TSTP Solution File: SYO068^4.020 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO068^4.020 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:02:42 EDT 2024
% Result : Theorem 1.61s 0.59s
% Output : Refutation 1.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYO068^4.020 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.15 % 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
% 0.16/0.39 % Computer : n008.cluster.edu
% 0.16/0.39 % Model : x86_64 x86_64
% 0.16/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.39 % Memory : 8042.1875MB
% 0.16/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.39 % CPULimit : 300
% 0.16/0.39 % WCLimit : 300
% 0.16/0.39 % DateTime : Mon May 20 08:50:53 EDT 2024
% 0.16/0.39 % CPUTime :
% 0.16/0.39 This is a TH0_THM_EQU_NAR problem
% 0.16/0.39 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
% 0.16/0.41 % (7371)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)
% 0.16/0.41 % (7370)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)
% 0.16/0.41 % (7372)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.41 % (7373)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)
% 0.16/0.41 % (7369)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.16/0.41 % (7375)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.16/0.41 % (7374)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)
% 0.16/0.41 % (7376)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)
% 0.16/0.41 % (7372)Instruction limit reached!
% 0.16/0.41 % (7372)------------------------------
% 0.16/0.41 % (7372)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (7372)Termination reason: Unknown
% 0.16/0.41 % (7372)Termination phase: shuffling
% 0.16/0.41 % (7373)Instruction limit reached!
% 0.16/0.41 % (7373)------------------------------
% 0.16/0.41 % (7373)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (7373)Termination reason: Unknown
% 0.16/0.41 % (7373)Termination phase: shuffling
% 0.16/0.41
% 0.16/0.41 % (7373)Memory used [KB]: 1023
% 0.16/0.41 % (7373)Time elapsed: 0.003 s
% 0.16/0.41 % (7373)Instructions burned: 2 (million)
% 0.16/0.41 % (7373)------------------------------
% 0.16/0.41 % (7373)------------------------------
% 0.16/0.41
% 0.16/0.41 % (7372)Memory used [KB]: 1023
% 0.16/0.41 % (7372)Time elapsed: 0.003 s
% 0.16/0.41 % (7372)Instructions burned: 2 (million)
% 0.16/0.41 % (7372)------------------------------
% 0.16/0.41 % (7372)------------------------------
% 0.16/0.41 % (7370)Instruction limit reached!
% 0.16/0.41 % (7370)------------------------------
% 0.16/0.41 % (7370)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (7370)Termination reason: Unknown
% 0.16/0.41 % (7370)Termination phase: Property scanning
% 0.16/0.41
% 0.16/0.41 % (7370)Memory used [KB]: 1023
% 0.16/0.41 % (7370)Time elapsed: 0.003 s
% 0.16/0.41 % (7370)Instructions burned: 4 (million)
% 0.16/0.41 % (7370)------------------------------
% 0.16/0.41 % (7370)------------------------------
% 0.16/0.41 % (7376)Instruction limit reached!
% 0.16/0.41 % (7376)------------------------------
% 0.16/0.41 % (7376)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (7376)Termination reason: Unknown
% 0.16/0.41 % (7376)Termination phase: Property scanning
% 0.16/0.41
% 0.16/0.41 % (7376)Memory used [KB]: 1023
% 0.16/0.41 % (7376)Time elapsed: 0.004 s
% 0.16/0.41 % (7376)Instructions burned: 4 (million)
% 0.16/0.41 % (7376)------------------------------
% 0.16/0.41 % (7376)------------------------------
% 0.16/0.42 % (7374)Refutation not found, incomplete strategy
% 0.16/0.42 % (7374)------------------------------
% 0.16/0.42 % (7374)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (7374)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.42
% 0.16/0.42
% 0.16/0.42 % (7374)Memory used [KB]: 5500
% 0.16/0.42 % (7374)Time elapsed: 0.005 s
% 0.16/0.42 % (7374)Instructions burned: 6 (million)
% 0.16/0.42 % (7374)------------------------------
% 0.16/0.42 % (7374)------------------------------
% 0.16/0.42 % (7375)Instruction limit reached!
% 0.16/0.42 % (7375)------------------------------
% 0.16/0.42 % (7375)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (7375)Termination reason: Unknown
% 0.16/0.42 % (7375)Termination phase: Property scanning
% 0.16/0.42
% 0.16/0.42 % (7375)Memory used [KB]: 1023
% 0.16/0.42 % (7375)Time elapsed: 0.010 s
% 0.16/0.42 % (7375)Instructions burned: 18 (million)
% 0.16/0.42 % (7375)------------------------------
% 0.16/0.42 % (7375)------------------------------
% 0.16/0.42 % (7371)Instruction limit reached!
% 0.16/0.42 % (7371)------------------------------
% 0.16/0.42 % (7371)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (7371)Termination reason: Unknown
% 0.16/0.42 % (7371)Termination phase: Saturation
% 0.16/0.42
% 0.16/0.42 % (7371)Memory used [KB]: 5628
% 0.16/0.42 % (7371)Time elapsed: 0.014 s
% 0.16/0.42 % (7371)Instructions burned: 27 (million)
% 0.16/0.42 % (7371)------------------------------
% 0.16/0.42 % (7371)------------------------------
% 0.16/0.43 % (7377)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)
% 0.16/0.43 % (7378)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)
% 0.16/0.43 % (7379)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)
% 0.16/0.43 % (7380)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)
% 0.16/0.43 % (7379)Instruction limit reached!
% 0.16/0.43 % (7379)------------------------------
% 0.16/0.43 % (7379)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.43 % (7379)Termination reason: Unknown
% 0.16/0.43 % (7379)Termination phase: Property scanning
% 0.16/0.43
% 0.16/0.43 % (7379)Memory used [KB]: 1023
% 0.16/0.43 % (7379)Time elapsed: 0.004 s
% 0.16/0.43 % (7379)Instructions burned: 4 (million)
% 0.16/0.43 % (7379)------------------------------
% 0.16/0.43 % (7379)------------------------------
% 0.16/0.43 % (7381)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.16/0.43 % (7378)Instruction limit reached!
% 0.16/0.43 % (7378)------------------------------
% 0.16/0.43 % (7378)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.43 % (7378)Termination reason: Unknown
% 0.16/0.43 % (7378)Termination phase: Property scanning
% 0.16/0.43 % (7382)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.16/0.43
% 0.16/0.43 % (7378)Memory used [KB]: 1023
% 0.16/0.43 % (7378)Time elapsed: 0.009 s
% 0.16/0.43 % (7378)Instructions burned: 16 (million)
% 0.16/0.43 % (7378)------------------------------
% 0.16/0.43 % (7378)------------------------------
% 0.16/0.43 % (7381)Instruction limit reached!
% 0.16/0.43 % (7381)------------------------------
% 0.16/0.43 % (7381)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.43 % (7381)Termination reason: Unknown
% 0.16/0.43 % (7381)Termination phase: Function definition elimination
% 0.16/0.43
% 0.16/0.43 % (7381)Memory used [KB]: 1023
% 0.16/0.43 % (7381)Time elapsed: 0.006 s
% 0.16/0.43 % (7381)Instructions burned: 8 (million)
% 0.16/0.43 % (7381)------------------------------
% 0.16/0.43 % (7381)------------------------------
% 0.25/0.44 % (7383)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)
% 0.25/0.44 % (7383)Instruction limit reached!
% 0.25/0.44 % (7383)------------------------------
% 0.25/0.44 % (7383)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.44 % (7383)Termination reason: Unknown
% 0.25/0.44 % (7383)Termination phase: shuffling
% 0.25/0.44
% 0.25/0.44 % (7383)Memory used [KB]: 1023
% 0.25/0.44 % (7383)Time elapsed: 0.004 s
% 0.25/0.44 % (7383)Instructions burned: 4 (million)
% 0.25/0.44 % (7383)------------------------------
% 0.25/0.44 % (7383)------------------------------
% 0.25/0.44 % (7382)Instruction limit reached!
% 0.25/0.44 % (7382)------------------------------
% 0.25/0.44 % (7382)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.44 % (7382)Termination reason: Unknown
% 0.25/0.44 % (7382)Termination phase: Property scanning
% 0.25/0.44
% 0.25/0.44 % (7382)Memory used [KB]: 1023
% 0.25/0.44 % (7382)Time elapsed: 0.009 s
% 0.25/0.44 % (7382)Instructions burned: 16 (million)
% 0.25/0.44 % (7382)------------------------------
% 0.25/0.44 % (7382)------------------------------
% 0.25/0.44 % (7377)Instruction limit reached!
% 0.25/0.44 % (7377)------------------------------
% 0.25/0.44 % (7377)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.44 % (7377)Termination reason: Unknown
% 0.25/0.44 % (7377)Termination phase: Saturation
% 0.25/0.44
% 0.25/0.44 % (7377)Memory used [KB]: 5756
% 0.25/0.44 % (7377)Time elapsed: 0.019 s
% 0.25/0.44 % (7377)Instructions burned: 38 (million)
% 0.25/0.44 % (7377)------------------------------
% 0.25/0.44 % (7377)------------------------------
% 0.25/0.44 % (7384)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)
% 0.25/0.45 % (7384)Instruction limit reached!
% 0.25/0.45 % (7384)------------------------------
% 0.25/0.45 % (7384)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.45 % (7384)Termination reason: Unknown
% 0.25/0.45 % (7384)Termination phase: Property scanning
% 0.25/0.45
% 0.25/0.45 % (7384)Memory used [KB]: 1023
% 0.25/0.45 % (7384)Time elapsed: 0.004 s
% 0.25/0.45 % (7384)Instructions burned: 4 (million)
% 0.25/0.45 % (7384)------------------------------
% 0.25/0.45 % (7384)------------------------------
% 0.25/0.45 % (7385)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)
% 0.25/0.45 % (7386)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)
% 0.25/0.45 % (7386)Instruction limit reached!
% 0.25/0.45 % (7386)------------------------------
% 0.25/0.45 % (7386)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.45 % (7386)Termination reason: Unknown
% 0.25/0.45 % (7386)Termination phase: Property scanning
% 0.25/0.45
% 0.25/0.45 % (7386)Memory used [KB]: 1023
% 0.25/0.45 % (7386)Time elapsed: 0.004 s
% 0.25/0.45 % (7386)Instructions burned: 4 (million)
% 0.25/0.45 % (7386)------------------------------
% 0.25/0.45 % (7386)------------------------------
% 0.25/0.45 % (7385)Instruction limit reached!
% 0.25/0.45 % (7385)------------------------------
% 0.25/0.45 % (7385)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.45 % (7385)Termination reason: Unknown
% 0.25/0.45 % (7385)Termination phase: Property scanning
% 0.25/0.45
% 0.25/0.45 % (7385)Memory used [KB]: 1023
% 0.25/0.45 % (7385)Time elapsed: 0.005 s
% 0.25/0.45 % (7385)Instructions burned: 7 (million)
% 0.25/0.45 % (7385)------------------------------
% 0.25/0.45 % (7385)------------------------------
% 0.25/0.46 % (7387)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.25/0.46 % (7388)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)
% 0.25/0.46 % (7387)Instruction limit reached!
% 0.25/0.46 % (7387)------------------------------
% 0.25/0.46 % (7387)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.46 % (7387)Termination reason: Unknown
% 0.25/0.46 % (7387)Termination phase: Property scanning
% 0.25/0.46
% 0.25/0.46 % (7387)Memory used [KB]: 1023
% 0.25/0.46 % (7387)Time elapsed: 0.004 s
% 0.25/0.46 % (7387)Instructions burned: 5 (million)
% 0.25/0.46 % (7387)------------------------------
% 0.25/0.46 % (7387)------------------------------
% 0.25/0.46 % (7389)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.25/0.46 % (7390)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.25/0.46 % (7389)Refutation not found, incomplete strategy
% 0.25/0.46 % (7389)------------------------------
% 0.25/0.46 % (7389)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.46 % (7389)Termination reason: Refutation not found, incomplete strategy
% 0.25/0.46
% 0.25/0.46
% 0.25/0.46 % (7389)Memory used [KB]: 5500
% 0.25/0.46 % (7389)Time elapsed: 0.027 s
% 0.25/0.46 % (7389)Instructions burned: 7 (million)
% 0.25/0.46 % (7389)------------------------------
% 0.25/0.46 % (7389)------------------------------
% 0.25/0.46 % (7390)Instruction limit reached!
% 0.25/0.46 % (7390)------------------------------
% 0.25/0.46 % (7390)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.46 % (7390)Termination reason: Unknown
% 0.25/0.46 % (7390)Termination phase: Property scanning
% 0.25/0.46
% 0.25/0.46 % (7390)Memory used [KB]: 1023
% 0.25/0.46 % (7390)Time elapsed: 0.005 s
% 0.25/0.46 % (7390)Instructions burned: 6 (million)
% 0.25/0.46 % (7390)------------------------------
% 0.25/0.46 % (7390)------------------------------
% 0.25/0.47 % (7391)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)
% 0.25/0.47 % (7388)Instruction limit reached!
% 0.25/0.47 % (7388)------------------------------
% 0.25/0.47 % (7388)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.47 % (7388)Termination reason: Unknown
% 0.25/0.47 % (7388)Termination phase: Saturation
% 0.25/0.47
% 0.25/0.47 % (7388)Memory used [KB]: 5628
% 0.25/0.47 % (7388)Time elapsed: 0.012 s
% 0.25/0.47 % (7388)Instructions burned: 18 (million)
% 0.25/0.47 % (7388)------------------------------
% 0.25/0.47 % (7388)------------------------------
% 0.25/0.47 % (7392)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)
% 0.25/0.47 % (7391)Refutation not found, incomplete strategy
% 0.25/0.47 % (7391)------------------------------
% 0.25/0.47 % (7391)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.47 % (7391)Termination reason: Refutation not found, incomplete strategy
% 0.25/0.47
% 0.25/0.47
% 0.25/0.47 % (7391)Memory used [KB]: 5500
% 0.25/0.47 % (7391)Time elapsed: 0.007 s
% 0.25/0.47 % (7391)Instructions burned: 10 (million)
% 0.25/0.47 % (7391)------------------------------
% 0.25/0.47 % (7391)------------------------------
% 0.25/0.47 % (7393)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.25/0.48 % (7393)Instruction limit reached!
% 0.25/0.48 % (7393)------------------------------
% 0.25/0.48 % (7393)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.48 % (7393)Termination reason: Unknown
% 0.25/0.48 % (7393)Termination phase: Function definition elimination
% 0.25/0.48
% 0.25/0.48 % (7393)Memory used [KB]: 1023
% 0.25/0.48 % (7393)Time elapsed: 0.005 s
% 0.25/0.48 % (7393)Instructions burned: 7 (million)
% 0.25/0.48 % (7393)------------------------------
% 0.25/0.48 % (7393)------------------------------
% 0.25/0.48 % (7392)Instruction limit reached!
% 0.25/0.48 % (7392)------------------------------
% 0.25/0.48 % (7392)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.48 % (7392)Termination reason: Unknown
% 0.25/0.48 % (7392)Termination phase: Saturation
% 0.25/0.48
% 0.25/0.48 % (7392)Memory used [KB]: 5628
% 0.25/0.48 % (7392)Time elapsed: 0.012 s
% 0.25/0.48 % (7392)Instructions burned: 22 (million)
% 0.25/0.48 % (7392)------------------------------
% 0.25/0.48 % (7392)------------------------------
% 0.25/0.48 % (7394)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)
% 0.25/0.48 % (7395)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.25/0.48 % (7396)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)
% 0.25/0.48 % (7394)Instruction limit reached!
% 0.25/0.48 % (7394)------------------------------
% 0.25/0.48 % (7394)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.48 % (7394)Termination reason: Unknown
% 0.25/0.48 % (7394)Termination phase: Saturation
% 0.25/0.48
% 0.25/0.48 % (7394)Memory used [KB]: 5500
% 0.25/0.48 % (7394)Time elapsed: 0.005 s
% 0.25/0.48 % (7394)Instructions burned: 6 (million)
% 0.25/0.48 % (7394)------------------------------
% 0.25/0.48 % (7394)------------------------------
% 0.25/0.49 % (7397)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)
% 0.25/0.49 % (7398)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)
% 0.25/0.49 % (7397)Refutation not found, incomplete strategy
% 0.25/0.49 % (7397)------------------------------
% 0.25/0.49 % (7397)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.49 % (7399)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.25/0.49 % (7397)Termination reason: Refutation not found, incomplete strategy
% 0.25/0.49
% 0.25/0.49
% 0.25/0.49 % (7397)Memory used [KB]: 5628
% 0.25/0.49 % (7397)Time elapsed: 0.007 s
% 0.25/0.49 % (7397)Instructions burned: 10 (million)
% 0.25/0.49 % (7397)------------------------------
% 0.25/0.49 % (7397)------------------------------
% 0.25/0.50 % (7400)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.25/0.50 % (7400)Instruction limit reached!
% 0.25/0.50 % (7400)------------------------------
% 0.25/0.50 % (7400)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.50 % (7400)Termination reason: Unknown
% 0.25/0.50 % (7400)Termination phase: Property scanning
% 0.25/0.50
% 0.25/0.50 % (7400)Memory used [KB]: 1023
% 0.25/0.50 % (7400)Time elapsed: 0.004 s
% 0.25/0.50 % (7400)Instructions burned: 4 (million)
% 0.25/0.50 % (7400)------------------------------
% 0.25/0.50 % (7400)------------------------------
% 0.25/0.50 % (7399)Instruction limit reached!
