TSTP Solution File: SYO068^4.010 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO068^4.010 : 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 : n022.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 0.16s 0.41s
% Output : Refutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SYO068^4.010 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.11 % 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
% 0.11/0.31 % Computer : n022.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon May 20 10:48:22 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.11/0.31 This is a TH0_THM_EQU_NAR problem
% 0.16/0.31 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
% 0.16/0.33 % (24031)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)
% 0.16/0.33 % (24030)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)
% 0.16/0.33 % (24032)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.16/0.33 % (24029)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.33 % (24030)Instruction limit reached!
% 0.16/0.33 % (24030)------------------------------
% 0.16/0.33 % (24030)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33 % (24026)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.16/0.33 % (24030)Termination reason: Unknown
% 0.16/0.33 % (24030)Termination phase: shuffling
% 0.16/0.33
% 0.16/0.33 % (24030)Memory used [KB]: 1023
% 0.16/0.33 % (24030)Time elapsed: 0.002 s
% 0.16/0.33 % (24030)Instructions burned: 2 (million)
% 0.16/0.33 % (24030)------------------------------
% 0.16/0.33 % (24030)------------------------------
% 0.16/0.33 % (24033)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)
% 0.16/0.33 % (24028)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)
% 0.16/0.33 % (24027)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)
% 0.16/0.33 % (24029)Instruction limit reached!
% 0.16/0.33 % (24029)------------------------------
% 0.16/0.33 % (24029)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33 % (24029)Termination reason: Unknown
% 0.16/0.33 % (24029)Termination phase: shuffling
% 0.16/0.33
% 0.16/0.33 % (24029)Memory used [KB]: 1023
% 0.16/0.33 % (24029)Time elapsed: 0.003 s
% 0.16/0.33 % (24029)Instructions burned: 2 (million)
% 0.16/0.33 % (24029)------------------------------
% 0.16/0.33 % (24029)------------------------------
% 0.16/0.33 % (24033)Instruction limit reached!
% 0.16/0.33 % (24033)------------------------------
% 0.16/0.33 % (24033)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33 % (24033)Termination reason: Unknown
% 0.16/0.33 % (24033)Termination phase: Property scanning
% 0.16/0.33
% 0.16/0.33 % (24033)Memory used [KB]: 1023
% 0.16/0.33 % (24033)Time elapsed: 0.003 s
% 0.16/0.33 % (24033)Instructions burned: 3 (million)
% 0.16/0.33 % (24033)------------------------------
% 0.16/0.33 % (24033)------------------------------
% 0.16/0.33 % (24031)Refutation not found, incomplete strategy
% 0.16/0.33 % (24031)------------------------------
% 0.16/0.33 % (24031)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33 % (24027)Instruction limit reached!
% 0.16/0.33 % (24027)------------------------------
% 0.16/0.33 % (24027)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33 % (24027)Termination reason: Unknown
% 0.16/0.33 % (24027)Termination phase: Property scanning
% 0.16/0.33
% 0.16/0.33 % (24027)Memory used [KB]: 1023
% 0.16/0.33 % (24027)Time elapsed: 0.003 s
% 0.16/0.33 % (24027)Instructions burned: 4 (million)
% 0.16/0.33 % (24027)------------------------------
% 0.16/0.33 % (24027)------------------------------
% 0.16/0.33 % (24031)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.33
% 0.16/0.33
% 0.16/0.33 % (24031)Memory used [KB]: 5500
% 0.16/0.33 % (24031)Time elapsed: 0.004 s
% 0.16/0.33 % (24031)Instructions burned: 5 (million)
% 0.16/0.33 % (24031)------------------------------
% 0.16/0.33 % (24031)------------------------------
% 0.16/0.34 % (24032)Instruction limit reached!
% 0.16/0.34 % (24032)------------------------------
% 0.16/0.34 % (24032)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (24032)Termination reason: Unknown
% 0.16/0.34 % (24032)Termination phase: Saturation
% 0.16/0.34
% 0.16/0.34 % (24032)Memory used [KB]: 5628
% 0.16/0.34 % (24032)Time elapsed: 0.009 s
% 0.16/0.34 % (24032)Instructions burned: 18 (million)
% 0.16/0.34 % (24032)------------------------------
% 0.16/0.34 % (24032)------------------------------
% 0.16/0.34 % (24028)Instruction limit reached!
% 0.16/0.34 % (24028)------------------------------
% 0.16/0.34 % (24028)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (24028)Termination reason: Unknown
% 0.16/0.34 % (24028)Termination phase: Saturation
% 0.16/0.34
% 0.16/0.34 % (24028)Memory used [KB]: 5628
% 0.16/0.34 % (24028)Time elapsed: 0.014 s
% 0.16/0.34 % (24028)Instructions burned: 28 (million)
% 0.16/0.34 % (24028)------------------------------
% 0.16/0.34 % (24028)------------------------------
% 0.16/0.34 % (24034)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)
% 0.16/0.34 % (24038)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.16/0.34 % (24035)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)
% 0.16/0.35 % (24036)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)
% 0.16/0.35 % (24037)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)
% 0.16/0.35 % (24036)Instruction limit reached!
% 0.16/0.35 % (24036)------------------------------
% 0.16/0.35 % (24036)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.35 % (24036)Termination reason: Unknown
% 0.16/0.35 % (24036)Termination phase: Property scanning
% 0.16/0.35
% 0.16/0.35 % (24036)Memory used [KB]: 1023
% 0.16/0.35 % (24036)Time elapsed: 0.003 s
% 0.16/0.35 % (24036)Instructions burned: 4 (million)
% 0.16/0.35 % (24036)------------------------------
% 0.16/0.35 % (24036)------------------------------
% 0.16/0.35 % (24038)Instruction limit reached!
% 0.16/0.35 % (24038)------------------------------
% 0.16/0.35 % (24038)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.35 % (24038)Termination reason: Unknown
% 0.16/0.35 % (24038)Termination phase: Property scanning
% 0.16/0.35
% 0.16/0.35 % (24038)Memory used [KB]: 1023
% 0.16/0.35 % (24038)Time elapsed: 0.005 s
% 0.16/0.35 % (24038)Instructions burned: 8 (million)
% 0.16/0.35 % (24038)------------------------------
% 0.16/0.35 % (24038)------------------------------
% 0.16/0.35 % (24039)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.16/0.35 % (24035)Instruction limit reached!
% 0.16/0.35 % (24035)------------------------------
% 0.16/0.35 % (24035)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.35 % (24035)Termination reason: Unknown
% 0.16/0.35 % (24035)Termination phase: Saturation
% 0.16/0.35
% 0.16/0.35 % (24035)Memory used [KB]: 1151
% 0.16/0.35 % (24035)Time elapsed: 0.008 s
% 0.16/0.35 % (24035)Instructions burned: 16 (million)
% 0.16/0.35 % (24035)------------------------------
% 0.16/0.35 % (24035)------------------------------
% 0.16/0.36 % (24040)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)
% 0.16/0.36 % (24040)Instruction limit reached!
