta_eta_normalization,[],[f176])).
% 0.14/0.35 thf(f176,plain,(
% 0.14/0.35 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4))) @ X1) = $true)) ) | ~spl0_2),
% 0.14/0.35 inference(pi_clausification,[],[f155])).
% 0.14/0.35 thf(f278,plain,(
% 0.14/0.35 ((sK5 @ sK6 @ sK7) = $true) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(boolean_simplification,[],[f277])).
% 0.14/0.35 thf(f277,plain,(
% 0.14/0.35 (($true => (sK5 @ sK6 @ sK7)) = $true) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(forward_demodulation,[],[f261,f173])).
% 0.14/0.35 thf(f261,plain,(
% 0.14/0.35 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK5 @ Y0 @ Y2) & (sK5 @ Y2 @ Y1)) => (sK5 @ Y0 @ Y1)))))))) => (sK5 @ sK6 @ sK7)) = $true) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(boolean_simplification,[],[f259])).
% 0.14/0.35 thf(f259,plain,(
% 0.14/0.35 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK5 @ Y0 @ Y2) & (sK5 @ Y2 @ Y1)) => (sK5 @ Y0 @ Y1)))))))) & $true) => (sK5 @ sK6 @ sK7)) = $true) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(superposition,[],[f246,f175])).
% 0.14/0.35 thf(f175,plain,(
% 0.14/0.35 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK5 @ Y0 @ Y1))))))) | ~spl0_3),
% 0.14/0.35 inference(boolean_simplification,[],[f174])).
% 0.14/0.35 thf(f174,plain,(
% 0.14/0.35 (($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK5 @ Y0 @ Y1))))))) = $true) | ~spl0_3),
% 0.14/0.35 inference(backward_demodulation,[],[f169,f173])).
% 0.14/0.35 thf(f246,plain,(
% 0.14/0.35 ( ! [X1 : $i > $i > $o] : (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X1 @ Y0 @ Y2) & (X1 @ Y2 @ Y1)) => (X1 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (X1 @ Y0 @ Y1))))))) => (X1 @ sK6 @ sK7)) = $true)) ) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(beta_eta_normalization,[],[f245])).
% 0.14/0.35 thf(f245,plain,(
% 0.14/0.35 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK6 @ sK7))) @ X1) = $true)) ) | (~spl0_2 | ~spl0_3)),
% 0.14/0.35 inference(pi_clausification,[],[f216])).
% 0.14/0.35 thf(f163,plain,(
% 0.14/0.35 spl0_3 | spl0_4),
% 0.14/0.35 inference(avatar_split_clause,[],[f149,f161,f158])).
% 0.14/0.35 thf(f149,plain,(
% 0.14/0.35 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4)))) = $false) | ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4)))))),
% 0.14/0.35 inference(binary_proxy_clausification,[],[f147])).
% 0.14/0.35 thf(f147,plain,(
% 0.14/0.35 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4)))) != (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4)))))),
% 0.14/0.35 inference(beta_eta_normalization,[],[f146])).
% 0.14/0.35 thf(f146,plain,(
% 0.14/0.35 (((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3)))) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK3 @ Y0))))) @ sK4) != ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK3 @ Y0))))) @ sK4))),
% 0.14/0.35 inference(negative_extensionality,[],[f145])).
% 0.14/0.35 thf(f145,plain,(
% 0.14/0.35 ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((sK2 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3)))) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK3 @ Y0))))) != (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK3 @ Y0))))))),
% 0.14/0.35 inference(beta_eta_normalization,[],[f144])).
% 0.14/0.35 thf(f144,plain,(
% 0.14/0.35 (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y6 @ Y7)))))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((sK2 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y3 @ Y4)))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) @ sK3) != ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) @ sK3))),
% 0.14/0.35 inference(negative_extensionality,[],[f143])).
% 0.14/0.35 thf(f143,plain,(
% 0.14/0.35 ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y6 @ Y7)))))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((sK2 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y3 @ Y4)))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))))),
% 0.14/0.35 inference(equality_proxy_clausification,[],[f142])).
% 0.14/0.35 thf(f142,plain,(
% 0.14/0.35 (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y6 @ Y7)))))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((sK2 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y3 @ Y4)))) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))) = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))))))) = $false)),
% 0.14/0.35 inference(beta_eta_normalization,[],[f141])).
% 0.14/0.35 thf(f141,plain,(
% 0.14/0.35 (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y7 @ Y8)))))))) & (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y4 @ Y5)))) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2))))))) = (^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2))))))))) @ sK2) = $false)),
% 0.14/0.35 inference(sigma_clausification,[],[f138])).
% 0.14/0.35 thf(f138,plain,(
% 0.14/0.35 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y7 @ Y8)))))))) & (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y4 @ Y5)))) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2))))))) = (^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))))))))) = $false)),
% 0.14/0.35 inference(not_proxy_clausification,[],[f137])).
% 0.14/0.35 thf(f137,plain,(
% 0.14/0.35 ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y7 @ Y8)))))))) & (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y4 @ Y5)))) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2))))))) = (^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2))))))))))) = $true)),
% 0.14/0.35 inference(beta_eta_normalization,[],[f136])).
% 0.14/0.35 thf(f136,plain,(
% 0.14/0.35 ((~ ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1))))) @ (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6))))))))) @ Y3) & ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))))) @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))) = $true)),
% 0.14/0.35 inference(definition_unfolding,[],[f111,f114,f123])).
% 0.14/0.35 thf(f123,plain,(
% 0.14/0.35 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6))))))))) @ Y3) & ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))))) @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.14/0.35 inference(definition_unfolding,[],[f109,f113,f107])).