% 0.25/0.50 % (7399)------------------------------
% 0.25/0.50 % (7399)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.50 % (7399)Termination reason: Unknown
% 0.25/0.50 % (7399)Termination phase: Saturation
% 0.25/0.50
% 0.25/0.50 % (7399)Memory used [KB]: 1023
% 0.25/0.50 % (7399)Time elapsed: 0.010 s
% 0.25/0.50 % (7399)Instructions burned: 18 (million)
% 0.25/0.50 % (7399)------------------------------
% 0.25/0.50 % (7399)------------------------------
% 0.25/0.50 % (7369)Instruction limit reached!
% 0.25/0.50 % (7369)------------------------------
% 0.25/0.50 % (7369)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.50 % (7369)Termination reason: Unknown
% 0.25/0.50 % (7369)Termination phase: Saturation
% 0.25/0.50
% 0.25/0.50 % (7369)Memory used [KB]: 6524
% 0.25/0.50 % (7369)Time elapsed: 0.092 s
% 0.25/0.50 % (7369)Instructions burned: 183 (million)
% 0.25/0.50 % (7369)------------------------------
% 0.25/0.50 % (7369)------------------------------
% 0.25/0.51 % (7401)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.25/0.51 % (7402)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 (2998ds/127Mi)
% 0.25/0.51 % (7403)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 (2998ds/100Mi)
% 0.25/0.52 % (7404)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 (2998ds/3Mi)
% 0.25/0.52 % (7404)Instruction limit reached!
% 0.25/0.52 % (7404)------------------------------
% 0.25/0.52 % (7404)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.52 % (7404)Termination reason: Unknown
% 0.25/0.52 % (7404)Termination phase: Property scanning
% 0.25/0.52
% 0.25/0.52 % (7404)Memory used [KB]: 1023
% 0.25/0.52 % (7404)Time elapsed: 0.003 s
% 0.25/0.52 % (7404)Instructions burned: 4 (million)
% 0.25/0.52 % (7404)------------------------------
% 0.25/0.52 % (7404)------------------------------
% 0.25/0.52 % (7401)Instruction limit reached!
% 0.25/0.52 % (7401)------------------------------
% 0.25/0.52 % (7401)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.52 % (7401)Termination reason: Unknown
% 0.25/0.52 % (7401)Termination phase: Saturation
% 0.25/0.52
% 0.25/0.52 % (7401)Memory used [KB]: 5628
% 0.25/0.52 % (7401)Time elapsed: 0.016 s
% 0.25/0.52 % (7401)Instructions burned: 31 (million)
% 0.25/0.52 % (7401)------------------------------
% 0.25/0.52 % (7401)------------------------------
% 0.25/0.53 % (7405)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)
% 0.25/0.53 % (7406)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)
% 0.25/0.54 % (7405)Refutation not found, incomplete strategy
% 0.25/0.54 % (7405)------------------------------
% 0.25/0.54 % (7405)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.54 % (7405)Termination reason: Refutation not found, incomplete strategy
% 0.25/0.54
% 0.25/0.54
% 0.25/0.54 % (7405)Memory used [KB]: 5628
% 0.25/0.54 % (7405)Time elapsed: 0.011 s
% 0.25/0.54 % (7405)Instructions burned: 17 (million)
% 0.25/0.54 % (7405)------------------------------
% 0.25/0.54 % (7405)------------------------------
% 1.34/0.56 % (7407)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)
% 1.34/0.56 % (7395)First to succeed.
% 1.34/0.56 % (7403)Instruction limit reached!
% 1.34/0.56 % (7403)------------------------------
% 1.34/0.56 % (7403)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.34/0.56 % (7403)Termination reason: Unknown
% 1.34/0.56 % (7403)Termination phase: Saturation
% 1.34/0.56
% 1.34/0.56 % (7403)Memory used [KB]: 6012
% 1.34/0.56 % (7403)Time elapsed: 0.051 s
% 1.34/0.56 % (7403)Instructions burned: 101 (million)
% 1.34/0.56 % (7403)------------------------------
% 1.34/0.56 % (7403)------------------------------
% 1.34/0.56 % (7407)Refutation not found, incomplete strategy
% 1.34/0.56 % (7407)------------------------------
% 1.34/0.56 % (7407)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.34/0.56 % (7407)Termination reason: Refutation not found, incomplete strategy
% 1.34/0.56
% 1.34/0.56
% 1.34/0.56 % (7407)Memory used [KB]: 5500
% 1.34/0.56 % (7407)Time elapsed: 0.006 s
% 1.34/0.56 % (7407)Instructions burned: 7 (million)
% 1.34/0.56 % (7407)------------------------------
% 1.34/0.56 % (7407)------------------------------
% 1.34/0.58 % (7402)Instruction limit reached!
% 1.34/0.58 % (7402)------------------------------
% 1.34/0.58 % (7402)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.34/0.58 % (7402)Termination reason: Unknown
% 1.34/0.58 % (7402)Termination phase: Saturation
% 1.34/0.58
% 1.34/0.58 % (7402)Memory used [KB]: 6012
% 1.34/0.58 % (7402)Time elapsed: 0.065 s
% 1.34/0.58 % (7402)Instructions burned: 128 (million)
% 1.34/0.58 % (7402)------------------------------
% 1.34/0.58 % (7402)------------------------------
% 1.34/0.58 % (7408)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on theBenchmark for (2998ds/39Mi)
% 1.34/0.58 % (7406)Instruction limit reached!
% 1.34/0.58 % (7406)------------------------------
% 1.34/0.58 % (7406)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.34/0.58 % (7406)Termination reason: Unknown
% 1.34/0.58 % (7406)Termination phase: Saturation
% 1.34/0.58
% 1.34/0.58 % (7406)Memory used [KB]: 6012
% 1.34/0.58 % (7406)Time elapsed: 0.045 s
% 1.34/0.58 % (7406)Instructions burned: 87 (million)
% 1.34/0.58 % (7406)------------------------------
% 1.34/0.58 % (7406)------------------------------
% 1.34/0.58 % (7409)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on theBenchmark for (2998ds/448Mi)
% 1.61/0.59 % (7410)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on theBenchmark for (2998ds/46Mi)
% 1.61/0.59 % (7411)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on theBenchmark for (2998ds/98Mi)
% 1.61/0.59 % (7395)Refutation found. Thanks to Tanya!
% 1.61/0.59 % SZS status Theorem for theBenchmark
% 1.61/0.59 % SZS output start Proof for theBenchmark
% 1.61/0.59 thf(func_def_0, type, irel: $i > $i > $o).
% 1.61/0.59 thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 1.61/0.59 thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 1.61/0.59 thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 1.61/0.59 thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 1.61/0.59 thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 1.61/0.59 thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 1.61/0.59 thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 1.61/0.59 thf(func_def_9, type, itrue: $i > $o).
% 1.61/0.59 thf(func_def_10, type, ifalse: $i > $o).
% 1.61/0.59 thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 1.61/0.59 thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 1.61/0.59 thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 1.61/0.59 thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 1.61/0.59 thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 1.61/0.59 thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 1.61/0.59 thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 1.61/0.59 thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 1.61/0.59 thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 1.61/0.59 thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 1.61/0.59 thf(func_def_21, type, p0: $i > $o).
% 1.61/0.59 thf(func_def_22, type, p1: $i > $o).
% 1.61/0.59 thf(func_def_23, type, p10: $i > $o).
% 1.61/0.59 thf(func_def_24, type, p11: $i > $o).
% 1.61/0.59 thf(func_def_25, type, p12: $i > $o).
% 1.61/0.59 thf(func_def_26, type, p13: $i > $o).
% 1.61/0.59 thf(func_def_27, type, p14: $i > $o).
% 1.61/0.59 thf(func_def_28, type, p15: $i > $o).
% 1.61/0.59 thf(func_def_29, type, p16: $i > $o).
% 1.61/0.59 thf(func_def_30, type, p17: $i > $o).
% 1.61/0.59 thf(func_def_31, type, p18: $i > $o).
% 1.61/0.59 thf(func_def_32, type, p19: $i > $o).
% 1.61/0.59 thf(func_def_33, type, p2: $i > $o).
% 1.61/0.59 thf(func_def_34, type, p20: $i > $o).
% 1.61/0.59 thf(func_def_35, type, p3: $i > $o).
% 1.61/0.59 thf(func_def_36, type, p4: $i > $o).
% 1.61/0.59 thf(func_def_37, type, p5: $i > $o).
% 1.61/0.59 thf(func_def_38, type, p6: $i > $o).
% 1.61/0.59 thf(func_def_39, type, p7: $i > $o).
% 1.61/0.59 thf(func_def_40, type, p8: $i > $o).
% 1.61/0.59 thf(func_def_41, type, p9: $i > $o).
% 1.61/0.59 thf(func_def_55, type, sK1: $i > $i).
% 1.61/0.59 thf(func_def_56, type, sK2: $i > $i).
% 1.61/0.59 thf(func_def_57, type, sK3: $i > $i).
% 1.61/0.59 thf(func_def_58, type, sK4: $i > $i).
% 1.61/0.59 thf(func_def_59, type, sK5: $i > $i).
% 1.61/0.59 thf(func_def_60, type, sK6: $i > $i).
% 1.61/0.59 thf(func_def_62, type, sK8: $i > $i).
% 1.61/0.59 thf(func_def_63, type, sK9: $i > $i).
% 1.61/0.59 thf(func_def_64, type, sK10: $i > $i).
% 1.61/0.59 thf(func_def_65, type, sK11: $i > $i).
% 1.61/0.59 thf(func_def_66, type, sK12: $i > $i).
% 1.61/0.59 thf(func_def_67, type, sK13: $i > $i).
% 1.61/0.59 thf(func_def_68, type, sK14: $i > $i).
% 1.61/0.59 thf(func_def_69, type, sK15: $i > $i).
% 1.61/0.59 thf(func_def_70, type, sK16: $i > $i).
% 1.61/0.59 thf(func_def_71, type, sK17: $i > $i).
% 1.61/0.59 thf(func_def_72, type, sK18: $i > $i).
% 1.61/0.59 thf(func_def_73, type, sK19: $i > $i).
% 1.61/0.59 thf(func_def_74, type, sK20: $i > $i).
% 1.61/0.59 thf(func_def_75, type, sK21: $i > $i).
% 1.61/0.59 thf(func_def_76, type, sK22: $i > $i).
% 1.61/0.59 thf(func_def_77, type, sK23: $i > $i).
% 1.61/0.59 thf(func_def_78, type, sK24: $i > $i).
% 1.61/0.59 thf(func_def_79, type, sK25: $i > $i).
% 1.61/0.59 thf(func_def_80, type, sK26: $i > $i).
% 1.61/0.59 thf(func_def_81, type, sK27: $i > $i).
% 1.61/0.59 thf(func_def_82, type, sK28: $i > $i).
% 1.61/0.59 thf(func_def_83, type, sK29: $i > $i).
% 1.61/0.59 thf(func_def_84, type, sK30: $i > $i).
% 1.61/0.59 thf(func_def_85, type, sK31: $i > $i).
% 1.61/0.59 thf(func_def_86, type, sK32: $i > $i).
% 1.61/0.59 thf(func_def_87, type, sK33: $i > $i).
% 1.61/0.59 thf(func_def_88, type, sK34: $i > $i).
% 1.61/0.59 thf(func_def_89, type, sK35: $i > $i).
% 1.61/0.59 thf(func_def_90, type, sK36: $i > $i).
% 1.61/0.59 thf(func_def_91, type, sK37: $i > $i).
% 1.61/0.59 thf(func_def_92, type, sK38: $i > $i).
% 1.61/0.59 thf(func_def_93, type, sK39: $i > $i).
% 1.61/0.59 thf(func_def_94, type, sK40: $i > $i).
% 1.61/0.59 thf(func_def_95, type, sK41: $i > $i).
% 1.61/0.59 thf(func_def_96, type, sK42: $i > $i).
% 1.61/0.59 thf(func_def_97, type, sK43: $i > $i).
% 1.61/0.59 thf(func_def_98, type, sK44: $i > $i).
% 1.61/0.59 thf(func_def_99, type, sK45: $i > $i).
% 1.61/0.59 thf(func_def_100, type, sK46: $i > $i).
% 1.61/0.59 thf(func_def_101, type, sK47: $i > $i).
% 1.61/0.59 thf(func_def_102, type, sK48: $i > $i).
% 1.61/0.59 thf(func_def_103, type, sK49: $i > $i).
% 1.61/0.59 thf(func_def_104, type, sK50: $i > $i).
% 1.61/0.59 thf(func_def_105, type, sK51: $i > $i).
% 1.61/0.59 thf(func_def_106, type, sK52: $i > $i).
% 1.61/0.59 thf(func_def_107, type, sK53: $i > $i).
% 1.61/0.59 thf(func_def_108, type, sK54: $i > $i).
% 1.61/0.59 thf(func_def_109, type, sK55: $i > $i).
% 1.61/0.59 thf(func_def_110, type, sK56: $i > $i).
% 1.61/0.59 thf(func_def_111, type, sK57: $i > $i).
% 1.61/0.59 thf(f1266,plain,(
% 1.61/0.59 $false),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1264])).
% 1.61/0.59 thf(f1264,plain,(
% 1.61/0.59 ($true = $false)),
% 1.61/0.59 inference(superposition,[],[f1261,f269])).
% 1.61/0.59 thf(f269,plain,(
% 1.61/0.59 ((p0 @ sK7) = $false)),
% 1.61/0.59 inference(sigma_clausification,[],[f268])).
% 1.61/0.59 thf(f268,plain,(
% 1.61/0.59 ((!! @ $i @ p0) != $true)),
% 1.61/0.59 inference(beta_eta_normalization,[],[f194])).
% 1.61/0.59 thf(f194,plain,(
% 1.61/0.59 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: (Y0)) @ p0)))),
% 1.61/0.59 inference(definition_unfolding,[],[f153,f139,f152])).
% 1.61/0.59 thf(f152,plain,(
% 1.61/0.59 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 1.61/0.59 inference(cnf_transformation,[],[f55])).
% 1.61/0.59 thf(f55,plain,(
% 1.61/0.59 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 1.61/0.59 inference(fool_elimination,[],[f54])).
% 1.61/0.59 thf(f54,plain,(
% 1.61/0.59 ((^[X0 : $i > $o] : (X0)) = iatom)),
% 1.61/0.59 inference(rectify,[],[f8])).
% 1.61/0.59 thf(f8,axiom,(
% 1.61/0.59 ((^[X5 : $i > $o] : (X5)) = iatom)),
% 1.61/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iatom)).
% 1.61/0.59 thf(f139,plain,(
% 1.61/0.59 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 1.61/0.59 inference(cnf_transformation,[],[f53])).
% 1.61/0.59 thf(f53,plain,(
% 1.61/0.59 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 1.61/0.59 inference(fool_elimination,[],[f52])).
% 1.61/0.59 thf(f52,plain,(
% 1.61/0.59 (ivalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 1.61/0.59 inference(rectify,[],[f18])).
% 1.61/0.59 thf(f18,axiom,(
% 1.61/0.59 (ivalid = (^[X8 : $i > $o] : (! [X6] : (X8 @ X6))))),
% 1.61/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ivalid)).
% 1.61/0.59 thf(f153,plain,(
% 1.61/0.59 ((ivalid @ (iatom @ p0)) != $true)),
% 1.61/0.59 inference(cnf_transformation,[],[f130])).
% 1.61/0.59 thf(f130,plain,(
% 1.61/0.59 ((ivalid @ (iatom @ p0)) != $true)),
% 1.61/0.59 inference(flattening,[],[f75])).
% 1.61/0.59 thf(f75,plain,(
% 1.61/0.59 ~((ivalid @ (iatom @ p0)) = $true)),
% 1.61/0.59 inference(fool_elimination,[],[f74])).
% 1.61/0.59 thf(f74,plain,(
% 1.61/0.59 ~(ivalid @ (iatom @ p0))),
% 1.61/0.59 inference(rectify,[],[f44])).
% 1.61/0.59 thf(f44,negated_conjecture,(
% 1.61/0.59 ~(ivalid @ (iatom @ p0))),
% 1.61/0.59 inference(negated_conjecture,[],[f43])).
% 1.61/0.59 thf(f43,conjecture,(
% 1.61/0.59 (ivalid @ (iatom @ p0))),
% 1.61/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 1.61/0.59 thf(f1261,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p0 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1258])).
% 1.61/0.59 thf(f1258,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = (p0 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f1255,f171])).
% 1.61/0.59 thf(f171,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (((irel @ X0 @ X0) = $true)) )),
% 1.61/0.59 inference(cnf_transformation,[],[f111])).
% 1.61/0.59 thf(f111,plain,(
% 1.61/0.59 ! [X0] : ((irel @ X0 @ X0) = $true)),
% 1.61/0.59 inference(fool_elimination,[],[f110])).
% 1.61/0.59 thf(f110,plain,(
% 1.61/0.59 ! [X0] : (irel @ X0 @ X0)),
% 1.61/0.59 inference(rectify,[],[f1])).