% 0.16/0.36 % (24040)------------------------------
% 0.16/0.36 % (24040)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.36 % (24040)Termination reason: Unknown
% 0.16/0.36 % (24040)Termination phase: shuffling
% 0.16/0.36
% 0.16/0.36 % (24040)Memory used [KB]: 1023
% 0.16/0.36 % (24040)Time elapsed: 0.003 s
% 0.16/0.36 % (24040)Instructions burned: 3 (million)
% 0.16/0.36 % (24040)------------------------------
% 0.16/0.36 % (24040)------------------------------
% 0.16/0.36 % (24034)Instruction limit reached!
% 0.16/0.36 % (24034)------------------------------
% 0.16/0.36 % (24034)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.36 % (24034)Termination reason: Unknown
% 0.16/0.36 % (24034)Termination phase: Saturation
% 0.16/0.36
% 0.16/0.36 % (24034)Memory used [KB]: 5628
% 0.16/0.36 % (24034)Time elapsed: 0.017 s
% 0.16/0.36 % (24034)Instructions burned: 37 (million)
% 0.16/0.36 % (24034)------------------------------
% 0.16/0.36 % (24034)------------------------------
% 0.16/0.36 % (24039)Instruction limit reached!
% 0.16/0.36 % (24039)------------------------------
% 0.16/0.36 % (24039)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.36 % (24039)Termination reason: Unknown
% 0.16/0.36 % (24039)Termination phase: Saturation
% 0.16/0.36
% 0.16/0.36 % (24039)Memory used [KB]: 5628
% 0.16/0.36 % (24039)Time elapsed: 0.009 s
% 0.16/0.36 % (24039)Instructions burned: 18 (million)
% 0.16/0.36 % (24039)------------------------------
% 0.16/0.36 % (24039)------------------------------
% 0.16/0.36 % (24042)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)
% 0.16/0.36 % (24041)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)
% 0.16/0.36 % (24041)Instruction limit reached!
% 0.16/0.36 % (24041)------------------------------
% 0.16/0.36 % (24041)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.36 % (24041)Termination reason: Unknown
% 0.16/0.36 % (24041)Termination phase: Property scanning
% 0.16/0.36
% 0.16/0.36 % (24041)Memory used [KB]: 1023
% 0.16/0.36 % (24041)Time elapsed: 0.003 s
% 0.16/0.36 % (24041)Instructions burned: 3 (million)
% 0.16/0.36 % (24041)------------------------------
% 0.16/0.36 % (24041)------------------------------
% 0.16/0.36 % (24042)Instruction limit reached!
% 0.16/0.36 % (24042)------------------------------
% 0.16/0.36 % (24042)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.36 % (24042)Termination reason: Unknown
% 0.16/0.36 % (24042)Termination phase: Property scanning
% 0.16/0.36
% 0.16/0.36 % (24042)Memory used [KB]: 1023
% 0.16/0.36 % (24042)Time elapsed: 0.004 s
% 0.16/0.36 % (24042)Instructions burned: 7 (million)
% 0.16/0.36 % (24042)------------------------------
% 0.16/0.36 % (24042)------------------------------
% 0.16/0.36 % (24043)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)
% 0.16/0.37 % (24043)Instruction limit reached!
% 0.16/0.37 % (24043)------------------------------
% 0.16/0.37 % (24043)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.37 % (24043)Termination reason: Unknown
% 0.16/0.37 % (24043)Termination phase: Property scanning
% 0.16/0.37
% 0.16/0.37 % (24043)Memory used [KB]: 1023
% 0.16/0.37 % (24043)Time elapsed: 0.003 s
% 0.16/0.37 % (24043)Instructions burned: 3 (million)
% 0.16/0.37 % (24043)------------------------------
% 0.16/0.37 % (24043)------------------------------
% 0.16/0.37 % (24045)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)
% 0.16/0.37 % (24044)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.16/0.37 % (24046)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.16/0.37 % (24044)Instruction limit reached!
% 0.16/0.37 % (24044)------------------------------
% 0.16/0.37 % (24044)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.37 % (24044)Termination reason: Unknown
% 0.16/0.37 % (24044)Termination phase: Property scanning
% 0.16/0.37
% 0.16/0.37 % (24044)Memory used [KB]: 1023
% 0.16/0.37 % (24044)Time elapsed: 0.004 s
% 0.16/0.37 % (24044)Instructions burned: 5 (million)
% 0.16/0.37 % (24044)------------------------------
% 0.16/0.37 % (24044)------------------------------
% 0.16/0.37 % (24048)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)
% 0.16/0.37 % (24047)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.16/0.37 % (24046)Refutation not found, incomplete strategy
% 0.16/0.37 % (24046)------------------------------
% 0.16/0.37 % (24046)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.37 % (24046)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.37
% 0.16/0.37
% 0.16/0.37 % (24046)Memory used [KB]: 5500
% 0.16/0.37 % (24046)Time elapsed: 0.004 s
% 0.16/0.37 % (24046)Instructions burned: 5 (million)
% 0.16/0.37 % (24046)------------------------------
% 0.16/0.37 % (24046)------------------------------
% 0.16/0.38 % (24047)Instruction limit reached!
% 0.16/0.38 % (24047)------------------------------
% 0.16/0.38 % (24047)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.38 % (24047)Termination reason: Unknown
% 0.16/0.38 % (24047)Termination phase: Function definition elimination
% 0.16/0.38
% 0.16/0.38 % (24047)Memory used [KB]: 1023
% 0.16/0.38 % (24047)Time elapsed: 0.004 s
% 0.16/0.38 % (24047)Instructions burned: 6 (million)
% 0.16/0.38 % (24047)------------------------------
% 0.16/0.38 % (24047)------------------------------
% 0.16/0.38 % (24048)Refutation not found, incomplete strategy
% 0.16/0.38 % (24048)------------------------------
% 0.16/0.38 % (24048)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.38 % (24048)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.38
% 0.16/0.38
% 0.16/0.38 % (24048)Memory used [KB]: 5500
% 0.16/0.38 % (24048)Time elapsed: 0.005 s
% 0.16/0.38 % (24048)Instructions burned: 7 (million)
% 0.16/0.38 % (24048)------------------------------
% 0.16/0.38 % (24048)------------------------------
% 0.16/0.38 % (24049)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)
% 0.16/0.38 % (24045)Instruction limit reached!