% 0.14/0.35 thf(f107,plain,(
% 0.14/0.35 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 0.14/0.35 inference(cnf_transformation,[],[f38])).
% 0.14/0.35 thf(f38,plain,(
% 0.14/0.35 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 0.14/0.35 inference(fool_elimination,[],[f37])).
% 0.14/0.35 thf(f37,plain,(
% 0.14/0.35 (subrel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X3 @ X2) => (X1 @ X3 @ X2)))))),
% 0.14/0.35 inference(rectify,[],[f1])).
% 0.14/0.35 thf(f1,axiom,(
% 0.14/0.35 (subrel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X3,X2] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))))),
% 0.14/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subrel)).
% 0.14/0.35 thf(f113,plain,(
% 0.14/0.35 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.14/0.35 inference(cnf_transformation,[],[f77])).
% 0.14/0.35 thf(f77,plain,(
% 0.14/0.35 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.14/0.35 inference(fool_elimination,[],[f76])).
% 0.14/0.35 thf(f76,plain,(
% 0.14/0.35 (trans = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X2) & (X0 @ X3 @ X1)) => (X0 @ X3 @ X2)))))),
% 0.14/0.35 inference(rectify,[],[f13])).
% 0.14/0.35 thf(f13,axiom,(
% 0.14/0.35 (trans = (^[X0 : $i > $i > $o] : (! [X3,X5,X2] : (((X0 @ X3 @ X5) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X5)))))),
% 0.14/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive)).
% 0.14/0.35 thf(f109,plain,(
% 0.14/0.35 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & (subrel @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.14/0.35 inference(cnf_transformation,[],[f54])).
% 0.14/0.35 thf(f54,plain,(
% 0.14/0.35 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & (subrel @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.14/0.35 inference(fool_elimination,[],[f53])).
% 0.14/0.35 thf(f53,plain,(
% 0.14/0.35 (tc = (^[X0 : $i > $i > $o, X1 : $i, X2 : $i] : (! [X3 : $i > $i > $o] : (((subrel @ X0 @ X3) & (trans @ X3)) => (X3 @ X1 @ X2)))))),
% 0.14/0.35 inference(rectify,[],[f14])).
% 0.14/0.35 thf(f14,axiom,(
% 0.14/0.35 (tc = (^[X0 : $i > $i > $o, X2 : $i, X3 : $i] : (! [X1 : $i > $i > $o] : (((subrel @ X0 @ X1) & (trans @ X1)) => (X1 @ X2 @ X3)))))),
% 0.14/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure)).
% 0.14/0.35 thf(f114,plain,(
% 0.14/0.35 (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1))))))),
% 0.14/0.35 inference(cnf_transformation,[],[f58])).
% 0.14/0.35 thf(f58,plain,(
% 0.14/0.35 (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1))))))),
% 0.14/0.35 inference(fool_elimination,[],[f57])).
% 0.14/0.35 thf(f57,plain,(
% 0.14/0.35 (idem = (^[X0 : ($i > $i > $o) > $i > $i > $o] : (! [X1 : $i > $i > $o] : ((X0 @ (X0 @ X1)) = (X0 @ X1)))))),
% 0.14/0.35 inference(rectify,[],[f3])).
% 0.14/0.35 thf(f3,axiom,(
% 0.14/0.35 (idem = (^[X4 : ($i > $i > $o) > $i > $i > $o] : (! [X0 : $i > $i > $o] : ((X4 @ X0) = (X4 @ (X4 @ X0))))))),
% 0.14/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotent)).
% 0.14/0.35 thf(f111,plain,(
% 0.14/0.35 ($true = (~ (idem @ tc)))),
% 0.14/0.35 inference(cnf_transformation,[],[f56])).
% 0.14/0.35 thf(f56,plain,(
% 0.14/0.35 ($true = (~ (idem @ tc)))),
% 0.14/0.35 inference(fool_elimination,[],[f55])).
% 0.14/0.35 thf(f55,plain,(
% 0.14/0.35 ~(idem @ tc)),
% 0.14/0.35 inference(rectify,[],[f31])).
% 0.14/0.35 thf(f31,negated_conjecture,(
% 0.14/0.35 ~(idem @ tc)),
% 0.14/0.35 inference(negated_conjecture,[],[f30])).
% 0.14/0.35 thf(f30,conjecture,(
% 0.14/0.35 (idem @ tc)),
% 0.14/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure_op_is_idempotent)).
% 0.14/0.35 thf(f156,plain,(
% 0.14/0.35 spl0_1 | spl0_2),
% 0.14/0.35 inference(avatar_split_clause,[],[f148,f154,f151])).
% 0.14/0.35 thf(f148,plain,(
% 0.14/0.35 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4)))) = $true) | ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK4)))) = $true)),
% 0.14/0.35 inference(binary_proxy_clausification,[],[f147])).
% 0.14/0.35 % SZS output end Proof for theBenchmark
% 0.14/0.35 % (22024)------------------------------
% 0.14/0.35 % (22024)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (22024)Termination reason: Refutation
% 0.14/0.35
% 0.14/0.35 % (22024)Memory used [KB]: 6012
% 0.14/0.35 % (22024)Time elapsed: 0.032 s
% 0.14/0.35 % (22024)Instructions burned: 64 (million)
% 0.14/0.35 % (22024)------------------------------
% 0.14/0.35 % (22024)------------------------------
% 0.14/0.35 % (22012)Success in time 0.039 s
% 0.14/0.35 % Vampire---4.8 exiting
%------------------------------------------------------------------------------