% 1.61/0.59 thf(f1,axiom,(
% 1.61/0.59 ! [X0] : (irel @ X0 @ X0)),
% 1.61/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom)).
% 1.61/0.59 thf(f1255,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p0 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1251])).
% 1.61/0.59 thf(f1251,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = $false) | ($true = (p0 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f171,f1247])).
% 1.61/0.59 thf(f1247,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ($true = (p0 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1246])).
% 1.61/0.59 thf(f1246,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = $false) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ($true = (p0 @ X3))) )),
% 1.61/0.59 inference(forward_demodulation,[],[f1245,f1239])).
% 1.61/0.59 thf(f1239,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p1 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1236])).
% 1.61/0.59 thf(f1236,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = (p1 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f171,f1233])).
% 1.61/0.59 thf(f1233,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p1 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1228])).
% 1.61/0.59 thf(f1228,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($true = (p1 @ X0)) | ((irel @ X1 @ X0) = $false)) )),
% 1.61/0.59 inference(superposition,[],[f171,f1224])).
% 1.61/0.59 thf(f1224,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ($true = (p1 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1223])).
% 1.61/0.59 thf(f1223,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = $false) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3)) | ($true = (p1 @ X3))) )),
% 1.61/0.59 inference(forward_demodulation,[],[f1222,f1216])).
% 1.61/0.59 thf(f1216,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p2 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1212])).
% 1.61/0.59 thf(f1212,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = (p2 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f1208,f171])).
% 1.61/0.59 thf(f1208,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p2 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1204])).
% 1.61/0.59 thf(f1204,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($true = (p2 @ X0)) | ((irel @ X1 @ X0) = $false)) )),
% 1.61/0.59 inference(superposition,[],[f1201,f171])).
% 1.61/0.59 thf(f1201,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p2 @ X3) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1200])).
% 1.61/0.59 thf(f1200,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p2 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ($true = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.59 inference(forward_demodulation,[],[f1197,f1193])).
% 1.61/0.59 thf(f1193,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p3 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1189])).
% 1.61/0.59 thf(f1189,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = (p3 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f1187,f171])).
% 1.61/0.59 thf(f1187,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p3 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1182])).
% 1.61/0.59 thf(f1182,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (($true = (p3 @ X0)) | ($true = $false) | ((irel @ X1 @ X0) = $false)) )),
% 1.61/0.59 inference(superposition,[],[f171,f1178])).
% 1.61/0.59 thf(f1178,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((p3 @ X3) = $true)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1177])).
% 1.61/0.59 thf(f1177,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p3 @ X3) = $true) | ($true = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.59 inference(forward_demodulation,[],[f1175,f1169])).
% 1.61/0.59 thf(f1169,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p4 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1167])).
% 1.61/0.59 thf(f1167,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p4 @ X0)) | ($true = $false)) )),
% 1.61/0.59 inference(superposition,[],[f171,f1164])).
% 1.61/0.59 thf(f1164,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p4 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1159])).
% 1.61/0.59 thf(f1159,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p4 @ X0)) | ($true = $false)) )),
% 1.61/0.59 inference(superposition,[],[f171,f1155])).
% 1.61/0.59 thf(f1155,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((p4 @ X3) = $true)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1154])).
% 1.61/0.59 thf(f1154,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = $false) | ($false = (irel @ X2 @ X3)) | ((p4 @ X3) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(forward_demodulation,[],[f1152,f1146])).
% 1.61/0.59 thf(f1146,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (((p5 @ X0) = $true)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1143])).
% 1.61/0.59 thf(f1143,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (((p5 @ X0) = $true) | ($true = $false)) )),
% 1.61/0.59 inference(superposition,[],[f1139,f171])).
% 1.61/0.59 thf(f1139,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ((p5 @ X0) = $true)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1136])).
% 1.61/0.59 thf(f1136,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ((irel @ X1 @ X0) = $false) | ((p5 @ X0) = $true)) )),
% 1.61/0.59 inference(superposition,[],[f171,f1132])).
% 1.61/0.59 thf(f1132,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ($true = (p5 @ X3))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1131])).
% 1.61/0.59 thf(f1131,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = $false) | ($false = (irel @ X2 @ X3)) | ($true = (p5 @ X3))) )),
% 1.61/0.59 inference(forward_demodulation,[],[f1130,f1124])).
% 1.61/0.59 thf(f1124,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p6 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1121])).
% 1.61/0.59 thf(f1121,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p6 @ X0)) | ($true = $false)) )),
% 1.61/0.59 inference(superposition,[],[f171,f1118])).
% 1.61/0.59 thf(f1118,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p6 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1113])).
% 1.61/0.59 thf(f1113,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (($true = (p6 @ X0)) | ((irel @ X1 @ X0) = $false) | ($true = $false)) )),
% 1.61/0.59 inference(superposition,[],[f171,f1109])).
% 1.61/0.59 thf(f1109,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ($true = (p6 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1108])).
% 1.61/0.59 thf(f1108,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (p6 @ X3)) | ($false = (irel @ X2 @ X3)) | ($true = $false)) )),
% 1.61/0.59 inference(forward_demodulation,[],[f1107,f1101])).
% 1.61/0.59 thf(f1101,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (((p7 @ X0) = $true)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1098])).
% 1.61/0.59 thf(f1098,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = $false) | ((p7 @ X0) = $true)) )),
% 1.61/0.59 inference(superposition,[],[f171,f1094])).
% 1.61/0.59 thf(f1094,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ((p7 @ X0) = $true)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1089])).
% 1.61/0.59 thf(f1089,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ((irel @ X1 @ X0) = $false) | ((p7 @ X0) = $true)) )),
% 1.61/0.59 inference(superposition,[],[f1086,f171])).
% 1.61/0.59 thf(f1086,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ($true = (p7 @ X3))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1085])).
% 1.61/0.59 thf(f1085,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ($true = $false) | ($true = (p7 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(forward_demodulation,[],[f1083,f1078])).
% 1.61/0.59 thf(f1078,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p8 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1074])).
% 1.61/0.59 thf(f1074,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p8 @ X0)) | ($true = $false)) )),
% 1.61/0.59 inference(superposition,[],[f1071,f171])).
% 1.61/0.59 thf(f1071,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p8 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1066])).
% 1.61/0.59 thf(f1066,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ((irel @ X1 @ X0) = $false) | ($true = (p8 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f1063,f171])).
% 1.61/0.59 thf(f1063,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ($true = (p8 @ X3))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1062])).
% 1.61/0.59 thf(f1062,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p8 @ X3)) | ($false = (irel @ X2 @ X3)) | ($true = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(forward_demodulation,[],[f1060,f1055])).
% 1.61/0.59 thf(f1055,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p9 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1051])).
% 1.61/0.59 thf(f1051,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = (p9 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f1048,f171])).
% 1.61/0.59 thf(f1048,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p9 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1044])).
% 1.61/0.59 thf(f1044,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (($true = (p9 @ X0)) | ($true = $false) | ((irel @ X1 @ X0) = $false)) )),
% 1.61/0.59 inference(superposition,[],[f171,f1040])).
% 1.61/0.59 thf(f1040,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ($true = (p9 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1039])).
% 1.61/0.59 thf(f1039,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = $false) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3)) | ($true = (p9 @ X3))) )),
% 1.61/0.59 inference(forward_demodulation,[],[f1037,f1032])).
% 1.61/0.59 thf(f1032,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p10 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1028])).
% 1.61/0.59 thf(f1028,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = (p10 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f1026,f171])).
% 1.61/0.59 thf(f1026,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p10 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1021])).
% 1.61/0.59 thf(f1021,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = $false) | ($true = (p10 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f171,f1017])).
% 1.61/0.59 thf(f1017,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p10 @ X3) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1016])).
% 1.61/0.59 thf(f1016,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = $false) | ((p10 @ X3) = $true) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(forward_demodulation,[],[f1014,f1009])).
% 1.61/0.59 thf(f1009,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p11 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f1005])).
% 1.61/0.59 thf(f1005,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = (p11 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f1002,f171])).
% 1.61/0.59 thf(f1002,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p11 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f997])).
% 1.61/0.59 thf(f997,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($true = (p11 @ X0)) | ((irel @ X1 @ X0) = $false)) )),
% 1.61/0.59 inference(superposition,[],[f994,f171])).
% 1.61/0.59 thf(f994,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p11 @ X3) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f993])).
% 1.61/0.59 thf(f993,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3)) | ($true = $false) | ((p11 @ X3) = $true)) )),
% 1.61/0.59 inference(forward_demodulation,[],[f992,f985])).
% 1.61/0.59 thf(f985,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p12 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f982])).
% 1.61/0.59 thf(f982,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = (p12 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f979,f171])).
% 1.61/0.59 thf(f979,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p12 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f974])).
% 1.61/0.59 thf(f974,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($true = (p12 @ X0)) | ((irel @ X1 @ X0) = $false)) )),
% 1.61/0.59 inference(superposition,[],[f971,f171])).
% 1.61/0.59 thf(f971,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ($true = (p12 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f970])).
% 1.61/0.59 thf(f970,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = $false) | ($true = (p12 @ X3)) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.59 inference(forward_demodulation,[],[f969,f963])).
% 1.61/0.59 thf(f963,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p13 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f959])).
% 1.61/0.59 thf(f959,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = (p13 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f957,f171])).
% 1.61/0.59 thf(f957,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p13 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f952])).
% 1.61/0.59 thf(f952,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = $false) | ($true = (p13 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f171,f948])).
% 1.61/0.59 thf(f948,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ($true = (p13 @ X3))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f947])).
% 1.61/0.59 thf(f947,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = $false) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3)) | ($true = (p13 @ X3))) )),
% 1.61/0.59 inference(forward_demodulation,[],[f944,f940])).
% 1.61/0.59 thf(f940,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p14 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f937])).
% 1.61/0.59 thf(f937,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = (p14 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f171,f932])).
% 1.61/0.59 thf(f932,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p14 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f929])).
% 1.61/0.59 thf(f929,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p14 @ X0)) | ($true = $false)) )),
% 1.61/0.59 inference(superposition,[],[f171,f925])).
% 1.61/0.59 thf(f925,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((p14 @ X3) = $true)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f924])).
% 1.61/0.59 thf(f924,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p14 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ($true = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.59 inference(forward_demodulation,[],[f923,f917])).
% 1.61/0.59 thf(f917,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p15 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f914])).
% 1.61/0.59 thf(f914,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = (p15 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f171,f910])).
% 1.61/0.59 thf(f910,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p15 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f906])).
% 1.61/0.59 thf(f906,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (($true = (p15 @ X0)) | ((irel @ X1 @ X0) = $false) | ($true = $false)) )),
% 1.61/0.59 inference(superposition,[],[f171,f902])).
% 1.61/0.59 thf(f902,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p15 @ X3) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f901])).
% 1.61/0.59 thf(f901,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = $false) | ($false = (irel @ X2 @ X3)) | ((p15 @ X3) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(forward_demodulation,[],[f899,f894])).
% 1.61/0.59 thf(f894,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p16 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f891])).
% 1.61/0.59 thf(f891,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = (p16 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f171,f887])).
% 1.61/0.59 thf(f887,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p16 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f882])).
% 1.61/0.59 thf(f882,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($true = (p16 @ X0)) | ((irel @ X1 @ X0) = $false)) )),
% 1.61/0.59 inference(superposition,[],[f879,f171])).
% 1.61/0.59 thf(f879,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ($true = (p16 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f878])).
% 1.61/0.59 thf(f878,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = $false) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3)) | ($true = (p16 @ X3))) )),
% 1.61/0.59 inference(forward_demodulation,[],[f877,f870])).
% 1.61/0.59 thf(f870,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p17 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f868])).
% 1.61/0.59 thf(f868,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = (p17 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f171,f864])).
% 1.61/0.59 thf(f864,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p17 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f860])).
% 1.61/0.59 thf(f860,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (($true = (p17 @ X0)) | ($true = $false) | ((irel @ X1 @ X0) = $false)) )),
% 1.61/0.59 inference(superposition,[],[f171,f856])).
% 1.61/0.59 thf(f856,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((p17 @ X3) = $true)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f855])).
% 1.61/0.59 thf(f855,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p17 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ($true = $false)) )),
% 1.61/0.59 inference(forward_demodulation,[],[f852,f848])).
% 1.61/0.59 thf(f848,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (((p18 @ X0) = $true)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f844])).
% 1.61/0.59 thf(f844,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (((p18 @ X0) = $true) | ($true = $false)) )),
% 1.61/0.59 inference(superposition,[],[f842,f171])).
% 1.61/0.59 thf(f842,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ((p18 @ X0) = $true)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f837])).
% 1.61/0.59 thf(f837,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((p18 @ X0) = $true) | ((irel @ X1 @ X0) = $false) | ($true = $false)) )),
% 1.61/0.59 inference(superposition,[],[f171,f833])).
% 1.61/0.59 thf(f833,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ($true = (p18 @ X3))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f832])).
% 1.61/0.59 thf(f832,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = $false) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ($true = (p18 @ X3))) )),
% 1.61/0.59 inference(forward_demodulation,[],[f830,f824])).
% 1.61/0.59 thf(f824,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = (p19 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f822])).
% 1.61/0.59 thf(f822,plain,(
% 1.61/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = (p19 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f171,f819])).
% 1.61/0.59 thf(f819,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p19 @ X0))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f813])).
% 1.61/0.59 thf(f813,plain,(
% 1.61/0.59 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ((irel @ X1 @ X0) = $false) | ($true = (p19 @ X0))) )),
% 1.61/0.59 inference(superposition,[],[f807,f171])).
% 1.61/0.59 thf(f807,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ($true = (p19 @ X3))) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f806])).
% 1.61/0.59 thf(f806,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (p19 @ X3)) | ($false = (irel @ X2 @ X3)) | ($true = $false)) )),
% 1.61/0.59 inference(forward_demodulation,[],[f803,f327])).
% 1.61/0.59 thf(f327,plain,(
% 1.61/0.59 ( ! [X1 : $i] : (($true = (p20 @ X1))) )),
% 1.61/0.59 inference(pi_clausification,[],[f326])).
% 1.61/0.59 thf(f326,plain,(
% 1.61/0.59 ($true = (!! @ $i @ p20))),
% 1.61/0.59 inference(beta_eta_normalization,[],[f204])).
% 1.61/0.59 thf(f204,plain,(
% 1.61/0.59 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: (Y0)) @ p20)))),
% 1.61/0.59 inference(definition_unfolding,[],[f170,f139,f152])).
% 1.61/0.59 thf(f170,plain,(
% 1.61/0.59 ((ivalid @ (iatom @ p20)) = $true)),
% 1.61/0.59 inference(cnf_transformation,[],[f69])).
% 1.61/0.59 thf(f69,plain,(
% 1.61/0.59 ((ivalid @ (iatom @ p20)) = $true)),
% 1.61/0.59 inference(fool_elimination,[],[f68])).
% 1.61/0.59 thf(f68,plain,(
% 1.61/0.59 (ivalid @ (iatom @ p20))),
% 1.61/0.59 inference(rectify,[],[f22])).
% 1.61/0.59 thf(f22,axiom,(
% 1.61/0.59 (ivalid @ (iatom @ p20))),
% 1.61/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1)).
% 1.61/0.59 thf(f803,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p19 @ X3)) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3)) | ((p20 @ (sK31 @ X1)) = $false)) )),
% 1.61/0.59 inference(trivial_inequality_removal,[],[f800])).
% 1.61/0.59 thf(f800,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p20 @ (sK31 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = $false) | ($true = (p19 @ X3)) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.59 inference(backward_demodulation,[],[f535,f327])).
% 1.61/0.59 thf(f535,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p20 @ (sK33 @ X2))) | ($true = (p19 @ X3)) | ((p20 @ (sK31 @ X1)) = $false) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(binary_proxy_clausification,[],[f534])).
% 1.61/0.59 thf(f534,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p20 @ (sK31 @ X1)) = $false) | (((irel @ X2 @ (sK33 @ X2)) => (p20 @ (sK33 @ X2))) = $false) | ($false = (irel @ X2 @ X3)) | ($true = (p19 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(binary_proxy_clausification,[],[f533])).
% 1.61/0.59 thf(f533,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((irel @ X2 @ X3) => (p19 @ X3))) | (((irel @ X2 @ (sK33 @ X2)) => (p20 @ (sK33 @ X2))) = $false) | ((irel @ X1 @ X2) = $false) | ((p20 @ (sK31 @ X1)) = $false)) )),
% 1.61/0.59 inference(beta_eta_normalization,[],[f532])).
% 1.61/0.59 thf(f532,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p20 @ Y0))) @ (sK33 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ((p20 @ (sK31 @ X1)) = $false) | ($true = ((irel @ X2 @ X3) => (p19 @ X3)))) )),
% 1.61/0.59 inference(sigma_clausification,[],[f531])).
% 1.61/0.59 thf(f531,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p20 @ Y0)))) = $false) | ($true = ((irel @ X2 @ X3) => (p19 @ X3))) | ((p20 @ (sK31 @ X1)) = $false)) )),
% 1.61/0.59 inference(beta_eta_normalization,[],[f530])).