% 0.16/0.38 % (24045)------------------------------
% 0.16/0.38 % (24045)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.38 % (24045)Termination reason: Unknown
% 0.16/0.38 % (24045)Termination phase: Saturation
% 0.16/0.38
% 0.16/0.38 % (24045)Memory used [KB]: 5628
% 0.16/0.38 % (24045)Time elapsed: 0.011 s
% 0.16/0.38 % (24045)Instructions burned: 18 (million)
% 0.16/0.38 % (24045)------------------------------
% 0.16/0.38 % (24045)------------------------------
% 0.16/0.39 % (24050)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.16/0.39 % (24051)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)
% 0.16/0.39 % (24049)Instruction limit reached!
% 0.16/0.39 % (24049)------------------------------
% 0.16/0.39 % (24049)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (24049)Termination reason: Unknown
% 0.16/0.39 % (24049)Termination phase: Saturation
% 0.16/0.39
% 0.16/0.39 % (24049)Memory used [KB]: 5628
% 0.16/0.39 % (24050)Instruction limit reached!
% 0.16/0.39 % (24050)------------------------------
% 0.16/0.39 % (24050)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (24050)Termination reason: Unknown
% 0.16/0.39 % (24050)Termination phase: Function definition elimination
% 0.16/0.39
% 0.16/0.39 % (24050)Memory used [KB]: 1023
% 0.16/0.39 % (24050)Time elapsed: 0.004 s
% 0.16/0.39 % (24050)Instructions burned: 6 (million)
% 0.16/0.39 % (24050)------------------------------
% 0.16/0.39 % (24050)------------------------------
% 0.16/0.39 % (24049)Time elapsed: 0.011 s
% 0.16/0.39 % (24049)Instructions burned: 22 (million)
% 0.16/0.39 % (24049)------------------------------
% 0.16/0.39 % (24049)------------------------------
% 0.16/0.39 % (24053)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)
% 0.16/0.39 % (24052)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.16/0.39 % (24051)Instruction limit reached!
% 0.16/0.39 % (24051)------------------------------
% 0.16/0.39 % (24051)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (24051)Termination reason: Unknown
% 0.16/0.39 % (24051)Termination phase: Saturation
% 0.16/0.39
% 0.16/0.39 % (24051)Memory used [KB]: 5500
% 0.16/0.39 % (24051)Time elapsed: 0.004 s
% 0.16/0.39 % (24051)Instructions burned: 6 (million)
% 0.16/0.39 % (24051)------------------------------
% 0.16/0.39 % (24051)------------------------------
% 0.16/0.39 % (24054)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)
% 0.16/0.40 % (24054)Refutation not found, incomplete strategy
% 0.16/0.40 % (24054)------------------------------
% 0.16/0.40 % (24054)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (24054)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.40
% 0.16/0.40
% 0.16/0.40 % (24054)Memory used [KB]: 5500
% 0.16/0.40 % (24054)Time elapsed: 0.005 s
% 0.16/0.40 % (24054)Instructions burned: 7 (million)
% 0.16/0.40 % (24054)------------------------------
% 0.16/0.40 % (24054)------------------------------
% 0.16/0.40 % (24026)First to succeed.
% 0.16/0.40 % (24055)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)
% 0.16/0.40 % (24056)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.16/0.40 % (24057)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.16/0.41 % (24057)Instruction limit reached!
% 0.16/0.41 % (24057)------------------------------
% 0.16/0.41 % (24057)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (24057)Termination reason: Unknown
% 0.16/0.41 % (24057)Termination phase: shuffling
% 0.16/0.41
% 0.16/0.41 % (24057)Memory used [KB]: 1023
% 0.16/0.41 % (24057)Time elapsed: 0.003 s
% 0.16/0.41 % (24057)Instructions burned: 4 (million)
% 0.16/0.41 % (24057)------------------------------
% 0.16/0.41 % (24057)------------------------------
% 0.16/0.41 % (24056)Instruction limit reached!
% 0.16/0.41 % (24056)------------------------------
% 0.16/0.41 % (24056)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (24056)Termination reason: Unknown
% 0.16/0.41 % (24056)Termination phase: Saturation
% 0.16/0.41
% 0.16/0.41 % (24056)Memory used [KB]: 5628
% 0.16/0.41 % (24056)Time elapsed: 0.009 s
% 0.16/0.41 % (24056)Instructions burned: 17 (million)
% 0.16/0.41 % (24056)------------------------------
% 0.16/0.41 % (24056)------------------------------
% 0.16/0.41 % (24058)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.16/0.41 % (24026)Refutation found. Thanks to Tanya!
% 0.16/0.41 % SZS status Theorem for theBenchmark
% 0.16/0.41 % SZS output start Proof for theBenchmark
% 0.16/0.41 thf(func_def_0, type, irel: $i > $i > $o).
% 0.16/0.41 thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 0.16/0.41 thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.41 thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.41 thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.41 thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 0.16/0.41 thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 0.16/0.41 thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 0.16/0.41 thf(func_def_9, type, itrue: $i > $o).
% 0.16/0.41 thf(func_def_10, type, ifalse: $i > $o).
% 0.16/0.41 thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.41 thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.41 thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.41 thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.41 thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.41 thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.41 thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 0.16/0.41 thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 0.16/0.41 thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 0.16/0.41 thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 0.16/0.41 thf(func_def_21, type, p0: $i > $o).
% 0.16/0.41 thf(func_def_22, type, p1: $i > $o).
% 0.16/0.41 thf(func_def_23, type, p10: $i > $o).
% 0.16/0.41 thf(func_def_24, type, p2: $i > $o).
% 0.16/0.41 thf(func_def_25, type, p3: $i > $o).
% 0.16/0.41 thf(func_def_26, type, p4: $i > $o).
% 0.16/0.41 thf(func_def_27, type, p5: $i > $o).
% 0.16/0.41 thf(func_def_28, type, p6: $i > $o).
% 0.16/0.41 thf(func_def_29, type, p7: $i > $o).
% 0.16/0.41 thf(func_def_30, type, p8: $i > $o).
% 0.16/0.41 thf(func_def_31, type, p9: $i > $o).
% 0.16/0.41 thf(func_def_45, type, sK1: $i > $i).
% 0.16/0.41 thf(func_def_46, type, sK2: $i > $i).
% 0.16/0.41 thf(func_def_47, type, sK3: $i > $i).
% 0.16/0.41 thf(func_def_48, type, sK4: $i > $i).
% 0.16/0.41 thf(func_def_49, type, sK5: $i > $i).
% 0.16/0.41 thf(func_def_50, type, sK6: $i > $i).
% 0.16/0.41 thf(func_def_51, type, sK7: $i > $i).
% 0.16/0.41 thf(func_def_52, type, sK8: $i > $i).
% 0.16/0.41 thf(func_def_53, type, sK9: $i > $i).
% 0.16/0.41 thf(func_def_55, type, sK11: $i > $i).
% 0.16/0.41 thf(func_def_56, type, sK12: $i > $i).
% 0.16/0.41 thf(func_def_57, type, sK13: $i > $i).
% 0.16/0.41 thf(func_def_58, type, sK14: $i > $i).
% 0.16/0.41 thf(func_def_59, type, sK15: $i > $i).
% 0.16/0.41 thf(func_def_60, type, sK16: $i > $i).
% 0.16/0.41 thf(func_def_61, type, sK17: $i > $i).
% 0.16/0.41 thf(func_def_62, type, sK18: $i > $i).
% 0.16/0.41 thf(func_def_63, type, sK19: $i > $i).
% 0.16/0.41 thf(func_def_64, type, sK20: $i > $i).
% 0.16/0.41 thf(func_def_65, type, sK21: $i > $i).
% 0.16/0.41 thf(func_def_66, type, sK22: $i > $i).
% 0.16/0.41 thf(func_def_67, type, sK23: $i > $i).
% 0.16/0.41 thf(func_def_68, type, sK24: $i > $i).
% 0.16/0.41 thf(func_def_69, type, sK25: $i > $i).
% 0.16/0.41 thf(func_def_70, type, sK26: $i > $i).
% 0.16/0.41 thf(func_def_71, type, sK27: $i > $i).
% 0.16/0.41 thf(func_def_72, type, sK28: $i > $i).
% 0.16/0.41 thf(func_def_73, type, sK29: $i > $i).
% 0.16/0.41 thf(func_def_74, type, sK30: $i > $i).
% 0.16/0.41 thf(f920,plain,(
% 0.16/0.41 $false),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f919])).
% 0.16/0.41 thf(f919,plain,(
% 0.16/0.41 ($false = $true)),
% 0.16/0.41 inference(superposition,[],[f258,f917])).
% 0.16/0.41 thf(f917,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($true = (p0 @ X0))) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f914])).
% 0.16/0.41 thf(f914,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($true = (p0 @ X0)) | ($false = $true)) )),
% 0.16/0.41 inference(superposition,[],[f913,f828])).
% 0.16/0.41 thf(f828,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p1 @ X0) = $true)) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f825])).
% 0.16/0.41 thf(f825,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($false = $true) | ((p1 @ X0) = $true)) )),
% 0.16/0.41 inference(superposition,[],[f824,f820])).
% 0.16/0.41 thf(f820,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p2 @ X0) = $true)) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f818])).
% 0.16/0.41 thf(f818,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($false = $true) | ((p2 @ X0) = $true)) )),
% 0.16/0.41 inference(superposition,[],[f812,f816])).
% 0.16/0.41 thf(f816,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p3 @ (sK1 @ X0)) = $false) | ((p2 @ X0) = $true)) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f814])).
% 0.16/0.41 thf(f814,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($false = $true) | ((p2 @ X0) = $true) | ((p3 @ (sK1 @ X0)) = $false)) )),
% 0.16/0.41 inference(superposition,[],[f496,f812])).
% 0.16/0.41 thf(f496,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p3 @ (sK3 @ X0)) = $false) | ((p2 @ X0) = $true) | ((p3 @ (sK1 @ X0)) = $false)) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f491])).
% 0.16/0.41 thf(f491,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p2 @ X0) = $true) | ($false = $true) | ((p3 @ (sK3 @ X0)) = $false) | ((p3 @ (sK1 @ X0)) = $false)) )),
% 0.16/0.41 inference(superposition,[],[f119,f488])).
% 0.16/0.41 thf(f488,plain,(
% 0.16/0.41 ( ! [X0 : $i,X1 : $i] : (($false = (irel @ X1 @ X0)) | ((p2 @ X0) = $true) | ($false = (p3 @ (sK1 @ X1))) | ((p3 @ (sK3 @ X0)) = $false)) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f479])).
% 0.16/0.41 thf(f479,plain,(
% 0.16/0.41 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ((p3 @ (sK3 @ X0)) = $false) | ((p2 @ X0) = $true) | ($false = (p3 @ (sK1 @ X1))) | ($false = (irel @ X1 @ X0))) )),
% 0.16/0.41 inference(superposition,[],[f190,f119])).
% 0.16/0.41 thf(f190,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((irel @ X1 @ X2) = $false) | ((p3 @ (sK3 @ X2)) = $false) | ((p2 @ X3) = $true) | ($false = (p3 @ (sK1 @ X1)))) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f187])).
% 0.16/0.41 thf(f187,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p3 @ (sK1 @ X1))) | (((irel @ X2 @ X3) => (p2 @ X3)) = $true) | ((irel @ X1 @ X2) = $false) | ((p3 @ (sK3 @ X2)) = $false)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f186])).
% 0.16/0.41 thf(f186,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = ((irel @ X2 @ (sK3 @ X2)) => (p3 @ (sK3 @ X2)))) | (((irel @ X2 @ X3) => (p2 @ X3)) = $true) | ($false = (p3 @ (sK1 @ X1)))) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f185])).
% 0.16/0.41 thf(f185,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p3 @ (sK1 @ X1))) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))) @ X3) = $true) | ($false = ((irel @ X2 @ (sK3 @ X2)) => (p3 @ (sK3 @ X2)))) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.41 inference(pi_clausification,[],[f184])).
% 0.16/0.41 thf(f184,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $true) | ($false = ((irel @ X2 @ (sK3 @ X2)) => (p3 @ (sK3 @ X2)))) | ((irel @ X1 @ X2) = $false) | ($false = (p3 @ (sK1 @ X1)))) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f183])).
% 0.16/0.41 thf(f183,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $true) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))) @ (sK3 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ($false = (p3 @ (sK1 @ X1)))) )),
% 0.16/0.41 inference(sigma_clausification,[],[f182])).
% 0.16/0.41 thf(f182,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) = $false) | ($false = (p3 @ (sK1 @ X1))) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $true)) )),
% 0.16/0.41 inference(not_proxy_clausification,[],[f181])).
% 0.16/0.41 thf(f181,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $true) | ($false = (p3 @ (sK1 @ X1)))) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f180])).
% 0.16/0.41 thf(f180,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))))))) | ($false = (p3 @ (sK1 @ X1))) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f179])).
% 0.16/0.41 thf(f179,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (($false = (p3 @ (sK1 @ X1))) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))))))) = $true)) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f178])).
% 0.16/0.41 thf(f178,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))))))) @ X2)) | ($false = (p3 @ (sK1 @ X1)))) )),
% 0.16/0.41 inference(pi_clausification,[],[f164])).
% 0.16/0.41 thf(f164,plain,(
% 0.16/0.41 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))))) = $true) | ($false = (p3 @ (sK1 @ X1)))) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f163])).
% 0.16/0.41 thf(f163,plain,(
% 0.16/0.41 ( ! [X1 : $i] : ((((irel @ X1 @ (sK1 @ X1)) => (p3 @ (sK1 @ X1))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))))) = $true)) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f162])).