% 1.61/0.59 thf(f530,plain,(
% 1.61/0.59 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p20 @ Y0)))) = $false) | ((p20 @ (sK31 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0))) @ X3))) )),
% 1.61/0.59 inference(pi_clausification,[],[f529])).
% 1.61/0.59 thf(f529,plain,(
% 1.61/0.59 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p20 @ (sK31 @ X1)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p20 @ Y0)))) = $false)) )),
% 1.61/0.59 inference(not_proxy_clausification,[],[f519])).
% 1.61/0.59 thf(f519,plain,(
% 1.61/0.59 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p20 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0))))) | ((p20 @ (sK31 @ X1)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(binary_proxy_clausification,[],[f518])).
% 1.61/0.59 thf(f518,plain,(
% 1.61/0.59 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK31 @ X1)) => (p20 @ (sK31 @ X1))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p20 @ Y0)))))) | ((irel @ X1 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0)))))) )),
% 1.61/0.59 inference(binary_proxy_clausification,[],[f517])).
% 1.61/0.59 thf(f517,plain,(
% 1.61/0.59 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p20 @ Y0))))))) | ((irel @ X1 @ X2) = $false) | (((irel @ X1 @ (sK31 @ X1)) => (p20 @ (sK31 @ X1))) = $false)) )),
% 1.61/0.59 inference(beta_eta_normalization,[],[f516])).
% 1.61/0.59 thf(f516,plain,(
% 1.61/0.59 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p20 @ Y0))) @ (sK31 @ X1)) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p20 @ Y0)))))))) )),
% 1.61/0.59 inference(sigma_clausification,[],[f515])).
% 1.61/0.59 thf(f515,plain,(
% 1.61/0.59 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p20 @ Y0))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p20 @ Y0))))))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.59 inference(binary_proxy_clausification,[],[f514])).
% 1.61/0.59 thf(f514,plain,(
% 1.61/0.59 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p20 @ Y0)))))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p20 @ Y0)))))) )),
% 1.61/0.59 inference(beta_eta_normalization,[],[f513])).
% 1.61/0.59 thf(f513,plain,(
% 1.61/0.59 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p20 @ Y0))))) | ($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p19 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p20 @ Y1)))))))) @ X2))) )),
% 1.61/0.59 inference(pi_clausification,[],[f512])).
% 1.61/0.59 thf(f512,plain,(
% 1.61/0.59 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p19 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p20 @ Y1)))))))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p20 @ Y0)))))) )),
% 1.61/0.59 inference(not_proxy_clausification,[],[f511])).
% 1.61/0.59 thf(f511,plain,(
% 1.61/0.59 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p20 @ Y0))))) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p19 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p20 @ Y1))))))))))) )),
% 1.61/0.59 inference(binary_proxy_clausification,[],[f510])).
% 1.61/0.59 thf(f510,plain,(
% 1.61/0.59 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p19 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p20 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p20 @ Y0)))))) = $true)) )),
% 1.61/0.59 inference(beta_eta_normalization,[],[f509])).
% 1.61/0.59 thf(f509,plain,(
% 1.61/0.59 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p19 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p20 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p20 @ Y1))))))) @ X1) = $true)) )),
% 1.61/0.59 inference(pi_clausification,[],[f508])).
% 1.61/0.59 thf(f508,plain,(
% 1.61/0.59 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p19 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p20 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p20 @ Y1)))))))) = $true)),
% 1.61/0.59 inference(beta_eta_normalization,[],[f206])).
% 1.61/0.59 thf(f206,plain,(
% 1.61/0.59 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p20) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p20) @ ((^[Y0 : $i > $o]: (Y0)) @ p19)))))),
% 1.61/0.59 inference(definition_unfolding,[],[f174,f139,f181,f152,f181,f152,f152])).
% 1.61/0.59 thf(f181,plain,(
% 1.61/0.59 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))))),
% 1.61/0.59 inference(definition_unfolding,[],[f143,f176,f173,f173])).
% 1.61/0.59 thf(f173,plain,(
% 1.61/0.59 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.61/0.60 inference(cnf_transformation,[],[f121])).
% 1.61/0.60 thf(f121,plain,(
% 1.61/0.60 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.61/0.60 inference(fool_elimination,[],[f120])).
% 1.61/0.60 thf(f120,plain,(
% 1.61/0.60 (mbox_s4 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((irel @ X1 @ X2) => (X0 @ X2)))))),
% 1.61/0.60 inference(rectify,[],[f7])).
% 1.61/0.60 thf(f7,axiom,(
% 1.61/0.60 (mbox_s4 = (^[X5 : $i > $o, X0 : $i] : (! [X1] : ((irel @ X0 @ X1) => (X5 @ X1)))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4)).
% 1.61/0.60 thf(f176,plain,(
% 1.61/0.60 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f156,f164,f166])).
% 1.61/0.60 thf(f166,plain,(
% 1.61/0.60 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 1.61/0.60 inference(cnf_transformation,[],[f105])).
% 1.61/0.60 thf(f105,plain,(
% 1.61/0.60 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 1.61/0.60 inference(fool_elimination,[],[f104])).
% 1.61/0.60 thf(f104,plain,(
% 1.61/0.60 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 1.61/0.60 inference(rectify,[],[f3])).
% 1.61/0.60 thf(f3,axiom,(
% 1.61/0.60 (mnot = (^[X0 : $i > $o, X3 : $i] : (~(X0 @ X3))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 1.61/0.60 thf(f164,plain,(
% 1.61/0.60 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 1.61/0.60 inference(cnf_transformation,[],[f99])).
% 1.61/0.60 thf(f99,plain,(
% 1.61/0.60 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 1.61/0.60 inference(fool_elimination,[],[f98])).
% 1.61/0.60 thf(f98,plain,(
% 1.61/0.60 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 1.61/0.60 inference(rectify,[],[f4])).
% 1.61/0.60 thf(f4,axiom,(
% 1.61/0.60 (mor = (^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X0 @ X3) | (X1 @ X3))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 1.61/0.60 thf(f156,plain,(
% 1.61/0.60 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 1.61/0.60 inference(cnf_transformation,[],[f79])).
% 1.61/0.60 thf(f79,plain,(
% 1.61/0.60 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 1.61/0.60 inference(fool_elimination,[],[f78])).
% 1.61/0.60 thf(f78,plain,(
% 1.61/0.60 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 1.61/0.60 inference(rectify,[],[f6])).
% 1.61/0.60 thf(f6,axiom,(
% 1.61/0.60 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 1.61/0.60 thf(f143,plain,(
% 1.61/0.60 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 1.61/0.60 inference(cnf_transformation,[],[f65])).
% 1.61/0.60 thf(f65,plain,(
% 1.61/0.60 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 1.61/0.60 inference(fool_elimination,[],[f64])).
% 1.61/0.60 thf(f64,plain,(
% 1.61/0.60 ((^[X0 : $i > $o, X1 : $i > $o] : (mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))) = iimplies)),
% 1.61/0.60 inference(rectify,[],[f14])).
% 1.61/0.60 thf(f14,axiom,(
% 1.61/0.60 ((^[X5 : $i > $o, X7 : $i > $o] : (mimplies @ (mbox_s4 @ X5) @ (mbox_s4 @ X7))) = iimplies)),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iimplies)).
% 1.61/0.60 thf(f174,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p20) @ (iimplies @ (iatom @ p20) @ (iatom @ p19)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f125])).
% 1.61/0.60 thf(f125,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p20) @ (iimplies @ (iatom @ p20) @ (iatom @ p19)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f124])).
% 1.61/0.60 thf(f124,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p20) @ (iimplies @ (iatom @ p20) @ (iatom @ p19))))),
% 1.61/0.60 inference(rectify,[],[f42])).
% 1.61/0.60 thf(f42,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p20) @ (iimplies @ (iatom @ p20) @ (iatom @ p19))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom21)).
% 1.61/0.60 thf(f830,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p19 @ (sK10 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (p18 @ X3))) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f827])).
% 1.61/0.60 thf(f827,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p18 @ X3)) | ((p19 @ (sK10 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(backward_demodulation,[],[f297,f824])).
% 1.61/0.60 thf(f297,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p18 @ X3)) | ((p19 @ (sK8 @ X1)) = $false) | ((p19 @ (sK10 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f296])).
% 1.61/0.60 thf(f296,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ (sK10 @ X2)) => (p19 @ (sK10 @ X2))) = $false) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((p19 @ (sK8 @ X1)) = $false) | ($true = (p18 @ X3))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f295])).
% 1.61/0.60 thf(f295,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p19 @ (sK8 @ X1)) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0))) @ (sK10 @ X2)) = $false) | ($true = (p18 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f294])).
% 1.61/0.60 thf(f294,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p18 @ X3)) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0)))) = $false) | ($false = (irel @ X2 @ X3)) | ((p19 @ (sK8 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f293])).
% 1.61/0.60 thf(f293,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p19 @ (sK8 @ X1)) = $false) | ($true = ((irel @ X2 @ X3) => (p18 @ X3))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f292])).
% 1.61/0.60 thf(f292,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0))) @ X3)) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false) | ((p19 @ (sK8 @ X1)) = $false)) )),
% 1.61/0.60 inference(pi_clausification,[],[f282])).
% 1.61/0.60 thf(f282,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((p19 @ (sK8 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f281])).
% 1.61/0.60 thf(f281,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK8 @ X1)) => (p19 @ (sK8 @ X1))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0)))))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f280])).
% 1.61/0.60 thf(f280,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0)))))) | (((irel @ X1 @ (sK8 @ X1)) => (p19 @ (sK8 @ X1))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0))))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f279])).
% 1.61/0.60 thf(f279,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0))))))) | (((irel @ X1 @ (sK8 @ X1)) => (p19 @ (sK8 @ X1))) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f278])).
% 1.61/0.60 thf(f278,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0)))))))) | (((irel @ X1 @ (sK8 @ X1)) => (p19 @ (sK8 @ X1))) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f277])).
% 1.61/0.60 thf(f277,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p19 @ Y0))) @ (sK8 @ X1)) = $false) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0))))))))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f276])).
% 1.61/0.60 thf(f276,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p19 @ Y0)))) = $false) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0))))))))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f275])).
% 1.61/0.60 thf(f275,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p19 @ Y0))))) = $true) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p19 @ Y0))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f274])).
% 1.61/0.60 thf(f274,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p18 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p19 @ Y1)))))))) @ X2)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p19 @ Y0))))) = $true)) )),
% 1.61/0.60 inference(pi_clausification,[],[f273])).
% 1.61/0.60 thf(f273,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p18 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p19 @ Y1)))))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p19 @ Y0))))) = $true)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f272])).
% 1.61/0.60 thf(f272,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p18 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p19 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p19 @ Y0)))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f271])).
% 1.61/0.60 thf(f271,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p18 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p19 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p19 @ Y1))))))) @ X1))) )),
% 1.61/0.60 inference(pi_clausification,[],[f270])).
% 1.61/0.60 thf(f270,plain,(
% 1.61/0.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p18 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p19 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p19 @ Y1)))))))))),
% 1.61/0.60 inference(beta_eta_normalization,[],[f198])).
% 1.61/0.60 thf(f198,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p19) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p19) @ ((^[Y0 : $i > $o]: (Y0)) @ p18)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f160,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f160,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p19) @ (iimplies @ (iatom @ p19) @ (iatom @ p18)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f97])).
% 1.61/0.60 thf(f97,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p19) @ (iimplies @ (iatom @ p19) @ (iatom @ p18)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f96])).
% 1.61/0.60 thf(f96,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p19) @ (iimplies @ (iatom @ p19) @ (iatom @ p18))))),
% 1.61/0.60 inference(rectify,[],[f41])).
% 1.61/0.60 thf(f41,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p19) @ (iimplies @ (iatom @ p19) @ (iatom @ p18))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom20)).
% 1.61/0.60 thf(f852,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p17 @ X3) = $true) | ((p18 @ (sK17 @ X1)) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f849])).
% 1.61/0.60 thf(f849,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p17 @ X3) = $true) | ($true = $false) | ($false = (irel @ X2 @ X3)) | ((p18 @ (sK17 @ X1)) = $false)) )),
% 1.61/0.60 inference(backward_demodulation,[],[f390,f848])).
% 1.61/0.60 thf(f390,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p18 @ (sK19 @ X2)) = $false) | ((p17 @ X3) = $true) | ($false = (irel @ X2 @ X3)) | ((p18 @ (sK17 @ X1)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f389])).
% 1.61/0.60 thf(f389,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p17 @ X3) = $true) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ (sK19 @ X2)) => (p18 @ (sK19 @ X2))) = $false) | ((p18 @ (sK17 @ X1)) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f388])).
% 1.61/0.60 thf(f388,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p17 @ X3) = $true) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0))) @ (sK19 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ((p18 @ (sK17 @ X1)) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f387])).
% 1.61/0.60 thf(f387,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p18 @ (sK17 @ X1)) = $false) | ($false = (irel @ X2 @ X3)) | ((p17 @ X3) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f386])).
% 1.61/0.60 thf(f386,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p18 @ (sK17 @ X1)) = $false) | ($true = ((irel @ X2 @ X3) => (p17 @ X3))) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f385])).
% 1.61/0.60 thf(f385,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p18 @ (sK17 @ X1)) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0)))))) | ($true = ((irel @ X2 @ X3) => (p17 @ X3))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f384])).
% 1.61/0.60 thf(f384,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p17 @ Y0))) @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0)))))) | ((p18 @ (sK17 @ X1)) = $false)) )),
% 1.61/0.60 inference(pi_clausification,[],[f383])).
% 1.61/0.60 thf(f383,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((p18 @ (sK17 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p17 @ Y0)))) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0)))))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f382])).
% 1.61/0.60 thf(f382,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p17 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0))))))) | ((irel @ X1 @ X2) = $false) | ((p18 @ (sK17 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f381])).
% 1.61/0.60 thf(f381,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p17 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p18 @ Y0)))))))) | ((p18 @ (sK17 @ X1)) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f380])).
% 1.61/0.60 thf(f380,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p17 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p18 @ Y1)))))))) @ X2)) | ((p18 @ (sK17 @ X1)) = $false)) )),
% 1.61/0.60 inference(pi_clausification,[],[f366])).
% 1.61/0.60 thf(f366,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (((p18 @ (sK17 @ X1)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p17 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p18 @ Y1))))))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f365])).
% 1.61/0.60 thf(f365,plain,(
% 1.61/0.60 ( ! [X1 : $i] : ((((irel @ X1 @ (sK17 @ X1)) => (p18 @ (sK17 @ X1))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p17 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p18 @ Y1))))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f364])).
% 1.61/0.60 thf(f364,plain,(
% 1.61/0.60 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p18 @ Y0))) @ (sK17 @ X1)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p17 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p18 @ Y1))))))))))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f363])).
% 1.61/0.60 thf(f363,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p18 @ Y0))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p17 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p18 @ Y1))))))))))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f362])).
% 1.61/0.60 thf(f362,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p18 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p17 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p18 @ Y1))))))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f361])).
% 1.61/0.60 thf(f361,plain,(
% 1.61/0.60 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p17 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p18 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p18 @ Y0)))))) = $true)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f360])).
% 1.61/0.60 thf(f360,plain,(
% 1.61/0.60 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p17 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p18 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p18 @ Y1))))))) @ X1) = $true)) )),
% 1.61/0.60 inference(pi_clausification,[],[f359])).
% 1.61/0.60 thf(f359,plain,(
% 1.61/0.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p17 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p18 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p18 @ Y1)))))))))),
% 1.61/0.60 inference(beta_eta_normalization,[],[f190])).
% 1.61/0.60 thf(f190,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p18) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p18) @ ((^[Y0 : $i > $o]: (Y0)) @ p17)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f148,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f148,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p18) @ (iimplies @ (iatom @ p18) @ (iatom @ p17)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f95])).
% 1.61/0.60 thf(f95,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p18) @ (iimplies @ (iatom @ p18) @ (iatom @ p17)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f94])).
% 1.61/0.60 thf(f94,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p18) @ (iimplies @ (iatom @ p18) @ (iatom @ p17))))),
% 1.61/0.60 inference(rectify,[],[f40])).
% 1.61/0.60 thf(f40,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p18) @ (iimplies @ (iatom @ p18) @ (iatom @ p17))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom19)).
% 1.61/0.60 thf(f877,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p17 @ (sK16 @ X2)) = $false) | ($false = (irel @ X2 @ X3)) | ($true = (p16 @ X3))) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f873])).
% 1.61/0.60 thf(f873,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = $false) | ($false = (irel @ X2 @ X3)) | ($true = (p16 @ X3)) | ((p17 @ (sK16 @ X2)) = $false)) )),
% 1.61/0.60 inference(backward_demodulation,[],[f357,f870])).
% 1.61/0.60 thf(f357,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((p17 @ (sK14 @ X1)) = $false) | ((p17 @ (sK16 @ X2)) = $false) | ($true = (p16 @ X3))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f356])).
% 1.61/0.60 thf(f356,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p17 @ (sK14 @ X1)) = $false) | ($false = (irel @ X2 @ X3)) | (((irel @ X2 @ (sK16 @ X2)) => (p17 @ (sK16 @ X2))) = $false) | ($true = (p16 @ X3))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f355])).
% 1.61/0.60 thf(f355,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p17 @ (sK14 @ X1)) = $false) | ($true = (p16 @ X3)) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3)) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p17 @ Y0))) @ (sK16 @ X2)) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f354])).
% 1.61/0.60 thf(f354,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p17 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3)) | ($true = (p16 @ X3)) | ((p17 @ (sK14 @ X1)) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f353])).
% 1.61/0.60 thf(f353,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p16 @ X3)) | ((irel @ X1 @ X2) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p17 @ Y0))))) = $true) | ((p17 @ (sK14 @ X1)) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f352])).
% 1.61/0.60 thf(f352,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((irel @ X2 @ X3) => (p16 @ X3))) | ((irel @ X1 @ X2) = $false) | ((p17 @ (sK14 @ X1)) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p17 @ Y0))))) = $true)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f351])).
% 1.61/0.60 thf(f351,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p17 @ (sK14 @ X1)) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p17 @ Y0))))) = $true) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0))) @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(pi_clausification,[],[f350])).
% 1.61/0.60 thf(f350,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p17 @ Y0))))) = $true) | ((p17 @ (sK14 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f349])).
% 1.61/0.60 thf(f349,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((p17 @ (sK14 @ X1)) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p17 @ Y0))))))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f337])).
% 1.61/0.60 thf(f337,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p17 @ Y0)))))))) | ((p17 @ (sK14 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f336])).
% 1.61/0.60 thf(f336,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK14 @ X1)) => (p17 @ (sK14 @ X1))) = $false) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p17 @ Y0))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f335])).
% 1.61/0.60 thf(f335,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p17 @ Y0)))))))) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p17 @ Y0))) @ (sK14 @ X1)) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f334])).
% 1.61/0.60 thf(f334,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p17 @ Y0)))) = $false) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p17 @ Y0))))))))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f333])).
% 1.61/0.60 thf(f333,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p17 @ Y0)))))) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p17 @ Y0))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f332])).
% 1.61/0.60 thf(f332,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p17 @ Y0)))))) | ($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p16 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p17 @ Y1)))))))) @ X2))) )),
% 1.61/0.60 inference(pi_clausification,[],[f331])).
% 1.61/0.60 thf(f331,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p16 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p17 @ Y1))))))))) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p17 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f330])).
% 1.61/0.60 thf(f330,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p16 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p17 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p17 @ Y0)))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f329])).
% 1.61/0.60 thf(f329,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p16 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p17 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p17 @ Y1))))))) @ X1))) )),
% 1.61/0.60 inference(pi_clausification,[],[f328])).
% 1.61/0.60 thf(f328,plain,(
% 1.61/0.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p16 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p17 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p17 @ Y1)))))))))),
% 1.61/0.60 inference(beta_eta_normalization,[],[f195])).
% 1.61/0.60 thf(f195,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p17) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p17) @ ((^[Y0 : $i > $o]: (Y0)) @ p16)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f154,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f154,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p17) @ (iimplies @ (iatom @ p17) @ (iatom @ p16)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f71])).
% 1.61/0.60 thf(f71,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p17) @ (iimplies @ (iatom @ p17) @ (iatom @ p16)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f70])).
% 1.61/0.60 thf(f70,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p17) @ (iimplies @ (iatom @ p17) @ (iatom @ p16))))),
% 1.61/0.60 inference(rectify,[],[f39])).
% 1.61/0.60 thf(f39,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p17) @ (iimplies @ (iatom @ p17) @ (iatom @ p16))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom18)).
% 1.61/0.60 thf(f899,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p15 @ X3) = $true) | ((p16 @ (sK47 @ X1)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f895])).
% 1.61/0.60 thf(f895,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = $false) | ((p16 @ (sK47 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((p15 @ X3) = $true) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(backward_demodulation,[],[f707,f894])).
% 1.61/0.60 thf(f707,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p16 @ (sK49 @ X2)) = $false) | ((p15 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ((p16 @ (sK47 @ X1)) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f706])).
% 1.61/0.60 thf(f706,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p16 @ (sK47 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((p15 @ X3) = $true) | (((irel @ X2 @ (sK49 @ X2)) => (p16 @ (sK49 @ X2))) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f705])).
% 1.61/0.60 thf(f705,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p16 @ (sK47 @ X1)) = $false) | ((p15 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0))) @ (sK49 @ X2)) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f704])).
% 1.61/0.60 thf(f704,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p15 @ X3) = $true) | ((p16 @ (sK47 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0)))) = $false) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f696])).
% 1.61/0.60 thf(f696,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ X3) => (p15 @ X3)) = $true) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0)))) = $false) | ((p16 @ (sK47 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f695])).
% 1.61/0.60 thf(f695,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = ((irel @ X1 @ (sK47 @ X1)) => (p16 @ (sK47 @ X1)))) | (((irel @ X2 @ X3) => (p15 @ X3)) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f694])).
% 1.61/0.60 thf(f694,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p16 @ Y0))) @ (sK47 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ X3) => (p15 @ X3)) = $true)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f693])).
% 1.61/0.60 thf(f693,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p16 @ Y0)))) = $false) | (((irel @ X2 @ X3) => (p15 @ X3)) = $true) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f692])).
% 1.61/0.60 thf(f692,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p16 @ Y0)))) = $false) | (((irel @ X2 @ X3) => (p15 @ X3)) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f691])).
% 1.61/0.60 thf(f691,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0))))) = $true) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p15 @ Y0))) @ X3)) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p16 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(pi_clausification,[],[f690])).
% 1.61/0.60 thf(f690,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p15 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p16 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f689])).
% 1.61/0.60 thf(f689,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p15 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0))))))) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p16 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f688])).
% 1.61/0.60 thf(f688,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p15 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p16 @ Y0)))))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p16 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f687])).
% 1.61/0.60 thf(f687,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p16 @ Y0)))) = $false) | ($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p15 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p16 @ Y1)))))))) @ X2))) )),
% 1.61/0.60 inference(pi_clausification,[],[f686])).
% 1.61/0.60 thf(f686,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p15 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p16 @ Y1)))))))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p16 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f685])).
% 1.61/0.60 thf(f685,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p16 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p15 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p16 @ Y1))))))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f684])).
% 1.61/0.60 thf(f684,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p15 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p16 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p16 @ Y0)))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f683])).
% 1.61/0.60 thf(f683,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p15 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p16 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p16 @ Y1))))))) @ X1))) )),
% 1.61/0.60 inference(pi_clausification,[],[f682])).
% 1.61/0.60 thf(f682,plain,(
% 1.61/0.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p15 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p16 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p16 @ Y1)))))))))),
% 1.61/0.60 inference(beta_eta_normalization,[],[f189])).
% 1.61/0.60 thf(f189,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p16) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p16) @ ((^[Y0 : $i > $o]: (Y0)) @ p15)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f145,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f145,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p16) @ (iimplies @ (iatom @ p16) @ (iatom @ p15)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f59])).
% 1.61/0.60 thf(f59,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p16) @ (iimplies @ (iatom @ p16) @ (iatom @ p15)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f58])).
% 1.61/0.60 thf(f58,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p16) @ (iimplies @ (iatom @ p16) @ (iatom @ p15))))),
% 1.61/0.60 inference(rectify,[],[f38])).
% 1.61/0.60 thf(f38,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p16) @ (iimplies @ (iatom @ p16) @ (iatom @ p15))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom17)).
% 1.61/0.60 thf(f923,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p14 @ X3) = $true) | ((p15 @ (sK6 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f919])).
% 1.61/0.60 thf(f919,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p14 @ X3) = $true) | ($true = $false) | ((irel @ X1 @ X2) = $false) | ((p15 @ (sK6 @ X2)) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(backward_demodulation,[],[f266,f917])).
% 1.61/0.60 thf(f266,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p15 @ (sK4 @ X1)) = $false) | ((p15 @ (sK6 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ((p14 @ X3) = $true) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f265])).
% 1.61/0.60 thf(f265,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | (((irel @ X2 @ (sK6 @ X2)) => (p15 @ (sK6 @ X2))) = $false) | ((p15 @ (sK4 @ X1)) = $false) | ((p14 @ X3) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f264])).
% 1.61/0.60 thf(f264,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p15 @ (sK4 @ X1)) = $false) | ($false = (irel @ X2 @ X3)) | ((p14 @ X3) = $true) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p15 @ Y0))) @ (sK6 @ X2)) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f263])).
% 1.61/0.60 thf(f263,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p15 @ Y0)))) = $false) | ((p14 @ X3) = $true) | ((p15 @ (sK4 @ X1)) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f262])).
% 1.61/0.60 thf(f262,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p15 @ (sK4 @ X1)) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p15 @ Y0)))))) | ((p14 @ X3) = $true) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f261])).
% 1.61/0.60 thf(f261,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p15 @ (sK4 @ X1)) = $false) | ($true = ((irel @ X2 @ X3) => (p14 @ X3))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p15 @ Y0))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f260])).
% 1.61/0.60 thf(f260,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p15 @ Y0)))))) | ((irel @ X1 @ X2) = $false) | ((p15 @ (sK4 @ X1)) = $false) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0))) @ X3))) )),
% 1.61/0.60 inference(pi_clausification,[],[f259])).
% 1.61/0.60 thf(f259,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false) | ((p15 @ (sK4 @ X1)) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p15 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f258])).
% 1.61/0.60 thf(f258,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p15 @ Y0))))))) | ((p15 @ (sK4 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f245])).
% 1.61/0.60 thf(f245,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((p15 @ (sK4 @ X1)) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p15 @ Y0))))))) = $true)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f244])).
% 1.61/0.60 thf(f244,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK4 @ X1)) => (p15 @ (sK4 @ X1))) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p15 @ Y0))))))) = $true)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f243])).
% 1.61/0.60 thf(f243,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p15 @ Y0))) @ (sK4 @ X1)) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p15 @ Y0))))))) = $true)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f242])).
% 1.61/0.60 thf(f242,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p15 @ Y0))))) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p15 @ Y0))))))) = $true)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f241])).
% 1.61/0.60 thf(f241,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p15 @ Y0)))))) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p15 @ Y0))))))) = $true)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f240])).
% 1.61/0.60 thf(f240,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p15 @ Y0)))))) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p14 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p15 @ Y1)))))))) @ X2) = $true)) )),
% 1.61/0.60 inference(pi_clausification,[],[f239])).
% 1.61/0.60 thf(f239,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p14 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p15 @ Y1)))))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p15 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f238])).
% 1.61/0.60 thf(f238,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p14 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p15 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p15 @ Y0)))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f237])).
% 1.61/0.60 thf(f237,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p14 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p15 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p15 @ Y1))))))) @ X1))) )),
% 1.61/0.60 inference(pi_clausification,[],[f236])).
% 1.61/0.60 thf(f236,plain,(
% 1.61/0.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p14 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p15 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p15 @ Y1)))))))))),
% 1.61/0.60 inference(beta_eta_normalization,[],[f201])).
% 1.61/0.60 thf(f201,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p15) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p15) @ ((^[Y0 : $i > $o]: (Y0)) @ p14)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f165,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f165,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p15) @ (iimplies @ (iatom @ p15) @ (iatom @ p14)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f129])).
% 1.61/0.60 thf(f129,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p15) @ (iimplies @ (iatom @ p15) @ (iatom @ p14)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f128])).
% 1.61/0.60 thf(f128,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p15) @ (iimplies @ (iatom @ p15) @ (iatom @ p14))))),
% 1.61/0.60 inference(rectify,[],[f37])).
% 1.61/0.60 thf(f37,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p15) @ (iimplies @ (iatom @ p15) @ (iatom @ p14))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom16)).
% 1.61/0.60 thf(f944,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p13 @ X3)) | ((p14 @ (sK25 @ X2)) = $false) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f942])).
% 1.61/0.60 thf(f942,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ($true = $false) | ((p14 @ (sK25 @ X2)) = $false) | ($true = (p13 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(backward_demodulation,[],[f447,f940])).
% 1.61/0.60 thf(f447,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p13 @ X3)) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3)) | ((p14 @ (sK23 @ X1)) = $false) | ((p14 @ (sK25 @ X2)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f446])).
% 1.61/0.60 thf(f446,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p14 @ (sK23 @ X1)) = $false) | ($true = (p13 @ X3)) | ($false = (irel @ X2 @ X3)) | (((irel @ X2 @ (sK25 @ X2)) => (p14 @ (sK25 @ X2))) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f445])).
% 1.61/0.60 thf(f445,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p14 @ (sK23 @ X1)) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0))) @ (sK25 @ X2)) = $false) | ($true = (p13 @ X3)) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f444])).
% 1.61/0.60 thf(f444,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0)))) = $false) | ((p14 @ (sK23 @ X1)) = $false) | ($true = (p13 @ X3)) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f443])).
% 1.61/0.60 thf(f443,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p13 @ X3)) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((p14 @ (sK23 @ X1)) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f442])).
% 1.61/0.60 thf(f442,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p14 @ (sK23 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ X3) => (p13 @ X3)) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f441])).
% 1.61/0.60 thf(f441,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0)))))) | ((p14 @ (sK23 @ X1)) = $false) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0))) @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(pi_clausification,[],[f440])).
% 1.61/0.60 thf(f440,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0))))) | ((p14 @ (sK23 @ X1)) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f439])).
% 1.61/0.60 thf(f439,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0))))))) | ((p14 @ (sK23 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f427])).
% 1.61/0.60 thf(f427,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0)))))))) | ((p14 @ (sK23 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f426])).
% 1.61/0.60 thf(f426,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK23 @ X1)) => (p14 @ (sK23 @ X1))) = $false) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f425])).
% 1.61/0.60 thf(f425,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p14 @ Y0))) @ (sK23 @ X1)) = $false) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0))))))))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f424])).
% 1.61/0.60 thf(f424,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p14 @ Y0)))) = $false) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p14 @ Y0))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f423])).
% 1.61/0.60 thf(f423,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p14 @ Y0)))) = $false) | ($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p13 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p14 @ Y1)))))))) @ X2))) )),
% 1.61/0.60 inference(pi_clausification,[],[f422])).
% 1.61/0.60 thf(f422,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p13 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p14 @ Y1)))))))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p14 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f421])).
% 1.61/0.60 thf(f421,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p14 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p13 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p14 @ Y1))))))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f420])).
% 1.61/0.60 thf(f420,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p13 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p14 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p14 @ Y0)))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f419])).
% 1.61/0.60 thf(f419,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p13 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p14 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p14 @ Y1))))))) @ X1))) )),
% 1.61/0.60 inference(pi_clausification,[],[f418])).
% 1.61/0.60 thf(f418,plain,(
% 1.61/0.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p13 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p14 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p14 @ Y1)))))))))),
% 1.61/0.60 inference(beta_eta_normalization,[],[f203])).
% 1.61/0.60 thf(f203,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p14) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p14) @ ((^[Y0 : $i > $o]: (Y0)) @ p13)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f169,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f169,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p14) @ (iimplies @ (iatom @ p14) @ (iatom @ p13)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f113])).
% 1.61/0.60 thf(f113,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p14) @ (iimplies @ (iatom @ p14) @ (iatom @ p13)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f112])).
% 1.61/0.60 thf(f112,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p14) @ (iimplies @ (iatom @ p14) @ (iatom @ p13))))),
% 1.61/0.60 inference(rectify,[],[f36])).
% 1.61/0.60 thf(f36,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p14) @ (iimplies @ (iatom @ p14) @ (iatom @ p13))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom15)).
% 1.61/0.60 thf(f969,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p12 @ X3)) | ((p13 @ (sK20 @ X1)) = $false) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f964])).
% 1.61/0.60 thf(f964,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p12 @ X3)) | ($true = $false) | ((p13 @ (sK20 @ X1)) = $false) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(backward_demodulation,[],[f416,f963])).
% 1.61/0.60 thf(f416,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (p12 @ X3)) | ($false = (p13 @ (sK22 @ X2))) | ((p13 @ (sK20 @ X1)) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f415])).
% 1.61/0.60 thf(f415,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p13 @ (sK20 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (p12 @ X3)) | ($false = (irel @ X2 @ X3)) | (((irel @ X2 @ (sK22 @ X2)) => (p13 @ (sK22 @ X2))) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f414])).
% 1.61/0.60 thf(f414,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p13 @ (sK20 @ X1)) = $false) | ($true = (p12 @ X3)) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ($false = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0))) @ (sK22 @ X2)))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f413])).
% 1.61/0.60 thf(f413,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p13 @ (sK20 @ X1)) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0))))) | ($true = (p12 @ X3)) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f406])).
% 1.61/0.60 thf(f406,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p13 @ (sK20 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (p12 @ X3)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f405])).
% 1.61/0.60 thf(f405,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p12 @ X3)) | ($false = ((irel @ X1 @ (sK20 @ X1)) => (p13 @ (sK20 @ X1)))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0)))))) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f404])).
% 1.61/0.60 thf(f404,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = ((irel @ X2 @ X3) => (p12 @ X3))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0)))))) | ($false = ((irel @ X1 @ (sK20 @ X1)) => (p13 @ (sK20 @ X1))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f403])).
% 1.61/0.60 thf(f403,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0)))))) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p12 @ Y0))) @ X3)) | ($false = ((irel @ X1 @ (sK20 @ X1)) => (p13 @ (sK20 @ X1))))) )),
% 1.61/0.60 inference(pi_clausification,[],[f402])).
% 1.61/0.60 thf(f402,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p12 @ Y0))))) | ($false = ((irel @ X1 @ (sK20 @ X1)) => (p13 @ (sK20 @ X1)))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0)))))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f401])).