% 0.16/0.41 thf(f162,plain,(
% 0.16/0.41 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p3 @ Y0))) @ (sK1 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))))) = $true)) )),
% 0.16/0.41 inference(sigma_clausification,[],[f161])).
% 0.16/0.41 thf(f161,plain,(
% 0.16/0.41 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p3 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))))) = $true)) )),
% 0.16/0.41 inference(not_proxy_clausification,[],[f160])).
% 0.16/0.41 thf(f160,plain,(
% 0.16/0.41 ( ! [X1 : $i] : (((~ (!! @ $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))))))))) = $true)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f159])).
% 0.16/0.41 thf(f159,plain,(
% 0.16/0.41 ( ! [X1 : $i] : ((((!! @ $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)))))) = $true)) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f158])).
% 0.16/0.41 thf(f158,plain,(
% 0.16/0.41 ( ! [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)) )),
% 0.16/0.41 inference(pi_clausification,[],[f157])).
% 0.16/0.41 thf(f157,plain,(
% 0.16/0.41 ((!! @ $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)),
% 0.16/0.41 inference(beta_eta_normalization,[],[f150])).
% 0.16/0.41 thf(f150,plain,(
% 0.16/0.41 (((^[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)))) = $true)),
% 0.16/0.41 inference(definition_unfolding,[],[f113,f120,f141,f128,f141,f128,f128])).
% 0.16/0.41 thf(f128,plain,(
% 0.16/0.41 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.16/0.41 inference(cnf_transformation,[],[f77])).
% 0.16/0.41 thf(f77,plain,(
% 0.16/0.41 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.16/0.41 inference(fool_elimination,[],[f76])).
% 0.16/0.41 thf(f76,plain,(
% 0.16/0.41 (iatom = (^[X0 : $i > $o] : (X0)))),
% 0.16/0.41 inference(rectify,[],[f8])).
% 0.16/0.41 thf(f8,axiom,(
% 0.16/0.41 (iatom = (^[X5 : $i > $o] : (X5)))),
% 0.16/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iatom)).
% 0.16/0.41 thf(f141,plain,(
% 0.16/0.41 (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))))))),
% 0.16/0.41 inference(definition_unfolding,[],[f131,f136,f117,f117])).
% 0.16/0.41 thf(f117,plain,(
% 0.16/0.41 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.16/0.41 inference(cnf_transformation,[],[f85])).
% 0.16/0.41 thf(f85,plain,(
% 0.16/0.41 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.16/0.41 inference(fool_elimination,[],[f84])).
% 0.16/0.41 thf(f84,plain,(
% 0.16/0.41 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((irel @ X1 @ X2) => (X0 @ X2)))) = mbox_s4)),
% 0.16/0.41 inference(rectify,[],[f7])).
% 0.16/0.41 thf(f7,axiom,(
% 0.16/0.41 ((^[X5 : $i > $o, X0 : $i] : (! [X1] : ((irel @ X0 @ X1) => (X5 @ X1)))) = mbox_s4)),
% 0.16/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4)).
% 0.16/0.41 thf(f136,plain,(
% 0.16/0.41 (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)))))),
% 0.16/0.41 inference(definition_unfolding,[],[f124,f127,f109])).
% 0.16/0.41 thf(f109,plain,(
% 0.16/0.41 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.16/0.41 inference(cnf_transformation,[],[f53])).
% 0.16/0.41 thf(f53,plain,(
% 0.16/0.41 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.16/0.41 inference(fool_elimination,[],[f52])).
% 0.16/0.41 thf(f52,plain,(
% 0.16/0.41 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.16/0.41 inference(rectify,[],[f3])).
% 0.16/0.41 thf(f3,axiom,(
% 0.16/0.41 ((^[X0 : $i > $o, X3 : $i] : (~(X0 @ X3))) = mnot)),
% 0.16/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.16/0.41 thf(f127,plain,(
% 0.16/0.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.16/0.41 inference(cnf_transformation,[],[f97])).
% 0.16/0.41 thf(f97,plain,(
% 0.16/0.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.16/0.41 inference(fool_elimination,[],[f96])).
% 0.16/0.41 thf(f96,plain,(
% 0.16/0.41 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.16/0.41 inference(rectify,[],[f4])).
% 0.16/0.41 thf(f4,axiom,(
% 0.16/0.41 ((^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X0 @ X3) | (X1 @ X3))) = mor)),
% 0.16/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.16/0.41 thf(f124,plain,(
% 0.16/0.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.16/0.41 inference(cnf_transformation,[],[f59])).
% 0.16/0.41 thf(f59,plain,(
% 0.16/0.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.16/0.41 inference(fool_elimination,[],[f58])).
% 0.16/0.41 thf(f58,plain,(
% 0.16/0.41 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.16/0.41 inference(rectify,[],[f6])).
% 0.16/0.41 thf(f6,axiom,(
% 0.16/0.41 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.16/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.16/0.41 thf(f131,plain,(
% 0.16/0.41 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.16/0.41 inference(cnf_transformation,[],[f47])).
% 0.16/0.41 thf(f47,plain,(
% 0.16/0.41 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.16/0.41 inference(fool_elimination,[],[f46])).
% 0.16/0.41 thf(f46,plain,(
% 0.16/0.41 (iimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))))),
% 0.16/0.41 inference(rectify,[],[f14])).
% 0.16/0.41 thf(f14,axiom,(
% 0.16/0.41 (iimplies = (^[X5 : $i > $o, X7 : $i > $o] : (mimplies @ (mbox_s4 @ X5) @ (mbox_s4 @ X7))))),
% 0.16/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iimplies)).
% 0.16/0.41 thf(f120,plain,(
% 0.16/0.41 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.16/0.41 inference(cnf_transformation,[],[f65])).
% 0.16/0.41 thf(f65,plain,(
% 0.16/0.41 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.16/0.41 inference(fool_elimination,[],[f64])).
% 0.16/0.41 thf(f64,plain,(
% 0.16/0.41 (ivalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.16/0.41 inference(rectify,[],[f18])).
% 0.16/0.41 thf(f18,axiom,(
% 0.16/0.41 (ivalid = (^[X8 : $i > $o] : (! [X6] : (X8 @ X6))))),
% 0.16/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ivalid)).
% 0.16/0.41 thf(f113,plain,(
% 0.16/0.41 ((ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2)))) = $true)),
% 0.16/0.41 inference(cnf_transformation,[],[f93])).
% 0.16/0.41 thf(f93,plain,(
% 0.16/0.41 ((ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2)))) = $true)),
% 0.16/0.41 inference(fool_elimination,[],[f92])).
% 0.16/0.41 thf(f92,plain,(
% 0.16/0.41 (ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2))))),
% 0.16/0.41 inference(rectify,[],[f25])).
% 0.16/0.41 thf(f25,axiom,(
% 0.16/0.41 (ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2))))),
% 0.16/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4)).
% 0.16/0.41 thf(f119,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((irel @ X0 @ X0) = $true)) )),
% 0.16/0.41 inference(cnf_transformation,[],[f71])).
% 0.16/0.41 thf(f71,plain,(
% 0.16/0.41 ! [X0] : ((irel @ X0 @ X0) = $true)),
% 0.16/0.41 inference(fool_elimination,[],[f70])).
% 0.16/0.41 thf(f70,plain,(
% 0.16/0.41 ! [X0] : (irel @ X0 @ X0)),
% 0.16/0.41 inference(rectify,[],[f1])).
% 0.16/0.41 thf(f1,axiom,(
% 0.16/0.41 ! [X0] : (irel @ X0 @ X0)),
% 0.16/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom)).
% 0.16/0.41 thf(f812,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p3 @ X0) = $true)) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f810])).
% 0.16/0.41 thf(f810,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p3 @ X0) = $true) | ($false = $true)) )),
% 0.16/0.41 inference(superposition,[],[f804,f808])).
% 0.16/0.41 thf(f808,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p4 @ (sK17 @ X0)) = $false) | ((p3 @ X0) = $true)) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f805])).
% 0.16/0.41 thf(f805,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p4 @ (sK17 @ X0)) = $false) | ($false = $true) | ((p3 @ X0) = $true)) )),
% 0.16/0.41 inference(superposition,[],[f804,f618])).
% 0.16/0.41 thf(f618,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($false = (p4 @ (sK18 @ X0))) | ((p4 @ (sK17 @ X0)) = $false) | ((p3 @ X0) = $true)) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f613])).
% 0.16/0.41 thf(f613,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p3 @ X0) = $true) | ((p4 @ (sK17 @ X0)) = $false) | ($false = $true) | ($false = (p4 @ (sK18 @ X0)))) )),
% 0.16/0.41 inference(superposition,[],[f119,f610])).
% 0.16/0.41 thf(f610,plain,(
% 0.16/0.41 ( ! [X0 : $i,X1 : $i] : (($false = (irel @ X1 @ X0)) | ((p4 @ (sK17 @ X0)) = $false) | ((p4 @ (sK18 @ X1)) = $false) | ((p3 @ X0) = $true)) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f603])).
% 0.16/0.41 thf(f603,plain,(
% 0.16/0.41 ( ! [X0 : $i,X1 : $i] : (((p4 @ (sK17 @ X0)) = $false) | ($false = $true) | ($false = (irel @ X1 @ X0)) | ((p3 @ X0) = $true) | ((p4 @ (sK18 @ X1)) = $false)) )),
% 0.16/0.41 inference(superposition,[],[f119,f349])).
% 0.16/0.41 thf(f349,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ($false = (p4 @ (sK17 @ X2))) | ((irel @ X1 @ X2) = $false) | ((p3 @ X3) = $true) | ((p4 @ (sK18 @ X1)) = $false)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f348])).
% 0.16/0.41 thf(f348,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p3 @ X3) = $true) | ((p4 @ (sK18 @ X1)) = $false) | ((irel @ X2 @ X3) = $false) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ (sK17 @ X2)) => (p4 @ (sK17 @ X2))) = $false)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f343])).
% 0.16/0.41 thf(f343,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p4 @ (sK18 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ X3) => (p3 @ X3)) = $true) | (((irel @ X2 @ (sK17 @ X2)) => (p4 @ (sK17 @ X2))) = $false)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f342])).
% 0.16/0.41 thf(f342,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X1 @ (sK18 @ X1)) => (p4 @ (sK18 @ X1))) = $false) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ (sK17 @ X2)) => (p4 @ (sK17 @ X2))) = $false) | (((irel @ X2 @ X3) => (p3 @ X3)) = $true)) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f341])).
% 0.16/0.41 thf(f341,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ X3) => (p3 @ X3)) = $true) | (((irel @ X2 @ (sK17 @ X2)) => (p4 @ (sK17 @ X2))) = $false) | ((irel @ X1 @ X2) = $false) | ($false = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0))) @ (sK18 @ X1)))) )),
% 0.16/0.41 inference(sigma_clausification,[],[f340])).
% 0.16/0.41 thf(f340,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0)))) = $false) | (((irel @ X2 @ X3) => (p3 @ X3)) = $true) | (((irel @ X2 @ (sK17 @ X2)) => (p4 @ (sK17 @ X2))) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f339])).
% 0.16/0.41 thf(f339,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))) @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0)))) = $false) | (((irel @ X2 @ (sK17 @ X2)) => (p4 @ (sK17 @ X2))) = $false)) )),
% 0.16/0.41 inference(pi_clausification,[],[f338])).
% 0.16/0.41 thf(f338,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) = $true) | (((irel @ X2 @ (sK17 @ X2)) => (p4 @ (sK17 @ X2))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0)))) = $false)) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f337])).
% 0.16/0.41 thf(f337,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) = $true) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))) @ (sK17 @ X2)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0)))) = $false)) )),
% 0.16/0.41 inference(sigma_clausification,[],[f336])).
% 0.16/0.41 thf(f336,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.41 inference(not_proxy_clausification,[],[f335])).
% 0.16/0.41 thf(f335,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f334])).
% 0.16/0.41 thf(f334,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f333])).
% 0.16/0.41 thf(f333,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0)))) = $false)) )),
% 0.16/0.41 inference(not_proxy_clausification,[],[f332])).
% 0.16/0.41 thf(f332,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0))))) = $true) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))))))) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f331])).
% 0.16/0.41 thf(f331,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))))))) @ X2)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0))))) = $true)) )),
% 0.16/0.41 inference(pi_clausification,[],[f330])).
% 0.16/0.41 thf(f330,plain,(
% 0.16/0.41 ( ! [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)))))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0))))) = $true)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f329])).
% 0.16/0.41 thf(f329,plain,(
% 0.16/0.41 ( ! [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))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0)))))))) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f328])).
% 0.16/0.41 thf(f328,plain,(
% 0.16/0.41 ( ! [X1 : $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))))))) @ X1) = $true)) )),
% 0.16/0.41 inference(pi_clausification,[],[f327])).
% 0.16/0.41 thf(f327,plain,(
% 0.16/0.41 ((!! @ $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)),
% 0.16/0.41 inference(beta_eta_normalization,[],[f146])).
% 0.16/0.41 thf(f146,plain,(
% 0.16/0.41 (((^[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)))) = $true)),
% 0.16/0.41 inference(definition_unfolding,[],[f104,f120,f141,f128,f141,f128,f128])).
% 0.16/0.41 thf(f104,plain,(
% 0.16/0.41 ((ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3)))) = $true)),
% 0.16/0.41 inference(cnf_transformation,[],[f81])).