% 1.61/0.60 thf(f401,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p12 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0))))))) | ((irel @ X1 @ X2) = $false) | ($false = ((irel @ X1 @ (sK20 @ X1)) => (p13 @ (sK20 @ X1))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f400])).
% 1.61/0.60 thf(f400,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p12 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0)))))))) | ($false = ((irel @ X1 @ (sK20 @ X1)) => (p13 @ (sK20 @ X1))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f399])).
% 1.61/0.60 thf(f399,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p12 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0)))))))) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p13 @ Y0))) @ (sK20 @ X1)) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f398])).
% 1.61/0.60 thf(f398,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p13 @ Y0)))) = $false) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p12 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p13 @ Y0))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f397])).
% 1.61/0.60 thf(f397,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p12 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p13 @ Y1)))))))) @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p13 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(pi_clausification,[],[f396])).
% 1.61/0.60 thf(f396,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p12 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p13 @ Y1))))))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p13 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f395])).
% 1.61/0.60 thf(f395,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p13 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p12 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p13 @ Y1))))))))) = $true)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f394])).
% 1.61/0.60 thf(f394,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p12 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p13 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p13 @ Y0)))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f393])).
% 1.61/0.60 thf(f393,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p12 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p13 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p13 @ Y1))))))) @ X1))) )),
% 1.61/0.60 inference(pi_clausification,[],[f392])).
% 1.61/0.60 thf(f392,plain,(
% 1.61/0.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p12 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p13 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p13 @ Y1)))))))))),
% 1.61/0.60 inference(beta_eta_normalization,[],[f200])).
% 1.61/0.60 thf(f200,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p13) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p13) @ ((^[Y0 : $i > $o]: (Y0)) @ p12)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f162,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f162,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p13) @ (iimplies @ (iatom @ p13) @ (iatom @ p12)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f89])).
% 1.61/0.60 thf(f89,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p13) @ (iimplies @ (iatom @ p13) @ (iatom @ p12)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f88])).
% 1.61/0.60 thf(f88,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p13) @ (iimplies @ (iatom @ p13) @ (iatom @ p12))))),
% 1.61/0.60 inference(rectify,[],[f35])).
% 1.61/0.60 thf(f35,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p13) @ (iimplies @ (iatom @ p13) @ (iatom @ p12))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom14)).
% 1.61/0.60 thf(f992,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p12 @ (sK52 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((p11 @ X3) = $true)) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f987])).
% 1.61/0.60 thf(f987,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = $false) | ($false = (irel @ X2 @ X3)) | ((p11 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ((p12 @ (sK52 @ X1)) = $false)) )),
% 1.61/0.60 inference(backward_demodulation,[],[f765,f985])).
% 1.61/0.60 thf(f765,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p12 @ (sK54 @ X2)) = $false) | ((p12 @ (sK52 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((p11 @ X3) = $true)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f764])).
% 1.61/0.60 thf(f764,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p12 @ (sK54 @ X2)) = $false) | ($true = ((irel @ X2 @ X3) => (p11 @ X3))) | ((p12 @ (sK52 @ X1)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f763])).
% 1.61/0.60 thf(f763,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p12 @ (sK52 @ X1)) = $false) | ((p12 @ (sK54 @ X2)) = $false) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0))) @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(pi_clausification,[],[f758])).
% 1.61/0.60 thf(f758,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((p12 @ (sK54 @ X2)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0))))) | ((irel @ X1 @ X2) = $false) | ((p12 @ (sK52 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f757])).
% 1.61/0.60 thf(f757,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((irel @ X2 @ (sK54 @ X2)) => (p12 @ (sK54 @ X2))) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0))))) | ((p12 @ (sK52 @ X1)) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f756])).
% 1.61/0.60 thf(f756,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0))))) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p12 @ Y0))) @ (sK54 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ((p12 @ (sK52 @ X1)) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f755])).
% 1.61/0.60 thf(f755,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p12 @ Y0))))) | ((irel @ X1 @ X2) = $false) | ((p12 @ (sK52 @ X1)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0)))))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f754])).
% 1.61/0.60 thf(f754,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p12 @ Y0))))) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0))))) | ((p12 @ (sK52 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f753])).
% 1.61/0.60 thf(f753,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p12 @ (sK52 @ X1)) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p12 @ Y0)))))) = $true)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f741])).
% 1.61/0.60 thf(f741,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((p12 @ (sK52 @ X1)) = $false) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p12 @ Y0))))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f740])).
% 1.61/0.60 thf(f740,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK52 @ X1)) => (p12 @ (sK52 @ X1))) = $false) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p12 @ Y0))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f739])).
% 1.61/0.60 thf(f739,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p12 @ Y0))) @ (sK52 @ X1)) = $false) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p12 @ Y0))))))))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f738])).
% 1.61/0.60 thf(f738,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p12 @ Y0))))) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p12 @ Y0))))))))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f737])).
% 1.61/0.60 thf(f737,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p12 @ Y0)))))) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p12 @ Y0))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f736])).
% 1.61/0.60 thf(f736,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p11 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p12 @ Y1)))))))) @ X2) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p12 @ Y0))))))) )),
% 1.61/0.60 inference(pi_clausification,[],[f735])).
% 1.61/0.60 thf(f735,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p11 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p12 @ Y1)))))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p12 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f734])).
% 1.61/0.60 thf(f734,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p11 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p12 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p12 @ Y0)))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f733])).
% 1.61/0.60 thf(f733,plain,(
% 1.61/0.60 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p11 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p12 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p12 @ Y1))))))) @ X1) = $true)) )),
% 1.61/0.60 inference(pi_clausification,[],[f732])).
% 1.61/0.60 thf(f732,plain,(
% 1.61/0.60 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p11 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p12 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p12 @ Y1)))))))) = $true)),
% 1.61/0.60 inference(beta_eta_normalization,[],[f196])).
% 1.61/0.60 thf(f196,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p12) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p12) @ ((^[Y0 : $i > $o]: (Y0)) @ p11)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f158,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f158,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p12) @ (iimplies @ (iatom @ p12) @ (iatom @ p11)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f119])).
% 1.61/0.60 thf(f119,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p12) @ (iimplies @ (iatom @ p12) @ (iatom @ p11)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f118])).
% 1.61/0.60 thf(f118,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p12) @ (iimplies @ (iatom @ p12) @ (iatom @ p11))))),
% 1.61/0.60 inference(rectify,[],[f34])).
% 1.61/0.60 thf(f34,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p12) @ (iimplies @ (iatom @ p12) @ (iatom @ p11))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom13)).
% 1.61/0.60 thf(f1014,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p11 @ (sK37 @ X2)) = $false) | ($false = (irel @ X2 @ X3)) | ((p10 @ X3) = $true)) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f1011])).
% 1.61/0.60 thf(f1011,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p10 @ X3) = $true) | ($true = $false) | ((p11 @ (sK37 @ X2)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(backward_demodulation,[],[f583,f1009])).
% 1.61/0.60 thf(f583,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3)) | ((p11 @ (sK36 @ X1)) = $false) | ((p11 @ (sK37 @ X2)) = $false) | ((p10 @ X3) = $true)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f579])).
% 1.61/0.60 thf(f579,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p11 @ (sK36 @ X1)) = $false) | ((p10 @ X3) = $true) | ($false = ((irel @ X2 @ (sK37 @ X2)) => (p11 @ (sK37 @ X2)))) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f578])).
% 1.61/0.60 thf(f578,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X1 @ (sK36 @ X1)) => (p11 @ (sK36 @ X1))) = $false) | ((p10 @ X3) = $true) | ($false = (irel @ X2 @ X3)) | ($false = ((irel @ X2 @ (sK37 @ X2)) => (p11 @ (sK37 @ X2)))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f577])).
% 1.61/0.60 thf(f577,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0))) @ (sK37 @ X2)) = $false) | ((p10 @ X3) = $true) | (((irel @ X1 @ (sK36 @ X1)) => (p11 @ (sK36 @ X1))) = $false) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f576])).
% 1.61/0.60 thf(f576,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p10 @ X3) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0)))) = $false) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | (((irel @ X1 @ (sK36 @ X1)) => (p11 @ (sK36 @ X1))) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f575])).
% 1.61/0.60 thf(f575,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0)))))) | ($false = (irel @ X2 @ X3)) | ((p10 @ X3) = $true) | (((irel @ X1 @ (sK36 @ X1)) => (p11 @ (sK36 @ X1))) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f574])).
% 1.61/0.60 thf(f574,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((irel @ X2 @ X3) => (p10 @ X3))) | (((irel @ X1 @ (sK36 @ X1)) => (p11 @ (sK36 @ X1))) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f573])).
% 1.61/0.60 thf(f573,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X1 @ (sK36 @ X1)) => (p11 @ (sK36 @ X1))) = $false) | ((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))) @ X3) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0))))))) )),
% 1.61/0.60 inference(pi_clausification,[],[f572])).
% 1.61/0.60 thf(f572,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0)))))) | ((irel @ X1 @ X2) = $false) | (((irel @ X1 @ (sK36 @ X1)) => (p11 @ (sK36 @ X1))) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f571])).
% 1.61/0.60 thf(f571,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0)))))) | ((irel @ X1 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p11 @ Y0))) @ (sK36 @ X1)) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f570])).
% 1.61/0.60 thf(f570,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p11 @ Y0)))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f569])).
% 1.61/0.60 thf(f569,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0))))))) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p11 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f568])).
% 1.61/0.60 thf(f568,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p11 @ Y0))))) = $true) | ((irel @ X1 @ X2) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0)))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f567])).
% 1.61/0.60 thf(f567,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p11 @ Y0)))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p11 @ Y0))))) = $true)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f566])).
% 1.61/0.60 thf(f566,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p11 @ Y0))))) = $true) | ($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p11 @ Y1)))))))) @ X2))) )),
% 1.61/0.60 inference(pi_clausification,[],[f565])).
% 1.61/0.60 thf(f565,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p11 @ Y1)))))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p11 @ Y0))))) = $true)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f564])).
% 1.61/0.60 thf(f564,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p11 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p11 @ Y0)))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f563])).
% 1.61/0.60 thf(f563,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p10 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p11 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p11 @ Y1))))))) @ X1))) )),
% 1.61/0.60 inference(pi_clausification,[],[f562])).
% 1.61/0.60 thf(f562,plain,(
% 1.61/0.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p10 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p11 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p11 @ Y1)))))))))),
% 1.61/0.60 inference(beta_eta_normalization,[],[f186])).
% 1.61/0.60 thf(f186,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p11) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p11) @ ((^[Y0 : $i > $o]: (Y0)) @ p10)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f137,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f137,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p11) @ (iimplies @ (iatom @ p11) @ (iatom @ p10)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f87])).
% 1.61/0.60 thf(f87,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p11) @ (iimplies @ (iatom @ p11) @ (iatom @ p10)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f86])).
% 1.61/0.60 thf(f86,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p11) @ (iimplies @ (iatom @ p11) @ (iatom @ p10))))),
% 1.61/0.60 inference(rectify,[],[f33])).
% 1.61/0.60 thf(f33,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p11) @ (iimplies @ (iatom @ p11) @ (iatom @ p10))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom12)).
% 1.61/0.60 thf(f1037,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p9 @ X3)) | ((irel @ X1 @ X2) = $false) | ($false = (p10 @ (sK46 @ X2))) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f1034])).
% 1.61/0.60 thf(f1034,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p10 @ (sK46 @ X2))) | ((irel @ X1 @ X2) = $false) | ($true = (p9 @ X3)) | ($true = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(backward_demodulation,[],[f680,f1032])).
% 1.61/0.60 thf(f680,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p10 @ (sK44 @ X1)) = $false) | ($false = (p10 @ (sK46 @ X2))) | ($true = (p9 @ X3)) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f679])).
% 1.61/0.60 thf(f679,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((p10 @ (sK44 @ X1)) = $false) | (((irel @ X2 @ (sK46 @ X2)) => (p10 @ (sK46 @ X2))) = $false) | ($true = (p9 @ X3))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f678])).
% 1.61/0.60 thf(f678,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p9 @ X3)) | ((p10 @ (sK44 @ X1)) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))) @ (sK46 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f677])).
% 1.61/0.60 thf(f677,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0)))) = $false) | ((p10 @ (sK44 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3)) | ($true = (p9 @ X3))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f676])).
% 1.61/0.60 thf(f676,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ($true = (p9 @ X3)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0)))))) | ((p10 @ (sK44 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f675])).
% 1.61/0.60 thf(f675,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = ((irel @ X2 @ X3) => (p9 @ X3))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0)))))) | ((p10 @ (sK44 @ X1)) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f674])).
% 1.61/0.60 thf(f674,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p10 @ (sK44 @ X1)) = $false) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))) @ X3)) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))))) )),
% 1.61/0.60 inference(pi_clausification,[],[f673])).
% 1.61/0.60 thf(f673,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))))) | ((irel @ X1 @ X2) = $false) | ((p10 @ (sK44 @ X1)) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f672])).
% 1.61/0.60 thf(f672,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))))) | ((irel @ X1 @ X2) = $false) | ((p10 @ (sK44 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f660])).
% 1.61/0.60 thf(f660,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((p10 @ (sK44 @ X1)) = $false) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f659])).
% 1.61/0.60 thf(f659,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ X1 @ (sK44 @ X1)) => (p10 @ (sK44 @ X1)))) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f658])).
% 1.61/0.60 thf(f658,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0)))))))) | ($false = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p10 @ Y0))) @ (sK44 @ X1)))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f657])).
% 1.61/0.60 thf(f657,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p10 @ Y0)))) = $false) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))))))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f656])).
% 1.61/0.60 thf(f656,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p10 @ Y0)))))) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f655])).
% 1.61/0.60 thf(f655,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1)))))))) @ X2)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p10 @ Y0))))))) )),
% 1.61/0.60 inference(pi_clausification,[],[f654])).
% 1.61/0.60 thf(f654,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1)))))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p10 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f653])).
% 1.61/0.60 thf(f653,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p10 @ Y0)))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f652])).
% 1.61/0.60 thf(f652,plain,(
% 1.61/0.60 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p9 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p10 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1))))))) @ X1) = $true)) )),
% 1.61/0.60 inference(pi_clausification,[],[f651])).
% 1.61/0.60 thf(f651,plain,(
% 1.61/0.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p9 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p10 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1)))))))))),
% 1.61/0.60 inference(beta_eta_normalization,[],[f199])).
% 1.61/0.60 thf(f199,plain,(
% 1.61/0.60 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p10) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p10) @ ((^[Y0 : $i > $o]: (Y0)) @ p9)))) = $true)),
% 1.61/0.60 inference(definition_unfolding,[],[f161,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f161,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p10) @ (iimplies @ (iatom @ p10) @ (iatom @ p9)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f123])).
% 1.61/0.60 thf(f123,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p10) @ (iimplies @ (iatom @ p10) @ (iatom @ p9)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f122])).
% 1.61/0.60 thf(f122,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p10) @ (iimplies @ (iatom @ p10) @ (iatom @ p9))))),
% 1.61/0.60 inference(rectify,[],[f32])).
% 1.61/0.60 thf(f32,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p10) @ (iimplies @ (iatom @ p10) @ (iatom @ p9))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom11)).
% 1.61/0.60 thf(f1060,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p8 @ X3)) | ($false = (irel @ X2 @ X3)) | ((p9 @ (sK11 @ X2)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f1056])).
% 1.61/0.60 thf(f1056,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p8 @ X3)) | ((p9 @ (sK11 @ X2)) = $false) | ($true = $false) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(backward_demodulation,[],[f324,f1055])).
% 1.61/0.60 thf(f324,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p9 @ (sK13 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3)) | ((p9 @ (sK11 @ X2)) = $false) | ($true = (p8 @ X3))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f323])).
% 1.61/0.60 thf(f323,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p9 @ (sK11 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (p8 @ X3)) | (((irel @ X1 @ (sK13 @ X1)) => (p9 @ (sK13 @ X1))) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f322])).
% 1.61/0.60 thf(f322,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3)) | ($true = (p8 @ X3)) | ((p9 @ (sK11 @ X2)) = $false) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0))) @ (sK13 @ X1)) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f321])).
% 1.61/0.60 thf(f321,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0))))) | ((p9 @ (sK11 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (p8 @ X3)) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f320])).
% 1.61/0.60 thf(f320,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = ((irel @ X2 @ X3) => (p8 @ X3))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0))))) | ((p9 @ (sK11 @ X2)) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f312])).
% 1.61/0.60 thf(f312,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0)))))) | ((irel @ X1 @ X2) = $false) | ((p9 @ (sK11 @ X2)) = $false) | ($true = ((irel @ X2 @ X3) => (p8 @ X3)))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f311])).
% 1.61/0.60 thf(f311,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((irel @ X2 @ (sK11 @ X2)) => (p9 @ (sK11 @ X2)))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0)))))) | ($true = ((irel @ X2 @ X3) => (p8 @ X3))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f310])).
% 1.61/0.60 thf(f310,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0)))))) | ((irel @ X1 @ X2) = $false) | ($false = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))) @ (sK11 @ X2))) | ($true = ((irel @ X2 @ X3) => (p8 @ X3)))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f309])).
% 1.61/0.60 thf(f309,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) = $false) | ($true = ((irel @ X2 @ X3) => (p8 @ X3))) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f308])).
% 1.61/0.60 thf(f308,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0)))))) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))) @ X3)) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(pi_clausification,[],[f307])).
% 1.61/0.60 thf(f307,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))))) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f306])).
% 1.61/0.60 thf(f306,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0)))))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f305])).
% 1.61/0.60 thf(f305,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))))))) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f304])).
% 1.61/0.60 thf(f304,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f303])).
% 1.61/0.60 thf(f303,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))))))) @ X2)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0))))))) )),
% 1.61/0.60 inference(pi_clausification,[],[f302])).
% 1.61/0.60 thf(f302,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f301])).
% 1.61/0.60 thf(f301,plain,(
% 1.61/0.60 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0)))))) = $true)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f300])).
% 1.61/0.60 thf(f300,plain,(
% 1.61/0.60 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p8 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p9 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1))))))) @ X1) = $true)) )),
% 1.61/0.60 inference(pi_clausification,[],[f299])).
% 1.61/0.60 thf(f299,plain,(
% 1.61/0.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p8 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p9 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))))))))),
% 1.61/0.60 inference(beta_eta_normalization,[],[f205])).
% 1.61/0.60 thf(f205,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p9) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p9) @ ((^[Y0 : $i > $o]: (Y0)) @ p8)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f172,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f172,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p9) @ (iimplies @ (iatom @ p9) @ (iatom @ p8)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f101])).
% 1.61/0.60 thf(f101,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p9) @ (iimplies @ (iatom @ p9) @ (iatom @ p8)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f100])).
% 1.61/0.60 thf(f100,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p9) @ (iimplies @ (iatom @ p9) @ (iatom @ p8))))),
% 1.61/0.60 inference(rectify,[],[f31])).
% 1.61/0.60 thf(f31,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p9) @ (iimplies @ (iatom @ p9) @ (iatom @ p8))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10)).
% 1.61/0.60 thf(f1083,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p7 @ X3)) | ((irel @ X1 @ X2) = $false) | ((p8 @ (sK1 @ X1)) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f1079])).
% 1.61/0.60 thf(f1079,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ($true = (p7 @ X3)) | ($true = $false) | ((irel @ X1 @ X2) = $false) | ((p8 @ (sK1 @ X1)) = $false)) )),
% 1.61/0.60 inference(backward_demodulation,[],[f234,f1078])).
% 1.61/0.60 thf(f234,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p7 @ X3)) | ((p8 @ (sK3 @ X2)) = $false) | ((p8 @ (sK1 @ X1)) = $false) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f233])).
% 1.61/0.60 thf(f233,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p7 @ X3)) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((p8 @ (sK1 @ X1)) = $false) | (((irel @ X2 @ (sK3 @ X2)) => (p8 @ (sK3 @ X2))) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f232])).
% 1.61/0.60 thf(f232,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ X3) => (p7 @ X3)) = $true) | ((p8 @ (sK1 @ X1)) = $false) | (((irel @ X2 @ (sK3 @ X2)) => (p8 @ (sK3 @ X2))) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f231])).
% 1.61/0.60 thf(f231,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p8 @ (sK1 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($false = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))) @ (sK3 @ X2))) | (((irel @ X2 @ X3) => (p7 @ X3)) = $true)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f230])).
% 1.61/0.60 thf(f230,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p8 @ (sK1 @ X1)) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))))) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ X3) => (p7 @ X3)) = $true)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f229])).
% 1.61/0.60 thf(f229,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))))) | ((p8 @ (sK1 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))) @ X3))) )),
% 1.61/0.60 inference(pi_clausification,[],[f228])).
% 1.61/0.60 thf(f228,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))))) | ((irel @ X1 @ X2) = $false) | ((p8 @ (sK1 @ X1)) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f218])).
% 1.61/0.60 thf(f218,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p8 @ (sK1 @ X1)) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f217])).
% 1.61/0.60 thf(f217,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK1 @ X1)) => (p8 @ (sK1 @ X1))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))))) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f216])).
% 1.61/0.60 thf(f216,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))))))) | (((irel @ X1 @ (sK1 @ X1)) => (p8 @ (sK1 @ X1))) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f215])).
% 1.61/0.60 thf(f215,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))))))) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0))) @ (sK1 @ X1)) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f214])).
% 1.61/0.60 thf(f214,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0)))) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))))))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f213])).
% 1.61/0.60 thf(f213,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0))))) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))))))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f212])).
% 1.61/0.60 thf(f212,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0))))) = $true)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f211])).
% 1.61/0.60 thf(f211,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))))))) @ X2)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0))))) = $true)) )),
% 1.61/0.60 inference(pi_clausification,[],[f210])).
% 1.61/0.60 thf(f210,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0))))) = $true)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f209])).
% 1.61/0.60 thf(f209,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0)))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f208])).
% 1.61/0.60 thf(f208,plain,(
% 1.61/0.60 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p7 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p8 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1))))))) @ X1) = $true)) )),
% 1.61/0.60 inference(pi_clausification,[],[f207])).
% 1.61/0.60 thf(f207,plain,(
% 1.61/0.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p7 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p8 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))))))))),
% 1.61/0.60 inference(beta_eta_normalization,[],[f191])).
% 1.61/0.60 thf(f191,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p8) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p8) @ ((^[Y0 : $i > $o]: (Y0)) @ p7)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f149,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f149,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p8) @ (iimplies @ (iatom @ p8) @ (iatom @ p7)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f83])).
% 1.61/0.60 thf(f83,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p8) @ (iimplies @ (iatom @ p8) @ (iatom @ p7)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f82])).
% 1.61/0.60 thf(f82,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p8) @ (iimplies @ (iatom @ p8) @ (iatom @ p7))))),
% 1.61/0.60 inference(rectify,[],[f30])).
% 1.61/0.60 thf(f30,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p8) @ (iimplies @ (iatom @ p8) @ (iatom @ p7))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9)).
% 1.61/0.60 thf(f1107,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ($true = (p6 @ X3)) | ($false = (p7 @ (sK50 @ X2)))) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f1103])).
% 1.61/0.60 thf(f1103,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = $false) | ($false = (p7 @ (sK50 @ X2))) | ($true = (p6 @ X3)) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(backward_demodulation,[],[f730,f1101])).
% 1.61/0.60 thf(f730,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p6 @ X3)) | ((p7 @ (sK51 @ X1)) = $false) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ($false = (p7 @ (sK50 @ X2)))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f726])).
% 1.61/0.60 thf(f726,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ($false = (p7 @ (sK50 @ X2))) | ($true = (p6 @ X3)) | (((irel @ X1 @ (sK51 @ X1)) => (p7 @ (sK51 @ X1))) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f725])).
% 1.61/0.60 thf(f725,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ (sK50 @ X2)) => (p7 @ (sK50 @ X2))) = $false) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | (((irel @ X1 @ (sK51 @ X1)) => (p7 @ (sK51 @ X1))) = $false) | ($true = (p6 @ X3))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f724])).
% 1.61/0.60 thf(f724,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = ((irel @ X2 @ X3) => (p6 @ X3))) | (((irel @ X2 @ (sK50 @ X2)) => (p7 @ (sK50 @ X2))) = $false) | (((irel @ X1 @ (sK51 @ X1)) => (p7 @ (sK51 @ X1))) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f723])).
% 1.61/0.60 thf(f723,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = ((irel @ X2 @ X3) => (p6 @ X3))) | (((irel @ X2 @ (sK50 @ X2)) => (p7 @ (sK50 @ X2))) = $false) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0))) @ (sK51 @ X1)) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f722])).
% 1.61/0.60 thf(f722,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0)))) = $false) | ($true = ((irel @ X2 @ X3) => (p6 @ X3))) | (((irel @ X2 @ (sK50 @ X2)) => (p7 @ (sK50 @ X2))) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f721])).
% 1.61/0.60 thf(f721,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((irel @ X2 @ X3) => (p6 @ X3))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))) @ (sK50 @ X2)) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f720])).
% 1.61/0.60 thf(f720,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0)))) = $false) | ($true = ((irel @ X2 @ X3) => (p6 @ X3)))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f719])).
% 1.61/0.60 thf(f719,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0))) @ X3) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(pi_clausification,[],[f718])).
% 1.61/0.60 thf(f718,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f717])).
% 1.61/0.60 thf(f717,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f716])).
% 1.61/0.60 thf(f716,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))))) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f715])).
% 1.61/0.60 thf(f715,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0)))))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f714])).
% 1.61/0.60 thf(f714,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f713])).
% 1.61/0.60 thf(f713,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))))))) @ X2)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0))))))) )),
% 1.61/0.60 inference(pi_clausification,[],[f712])).
% 1.61/0.60 thf(f712,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f711])).
% 1.61/0.60 thf(f711,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0)))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f710])).
% 1.61/0.60 thf(f710,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p6 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p7 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1))))))) @ X1))) )),
% 1.61/0.60 inference(pi_clausification,[],[f709])).
% 1.61/0.60 thf(f709,plain,(
% 1.61/0.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p6 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p7 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))))))))),
% 1.61/0.60 inference(beta_eta_normalization,[],[f192])).
% 1.61/0.60 thf(f192,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p7) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p7) @ ((^[Y0 : $i > $o]: (Y0)) @ p6)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f150,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f150,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p7) @ (iimplies @ (iatom @ p7) @ (iatom @ p6)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f93])).
% 1.61/0.60 thf(f93,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p7) @ (iimplies @ (iatom @ p7) @ (iatom @ p6)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f92])).
% 1.61/0.60 thf(f92,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p7) @ (iimplies @ (iatom @ p7) @ (iatom @ p6))))),
% 1.61/0.60 inference(rectify,[],[f29])).
% 1.61/0.60 thf(f29,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p7) @ (iimplies @ (iatom @ p7) @ (iatom @ p6))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8)).
% 1.61/0.60 thf(f1130,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p6 @ (sK57 @ X2)) = $false) | ($true = (p5 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f1126])).
% 1.61/0.60 thf(f1126,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p6 @ (sK57 @ X2)) = $false) | ($true = $false) | ($false = (irel @ X2 @ X3)) | ($true = (p5 @ X3))) )),
% 1.61/0.60 inference(backward_demodulation,[],[f798,f1124])).
% 1.61/0.60 thf(f798,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (p6 @ (sK55 @ X1))) | ((p6 @ (sK57 @ X2)) = $false) | ($true = (p5 @ X3)) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f797])).
% 1.61/0.60 thf(f797,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p5 @ X3)) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ (sK57 @ X2)) => (p6 @ (sK57 @ X2))) = $false) | ($false = (p6 @ (sK55 @ X1)))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f796])).
% 1.61/0.60 thf(f796,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ($true = (p5 @ X3)) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0))) @ (sK57 @ X2)) = $false) | ($false = (p6 @ (sK55 @ X1))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f795])).
% 1.61/0.60 thf(f795,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) = $false) | ($false = (irel @ X2 @ X3)) | ($false = (p6 @ (sK55 @ X1))) | ((irel @ X1 @ X2) = $false) | ($true = (p5 @ X3))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f794])).
% 1.61/0.60 thf(f794,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (p5 @ X3)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))))) | ($false = (irel @ X2 @ X3)) | ($false = (p6 @ (sK55 @ X1)))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f793])).
% 1.61/0.60 thf(f793,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ X3) => (p5 @ X3)) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))))) | ((irel @ X1 @ X2) = $false) | ($false = (p6 @ (sK55 @ X1)))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f792])).
% 1.61/0.60 thf(f792,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))))) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))) @ X3)) | ($false = (p6 @ (sK55 @ X1)))) )),
% 1.61/0.60 inference(pi_clausification,[],[f791])).
% 1.61/0.60 thf(f791,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))))) | ($false = (p6 @ (sK55 @ X1))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f790])).
% 1.61/0.60 thf(f790,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($false = (p6 @ (sK55 @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0))))))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f789])).
% 1.61/0.60 thf(f789,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($false = (p6 @ (sK55 @ X1))) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f788])).
% 1.61/0.60 thf(f788,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))))))) @ X2)) | ($false = (p6 @ (sK55 @ X1)))) )),
% 1.61/0.60 inference(pi_clausification,[],[f773])).
% 1.61/0.60 thf(f773,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($false = (p6 @ (sK55 @ X1))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1))))))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f772])).
% 1.61/0.60 thf(f772,plain,(
% 1.61/0.60 ( ! [X1 : $i] : ((((irel @ X1 @ (sK55 @ X1)) => (p6 @ (sK55 @ X1))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1))))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f771])).
% 1.61/0.60 thf(f771,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))))))))) | ($false = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p6 @ Y0))) @ (sK55 @ X1)))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f770])).
% 1.61/0.60 thf(f770,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p6 @ Y0)))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1))))))))))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f769])).
% 1.61/0.60 thf(f769,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p6 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1))))))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f768])).
% 1.61/0.60 thf(f768,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p6 @ Y0)))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f767])).
% 1.61/0.60 thf(f767,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p5 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p6 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1))))))) @ X1))) )),
% 1.61/0.60 inference(pi_clausification,[],[f766])).
% 1.61/0.60 thf(f766,plain,(
% 1.61/0.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p5 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p6 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))))))))),
% 1.61/0.60 inference(beta_eta_normalization,[],[f193])).
% 1.61/0.60 thf(f193,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p6) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p6) @ ((^[Y0 : $i > $o]: (Y0)) @ p5)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f151,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f151,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p6) @ (iimplies @ (iatom @ p6) @ (iatom @ p5)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f61])).
% 1.61/0.60 thf(f61,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p6) @ (iimplies @ (iatom @ p6) @ (iatom @ p5)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f60])).
% 1.61/0.60 thf(f60,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p6) @ (iimplies @ (iatom @ p6) @ (iatom @ p5))))),
% 1.61/0.60 inference(rectify,[],[f28])).
% 1.61/0.60 thf(f28,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p6) @ (iimplies @ (iatom @ p6) @ (iatom @ p5))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom7)).
% 1.61/0.60 thf(f1152,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p5 @ (sK26 @ X2)) = $false) | ((p4 @ X3) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f1149])).
% 1.61/0.60 thf(f1149,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p4 @ X3) = $true) | ((p5 @ (sK26 @ X2)) = $false) | ($false = (irel @ X2 @ X3)) | ($true = $false)) )),
% 1.61/0.60 inference(backward_demodulation,[],[f480,f1146])).
% 1.61/0.60 thf(f480,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p4 @ X3) = $true) | ($false = (p5 @ (sK27 @ X1))) | ((irel @ X1 @ X2) = $false) | ((p5 @ (sK26 @ X2)) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f479])).
% 1.61/0.60 thf(f479,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((irel @ X2 @ X3) => (p4 @ X3))) | ((p5 @ (sK26 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ($false = (p5 @ (sK27 @ X1)))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f478])).
% 1.61/0.60 thf(f478,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))) @ X3)) | ((p5 @ (sK26 @ X2)) = $false) | ($false = (p5 @ (sK27 @ X1)))) )),
% 1.61/0.60 inference(pi_clausification,[],[f473])).
% 1.61/0.60 thf(f473,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) | ((p5 @ (sK26 @ X2)) = $false) | ($false = (p5 @ (sK27 @ X1))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f463])).
% 1.61/0.60 thf(f463,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK27 @ X1)) => (p5 @ (sK27 @ X1))) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) | ((p5 @ (sK26 @ X2)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f462])).
% 1.61/0.60 thf(f462,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((irel @ X2 @ (sK26 @ X2)) => (p5 @ (sK26 @ X2))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) | (((irel @ X1 @ (sK27 @ X1)) => (p5 @ (sK27 @ X1))) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f461])).
% 1.61/0.60 thf(f461,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0))) @ (sK27 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ (sK26 @ X2)) => (p5 @ (sK26 @ X2))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f460])).
% 1.61/0.60 thf(f460,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0)))) = $false) | (((irel @ X2 @ (sK26 @ X2)) => (p5 @ (sK26 @ X2))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f459])).
% 1.61/0.60 thf(f459,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))) @ (sK26 @ X2)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f458])).
% 1.61/0.60 thf(f458,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f457])).
% 1.61/0.60 thf(f457,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f456])).
% 1.61/0.60 thf(f456,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f455])).
% 1.61/0.60 thf(f455,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f454])).
% 1.61/0.60 thf(f454,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0)))))) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f453])).
% 1.61/0.60 thf(f453,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))))))) @ X2)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0))))))) )),
% 1.61/0.60 inference(pi_clausification,[],[f452])).
% 1.61/0.60 thf(f452,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f451])).
% 1.61/0.60 thf(f451,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0)))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f450])).
% 1.61/0.60 thf(f450,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p4 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p5 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1))))))) @ X1))) )),
% 1.61/0.60 inference(pi_clausification,[],[f449])).
% 1.61/0.60 thf(f449,plain,(
% 1.61/0.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p4 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p5 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))))))))),
% 1.61/0.60 inference(beta_eta_normalization,[],[f187])).
% 1.61/0.60 thf(f187,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p5) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p5) @ ((^[Y0 : $i > $o]: (Y0)) @ p4)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f140,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f140,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f115])).
% 1.61/0.60 thf(f115,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f114])).
% 1.61/0.60 thf(f114,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4))))),
% 1.61/0.60 inference(rectify,[],[f27])).