% 0.16/0.41 thf(f81,plain,(
% 0.16/0.41 ((ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3)))) = $true)),
% 0.16/0.41 inference(fool_elimination,[],[f80])).
% 0.16/0.41 thf(f80,plain,(
% 0.16/0.41 (ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3))))),
% 0.16/0.41 inference(rectify,[],[f26])).
% 0.16/0.41 thf(f26,axiom,(
% 0.16/0.41 (ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3))))),
% 0.16/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5)).
% 0.16/0.41 thf(f804,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($true = (p4 @ X0))) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f801])).
% 0.16/0.41 thf(f801,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($true = (p4 @ X0)) | ($false = $true)) )),
% 0.16/0.41 inference(superposition,[],[f800,f714])).
% 0.16/0.41 thf(f714,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($true = (p5 @ X0))) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f712])).
% 0.16/0.41 thf(f712,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($true = (p5 @ X0)) | ($false = $true)) )),
% 0.16/0.41 inference(superposition,[],[f706,f710])).
% 0.16/0.41 thf(f710,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p6 @ (sK25 @ X0)) = $false) | ($true = (p5 @ X0))) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f707])).
% 0.16/0.41 thf(f707,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p6 @ (sK25 @ X0)) = $false) | ($false = $true) | ($true = (p5 @ X0))) )),
% 0.16/0.41 inference(superposition,[],[f706,f679])).
% 0.16/0.41 thf(f679,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p6 @ (sK27 @ X0)) = $false) | ((p6 @ (sK25 @ X0)) = $false) | ($true = (p5 @ X0))) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f675])).
% 0.16/0.41 thf(f675,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p6 @ (sK27 @ X0)) = $false) | ($true = (p5 @ X0)) | ((p6 @ (sK25 @ X0)) = $false) | ($false = $true)) )),
% 0.16/0.41 inference(superposition,[],[f119,f672])).
% 0.16/0.41 thf(f672,plain,(
% 0.16/0.41 ( ! [X0 : $i,X1 : $i] : (($false = (irel @ X1 @ X0)) | ($true = (p5 @ X0)) | ((p6 @ (sK25 @ X1)) = $false) | ((p6 @ (sK27 @ X0)) = $false)) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f663])).
% 0.16/0.41 thf(f663,plain,(
% 0.16/0.41 ( ! [X0 : $i,X1 : $i] : (($true = (p5 @ X0)) | ($false = (irel @ X1 @ X0)) | ((p6 @ (sK25 @ X1)) = $false) | ($false = $true) | ((p6 @ (sK27 @ X0)) = $false)) )),
% 0.16/0.41 inference(superposition,[],[f445,f119])).
% 0.16/0.41 thf(f445,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p6 @ (sK25 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((p5 @ X3) = $true) | ((p6 @ (sK27 @ X2)) = $false)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f444])).
% 0.16/0.41 thf(f444,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p6 @ (sK25 @ X1)) = $false) | ((p5 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ (sK27 @ X2)) => (p6 @ (sK27 @ X2))) = $false) | ((irel @ X2 @ X3) = $false)) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f443])).
% 0.16/0.41 thf(f443,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p6 @ (sK25 @ X1)) = $false) | ($false = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0))) @ (sK27 @ X2))) | ((p5 @ X3) = $true) | ((irel @ X2 @ X3) = $false)) )),
% 0.16/0.41 inference(sigma_clausification,[],[f442])).
% 0.16/0.41 thf(f442,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p6 @ (sK25 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((irel @ X2 @ X3) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0))))) | ((p5 @ X3) = $true)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f441])).
% 0.16/0.41 thf(f441,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p6 @ (sK25 @ X1)) = $false) | (((irel @ X2 @ X3) => (p5 @ X3)) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))))) )),
% 0.16/0.41 inference(not_proxy_clausification,[],[f440])).
% 0.16/0.41 thf(f440,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p6 @ (sK25 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))))) | (((irel @ X2 @ X3) => (p5 @ X3)) = $true)) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f439])).
% 0.16/0.41 thf(f439,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))))) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))) @ X3)) | ((irel @ X1 @ X2) = $false) | ((p6 @ (sK25 @ X1)) = $false)) )),
% 0.16/0.41 inference(pi_clausification,[],[f428])).
% 0.16/0.41 thf(f428,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (((p6 @ (sK25 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0))))))) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f427])).
% 0.16/0.41 thf(f427,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK25 @ X1)) => (p6 @ (sK25 @ X1))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f426])).
% 0.16/0.41 thf(f426,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))))) = $true) | (((irel @ X1 @ (sK25 @ X1)) => (p6 @ (sK25 @ X1))) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f425])).
% 0.16/0.41 thf(f425,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p6 @ Y0))) @ (sK25 @ X1)) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))))) = $true)) )),
% 0.16/0.41 inference(sigma_clausification,[],[f424])).
% 0.16/0.41 thf(f424,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p6 @ Y0))))) | ((irel @ X1 @ X2) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))))) = $true)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f423])).
% 0.16/0.41 thf(f423,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p6 @ Y0)))))) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f422])).
% 0.16/0.41 thf(f422,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p6 @ Y0))))) | ($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))))))) @ X2))) )),
% 0.16/0.41 inference(pi_clausification,[],[f421])).
% 0.16/0.41 thf(f421,plain,(
% 0.16/0.41 ( ! [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 = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p6 @ Y0)))))) )),
% 0.16/0.41 inference(not_proxy_clausification,[],[f420])).
% 0.16/0.41 thf(f420,plain,(
% 0.16/0.41 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p6 @ Y0))))) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1))))))))))) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f419])).
% 0.16/0.41 thf(f419,plain,(
% 0.16/0.41 ( ! [X1 : $i] : ((((!! @ $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)))))) = $true)) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f418])).
% 0.16/0.41 thf(f418,plain,(
% 0.16/0.41 ( ! [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))) )),
% 0.16/0.41 inference(pi_clausification,[],[f417])).
% 0.16/0.41 thf(f417,plain,(
% 0.16/0.41 ((!! @ $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)))))))) = $true)),
% 0.16/0.41 inference(beta_eta_normalization,[],[f154])).
% 0.16/0.41 thf(f154,plain,(
% 0.16/0.41 ($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)))))),
% 0.16/0.41 inference(definition_unfolding,[],[f123,f120,f141,f128,f141,f128,f128])).
% 0.16/0.41 thf(f123,plain,(
% 0.16/0.41 ((ivalid @ (iimplies @ (iatom @ p6) @ (iimplies @ (iatom @ p6) @ (iatom @ p5)))) = $true)),
% 0.16/0.41 inference(cnf_transformation,[],[f43])).