% 1.61/0.60 thf(f27,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6)).
% 1.61/0.60 thf(f1175,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3)) | ((p4 @ (sK38 @ X1)) = $false) | ((p3 @ X3) = $true)) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f1171])).
% 1.61/0.60 thf(f1171,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p3 @ X3) = $true) | ($true = $false) | ($false = (irel @ X2 @ X3)) | ((p4 @ (sK38 @ X1)) = $false)) )),
% 1.61/0.60 inference(backward_demodulation,[],[f614,f1169])).
% 1.61/0.60 thf(f614,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p3 @ X3) = $true) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((p4 @ (sK40 @ X2)) = $false) | ((p4 @ (sK38 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f611])).
% 1.61/0.60 thf(f611,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p4 @ (sK40 @ X2)) = $false) | ((p4 @ (sK38 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = ((irel @ X2 @ X3) => (p3 @ X3)))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f610])).
% 1.61/0.60 thf(f610,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p4 @ (sK38 @ X1)) = $false) | (((irel @ X2 @ (sK40 @ X2)) => (p4 @ (sK40 @ X2))) = $false) | ((irel @ X1 @ X2) = $false) | ($true = ((irel @ X2 @ X3) => (p3 @ X3)))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f609])).
% 1.61/0.60 thf(f609,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((irel @ X2 @ X3) => (p3 @ X3))) | ((irel @ X1 @ X2) = $false) | ((p4 @ (sK38 @ X1)) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))) @ (sK40 @ X2)) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f608])).
% 1.61/0.60 thf(f608,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) | ($true = ((irel @ X2 @ X3) => (p3 @ X3))) | ((p4 @ (sK38 @ X1)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f607])).
% 1.61/0.60 thf(f607,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) | ((p4 @ (sK38 @ X1)) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))) @ X3) = $true)) )),
% 1.61/0.60 inference(pi_clausification,[],[f606])).
% 1.61/0.60 thf(f606,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) = $true) | ((p4 @ (sK38 @ X1)) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f596])).
% 1.61/0.60 thf(f596,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) = $true) | ((p4 @ (sK38 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f595])).
% 1.61/0.60 thf(f595,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK38 @ X1)) => (p4 @ (sK38 @ X1))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f594])).
% 1.61/0.60 thf(f594,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))))) | ((irel @ X1 @ X2) = $false) | (((irel @ X1 @ (sK38 @ X1)) => (p4 @ (sK38 @ X1))) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f593])).
% 1.61/0.60 thf(f593,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))))))) | (((irel @ X1 @ (sK38 @ X1)) => (p4 @ (sK38 @ X1))) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f592])).
% 1.61/0.60 thf(f592,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK38 @ X1)) => (p4 @ (sK38 @ X1))) = $false) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))))))) @ X2) = $true)) )),
% 1.61/0.60 inference(pi_clausification,[],[f591])).
% 1.61/0.60 thf(f591,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))))))))) | (((irel @ X1 @ (sK38 @ X1)) => (p4 @ (sK38 @ X1))) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f590])).
% 1.61/0.60 thf(f590,plain,(
% 1.61/0.60 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0))) @ (sK38 @ X1)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1))))))))))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f589])).
% 1.61/0.60 thf(f589,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1))))))))))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f588])).
% 1.61/0.60 thf(f588,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1))))))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f587])).
% 1.61/0.60 thf(f587,plain,(
% 1.61/0.60 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0)))))) = $true)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f586])).
% 1.61/0.60 thf(f586,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p3 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1))))))) @ X1))) )),
% 1.61/0.60 inference(pi_clausification,[],[f585])).
% 1.61/0.60 thf(f585,plain,(
% 1.61/0.60 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p3 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))))))) = $true)),
% 1.61/0.60 inference(beta_eta_normalization,[],[f188])).
% 1.61/0.60 thf(f188,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p4) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p4) @ ((^[Y0 : $i > $o]: (Y0)) @ p3)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f141,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f141,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f47])).
% 1.61/0.60 thf(f47,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f46])).
% 1.61/0.60 thf(f46,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3))))),
% 1.61/0.60 inference(rectify,[],[f26])).
% 1.61/0.60 thf(f26,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5)).
% 1.61/0.60 thf(f1197,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((p3 @ (sK41 @ X1)) = $false) | ((p2 @ X3) = $true)) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f1194])).
% 1.61/0.60 thf(f1194,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p2 @ X3) = $true) | ((p3 @ (sK41 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(backward_demodulation,[],[f650,f1193])).
% 1.61/0.60 thf(f650,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p3 @ (sK43 @ X2)) = $false) | ($false = (irel @ X2 @ X3)) | ((p3 @ (sK41 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((p2 @ X3) = $true)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f649])).
% 1.61/0.60 thf(f649,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p3 @ (sK43 @ X2)) = $false) | ($true = ((irel @ X2 @ X3) => (p2 @ X3))) | ((p3 @ (sK41 @ X1)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f648])).
% 1.61/0.60 thf(f648,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))) @ X3)) | ((p3 @ (sK41 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((p3 @ (sK43 @ X2)) = $false)) )),
% 1.61/0.60 inference(pi_clausification,[],[f643])).
% 1.61/0.60 thf(f643,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $true) | ((p3 @ (sK43 @ X2)) = $false) | ((p3 @ (sK41 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f642])).
% 1.61/0.60 thf(f642,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : ((((irel @ X2 @ (sK43 @ X2)) => (p3 @ (sK43 @ X2))) = $false) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $true) | ((p3 @ (sK41 @ X1)) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f641])).
% 1.61/0.60 thf(f641,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))) @ (sK43 @ X2))) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $true) | ((p3 @ (sK41 @ X1)) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f640])).
% 1.61/0.60 thf(f640,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $true) | ((p3 @ (sK41 @ X1)) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f639])).
% 1.61/0.60 thf(f639,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((p3 @ (sK41 @ X1)) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))))) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $true)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f638])).
% 1.61/0.60 thf(f638,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))))))) | ((p3 @ (sK41 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f637])).
% 1.61/0.60 thf(f637,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((p3 @ (sK41 @ X1)) = $false) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f636])).
% 1.61/0.60 thf(f636,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((p3 @ (sK41 @ X1)) = $false) | ($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))))))) @ X2))) )),
% 1.61/0.60 inference(pi_clausification,[],[f622])).
% 1.61/0.60 thf(f622,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))))))))) | ((p3 @ (sK41 @ X1)) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f621])).
% 1.61/0.60 thf(f621,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($false = ((irel @ X1 @ (sK41 @ X1)) => (p3 @ (sK41 @ X1)))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f620])).
% 1.61/0.60 thf(f620,plain,(
% 1.61/0.60 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p3 @ Y0))) @ (sK41 @ X1)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))))))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f619])).
% 1.61/0.60 thf(f619,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p3 @ Y0)))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))))))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f618])).
% 1.61/0.60 thf(f618,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p3 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f617])).
% 1.61/0.60 thf(f617,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p3 @ Y0)))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f616])).
% 1.61/0.60 thf(f616,plain,(
% 1.61/0.60 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p2 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p3 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))) @ X1) = $true)) )),
% 1.61/0.60 inference(pi_clausification,[],[f615])).
% 1.61/0.60 thf(f615,plain,(
% 1.61/0.60 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p2 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p3 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))))))) = $true)),
% 1.61/0.60 inference(beta_eta_normalization,[],[f185])).
% 1.61/0.60 thf(f185,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p3) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p3) @ ((^[Y0 : $i > $o]: (Y0)) @ p2)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f136,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f136,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f73])).
% 1.61/0.60 thf(f73,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f72])).
% 1.61/0.60 thf(f72,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2))))),
% 1.61/0.60 inference(rectify,[],[f25])).
% 1.61/0.60 thf(f25,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4)).
% 1.61/0.60 thf(f1222,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (p1 @ X3)) | ($false = (irel @ X2 @ X3)) | ($false = (p2 @ (sK28 @ X1)))) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f1217])).
% 1.61/0.60 thf(f1217,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (p1 @ X3)) | ((irel @ X1 @ X2) = $false) | ($false = (p2 @ (sK28 @ X1))) | ($true = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(backward_demodulation,[],[f506,f1216])).
% 1.61/0.60 thf(f506,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p2 @ (sK30 @ X2)) = $false) | ($true = (p1 @ X3)) | ($false = (p2 @ (sK28 @ X1))) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f505])).
% 1.61/0.60 thf(f505,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ($true = (p1 @ X3)) | ($false = (p2 @ (sK28 @ X1))) | (((irel @ X2 @ (sK30 @ X2)) => (p2 @ (sK30 @ X2))) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f504])).
% 1.61/0.60 thf(f504,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))) @ (sK30 @ X2)) = $false) | ($false = (p2 @ (sK28 @ X1))) | ($false = (irel @ X2 @ X3)) | ($true = (p1 @ X3))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f503])).
% 1.61/0.60 thf(f503,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $false) | ($true = (p1 @ X3)) | ($false = (p2 @ (sK28 @ X1))) | ((irel @ X1 @ X2) = $false) | ($false = (irel @ X2 @ X3))) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f502])).
% 1.61/0.60 thf(f502,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ($true = (p1 @ X3)) | ($false = (p2 @ (sK28 @ X1))) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f494])).
% 1.61/0.60 thf(f494,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p2 @ (sK28 @ X1))) | ($true = ((irel @ X2 @ X3) => (p1 @ X3))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f493])).
% 1.61/0.60 thf(f493,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X1 @ (sK28 @ X1)) => (p2 @ (sK28 @ X1))) = $false) | ((irel @ X1 @ X2) = $false) | ($true = ((irel @ X2 @ X3) => (p1 @ X3))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f492])).
% 1.61/0.60 thf(f492,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X1 @ (sK28 @ X1)) => (p2 @ (sK28 @ X1))) = $false) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))) @ X3)) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))))) )),
% 1.61/0.60 inference(pi_clausification,[],[f491])).
% 1.61/0.60 thf(f491,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))))) | (((irel @ X1 @ (sK28 @ X1)) => (p2 @ (sK28 @ X1))) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f490])).
% 1.61/0.60 thf(f490,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))))) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0))) @ (sK28 @ X1)) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f489])).
% 1.61/0.60 thf(f489,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0)))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f488])).
% 1.61/0.60 thf(f488,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f487])).
% 1.61/0.60 thf(f487,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0)))) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f486])).
% 1.61/0.60 thf(f486,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0)))))) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f485])).
% 1.61/0.60 thf(f485,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0)))))) | ($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))))))) @ X2))) )),
% 1.61/0.60 inference(pi_clausification,[],[f484])).
% 1.61/0.60 thf(f484,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f483])).
% 1.61/0.60 thf(f483,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0)))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f482])).
% 1.61/0.60 thf(f482,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p1 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p2 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1))))))) @ X1))) )),
% 1.61/0.60 inference(pi_clausification,[],[f481])).
% 1.61/0.60 thf(f481,plain,(
% 1.61/0.60 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p1 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p2 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))))))))),
% 1.61/0.60 inference(beta_eta_normalization,[],[f202])).
% 1.61/0.60 thf(f202,plain,(
% 1.61/0.60 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p2) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p2) @ ((^[Y0 : $i > $o]: (Y0)) @ p1)))))),
% 1.61/0.60 inference(definition_unfolding,[],[f167,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f167,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f91])).
% 1.61/0.60 thf(f91,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f90])).
% 1.61/0.60 thf(f90,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1))))),
% 1.61/0.60 inference(rectify,[],[f24])).
% 1.61/0.60 thf(f24,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3)).
% 1.61/0.60 thf(f1245,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p1 @ (sK34 @ X1))) | ($false = (irel @ X2 @ X3)) | ($true = (p0 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(trivial_inequality_removal,[],[f1241])).
% 1.61/0.60 thf(f1241,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (p0 @ X3)) | ($false = (irel @ X2 @ X3)) | ($true = $false) | ($false = (p1 @ (sK34 @ X1)))) )),
% 1.61/0.60 inference(backward_demodulation,[],[f561,f1239])).
% 1.61/0.60 thf(f561,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p1 @ (sK35 @ X2)) = $false) | ($true = (p0 @ X3)) | ($false = (p1 @ (sK34 @ X1))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f558])).
% 1.61/0.60 thf(f558,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p1 @ (sK35 @ X2)) = $false) | ($false = (p1 @ (sK34 @ X1))) | ((irel @ X1 @ X2) = $false) | ($true = ((irel @ X2 @ X3) => (p0 @ X3)))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f553])).
% 1.61/0.60 thf(f553,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p1 @ (sK35 @ X2)) = $false) | (((irel @ X1 @ (sK34 @ X1)) => (p1 @ (sK34 @ X1))) = $false) | ($true = ((irel @ X2 @ X3) => (p0 @ X3)))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f552])).
% 1.61/0.60 thf(f552,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ (sK35 @ X2)) => (p1 @ (sK35 @ X2))) = $false) | ((irel @ X1 @ X2) = $false) | ($true = ((irel @ X2 @ X3) => (p0 @ X3))) | (((irel @ X1 @ (sK34 @ X1)) => (p1 @ (sK34 @ X1))) = $false)) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f551])).
% 1.61/0.60 thf(f551,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((irel @ X2 @ X3) => (p0 @ X3))) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))) @ (sK35 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | (((irel @ X1 @ (sK34 @ X1)) => (p1 @ (sK34 @ X1))) = $false)) )),
% 1.61/0.60 inference(sigma_clausification,[],[f550])).
% 1.61/0.60 thf(f550,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) = $false) | ($true = ((irel @ X2 @ X3) => (p0 @ X3))) | (((irel @ X1 @ (sK34 @ X1)) => (p1 @ (sK34 @ X1))) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f549])).
% 1.61/0.60 thf(f549,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))))) | (((irel @ X1 @ (sK34 @ X1)) => (p1 @ (sK34 @ X1))) = $false) | ((irel @ X1 @ X2) = $false) | ($true = ((irel @ X2 @ X3) => (p0 @ X3)))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f548])).
% 1.61/0.60 thf(f548,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))) @ (sK34 @ X1)) = $false) | ($true = ((irel @ X2 @ X3) => (p0 @ X3))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))))) )),
% 1.61/0.60 inference(sigma_clausification,[],[f547])).
% 1.61/0.60 thf(f547,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0)))) = $false) | ($true = ((irel @ X2 @ X3) => (p0 @ X3))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f546])).
% 1.61/0.60 thf(f546,plain,(
% 1.61/0.60 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0))) @ X3)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))))) )),
% 1.61/0.60 inference(pi_clausification,[],[f545])).
% 1.61/0.60 thf(f545,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0)))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))))) | ((irel @ X1 @ X2) = $false)) )),
% 1.61/0.60 inference(not_proxy_clausification,[],[f544])).
% 1.61/0.60 thf(f544,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0)))))) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f543])).
% 1.61/0.60 thf(f543,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f542])).
% 1.61/0.60 thf(f542,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f541])).
% 1.61/0.60 thf(f541,plain,(
% 1.61/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0)))))) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))))))) @ X2) = $true)) )),
% 1.61/0.60 inference(pi_clausification,[],[f540])).
% 1.61/0.60 thf(f540,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))))))) )),
% 1.61/0.60 inference(binary_proxy_clausification,[],[f539])).
% 1.61/0.60 thf(f539,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0)))))))) )),
% 1.61/0.60 inference(beta_eta_normalization,[],[f538])).
% 1.61/0.60 thf(f538,plain,(
% 1.61/0.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p0 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p1 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))))) @ X1))) )),
% 1.61/0.60 inference(pi_clausification,[],[f537])).
% 1.61/0.60 thf(f537,plain,(
% 1.61/0.60 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p0 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p1 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))))))) = $true)),
% 1.61/0.60 inference(beta_eta_normalization,[],[f197])).
% 1.61/0.60 thf(f197,plain,(
% 1.61/0.60 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p1) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p1) @ ((^[Y0 : $i > $o]: (Y0)) @ p0)))) = $true)),
% 1.61/0.60 inference(definition_unfolding,[],[f159,f139,f181,f152,f181,f152,f152])).
% 1.61/0.60 thf(f159,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0)))) = $true)),
% 1.61/0.60 inference(cnf_transformation,[],[f51])).
% 1.61/0.60 thf(f51,plain,(
% 1.61/0.60 ((ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0)))) = $true)),
% 1.61/0.60 inference(fool_elimination,[],[f50])).
% 1.61/0.60 thf(f50,plain,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0))))),
% 1.61/0.60 inference(rectify,[],[f23])).
% 1.61/0.60 thf(f23,axiom,(
% 1.61/0.60 (ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0))))),
% 1.61/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2)).
% 1.61/0.60 % SZS output end Proof for theBenchmark
% 1.61/0.60 % (7395)------------------------------
% 1.61/0.60 % (7395)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.61/0.60 % (7395)Termination reason: Refutation
% 1.61/0.60
% 1.61/0.60 % (7395)Memory used [KB]: 6268
% 1.61/0.60 % (7395)Time elapsed: 0.115 s
% 1.61/0.60 % (7395)Instructions burned: 156 (million)
% 1.61/0.60 % (7395)------------------------------
% 1.61/0.60 % (7395)------------------------------
% 1.61/0.60 % (7368)Success in time 0.196 s
% 1.61/0.60 % Vampire---4.8 exiting
%------------------------------------------------------------------------------