% 0.16/0.41 thf(f43,plain,(
% 0.16/0.41 ((ivalid @ (iimplies @ (iatom @ p6) @ (iimplies @ (iatom @ p6) @ (iatom @ p5)))) = $true)),
% 0.16/0.41 inference(fool_elimination,[],[f42])).
% 0.16/0.41 thf(f42,plain,(
% 0.16/0.41 (ivalid @ (iimplies @ (iatom @ p6) @ (iimplies @ (iatom @ p6) @ (iatom @ p5))))),
% 0.16/0.41 inference(rectify,[],[f28])).
% 0.16/0.41 thf(f28,axiom,(
% 0.16/0.41 (ivalid @ (iimplies @ (iatom @ p6) @ (iimplies @ (iatom @ p6) @ (iatom @ p5))))),
% 0.16/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom7)).
% 0.16/0.41 thf(f706,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($true = (p6 @ X0))) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f703])).
% 0.16/0.41 thf(f703,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($true = (p6 @ X0)) | ($false = $true)) )),
% 0.16/0.41 inference(superposition,[],[f702,f662])).
% 0.16/0.41 thf(f662,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p7 @ X0) = $true)) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f659])).
% 0.16/0.41 thf(f659,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($false = $true) | ((p7 @ X0) = $true)) )),
% 0.16/0.41 inference(superposition,[],[f658,f600])).
% 0.16/0.41 thf(f600,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($true = (p8 @ X0))) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f598])).
% 0.16/0.41 thf(f598,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($false = $true) | ($true = (p8 @ X0))) )),
% 0.16/0.41 inference(superposition,[],[f532,f596])).
% 0.16/0.41 thf(f596,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p9 @ (sK14 @ X0)) = $false) | ($true = (p8 @ X0))) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f593])).
% 0.16/0.41 thf(f593,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($true = (p8 @ X0)) | ((p9 @ (sK14 @ X0)) = $false) | ($false = $true)) )),
% 0.16/0.41 inference(superposition,[],[f591,f532])).
% 0.16/0.41 thf(f591,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p9 @ (sK16 @ X0)) = $false) | ((p9 @ (sK14 @ X0)) = $false) | ($true = (p8 @ X0))) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f585])).
% 0.16/0.41 thf(f585,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p9 @ (sK16 @ X0)) = $false) | ($false = $true) | ((p9 @ (sK14 @ X0)) = $false) | ($true = (p8 @ X0))) )),
% 0.16/0.41 inference(superposition,[],[f576,f119])).
% 0.16/0.41 thf(f576,plain,(
% 0.16/0.41 ( ! [X0 : $i,X1 : $i] : (($false = (irel @ X1 @ X0)) | ((p9 @ (sK14 @ X1)) = $false) | ((p9 @ (sK16 @ X0)) = $false) | ($true = (p8 @ X0))) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f569])).
% 0.16/0.41 thf(f569,plain,(
% 0.16/0.41 ( ! [X0 : $i,X1 : $i] : (($false = (irel @ X1 @ X0)) | ($true = (p8 @ X0)) | ((p9 @ (sK16 @ X0)) = $false) | ((p9 @ (sK14 @ X1)) = $false) | ($false = $true)) )),
% 0.16/0.41 inference(superposition,[],[f119,f325])).
% 0.16/0.41 thf(f325,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p9 @ (sK14 @ X1)) = $false) | ((p8 @ X3) = $true) | ($false = (p9 @ (sK16 @ X2))) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f324])).
% 0.16/0.41 thf(f324,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | (((irel @ X2 @ (sK16 @ X2)) => (p9 @ (sK16 @ X2))) = $false) | ((p9 @ (sK14 @ X1)) = $false) | ((irel @ X2 @ X3) = $false) | ((p8 @ X3) = $true)) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f323])).
% 0.16/0.41 thf(f323,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p9 @ (sK14 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((irel @ X2 @ X3) = $false) | ((p8 @ X3) = $true) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))) @ (sK16 @ X2)) = $false)) )),
% 0.16/0.41 inference(sigma_clausification,[],[f322])).
% 0.16/0.41 thf(f322,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p9 @ (sK14 @ X1)) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))))) | ((irel @ X1 @ X2) = $false) | ((irel @ X2 @ X3) = $false) | ((p8 @ X3) = $true)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f321])).
% 0.16/0.41 thf(f321,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ X3) => (p8 @ X3)) = $true) | ((p9 @ (sK14 @ X1)) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))))) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f320])).
% 0.16/0.41 thf(f320,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))) @ X3)) | ((irel @ X1 @ X2) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))))) | ((p9 @ (sK14 @ X1)) = $false)) )),
% 0.16/0.41 inference(pi_clausification,[],[f319])).
% 0.16/0.41 thf(f319,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (((p9 @ (sK14 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))))) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.41 inference(not_proxy_clausification,[],[f318])).
% 0.16/0.41 thf(f318,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))))) | ((p9 @ (sK14 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))) = $true)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f304])).
% 0.16/0.41 thf(f304,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (((p9 @ (sK14 @ X1)) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))))) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f303])).
% 0.16/0.41 thf(f303,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK14 @ X1)) => (p9 @ (sK14 @ X1))) = $false) | ((irel @ X1 @ X2) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))))) = $true)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f302])).
% 0.16/0.41 thf(f302,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))))))) = $true) | (((irel @ X1 @ (sK14 @ X1)) => (p9 @ (sK14 @ X1))) = $false)) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f301])).
% 0.16/0.41 thf(f301,plain,(
% 0.16/0.41 ( ! [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)) | (((irel @ X1 @ (sK14 @ X1)) => (p9 @ (sK14 @ X1))) = $false)) )),
% 0.16/0.41 inference(pi_clausification,[],[f300])).
% 0.16/0.41 thf(f300,plain,(
% 0.16/0.41 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1))))))))) = $true) | (((irel @ X1 @ (sK14 @ X1)) => (p9 @ (sK14 @ X1))) = $false)) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f299])).
% 0.16/0.41 thf(f299,plain,(
% 0.16/0.41 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1))))))))) = $true) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0))) @ (sK14 @ X1)) = $false)) )),
% 0.16/0.41 inference(sigma_clausification,[],[f298])).
% 0.16/0.41 thf(f298,plain,(
% 0.16/0.41 ( ! [X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1))))))))) = $true)) )),
% 0.16/0.41 inference(not_proxy_clausification,[],[f297])).
% 0.16/0.41 thf(f297,plain,(
% 0.16/0.41 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1))))))))) = $true)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f296])).
% 0.16/0.41 thf(f296,plain,(
% 0.16/0.41 ( ! [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))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0)))))))) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f295])).
% 0.16/0.41 thf(f295,plain,(
% 0.16/0.41 ( ! [X1 : $i] : (($true = ((^[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))) )),
% 0.16/0.41 inference(pi_clausification,[],[f294])).
% 0.16/0.41 thf(f294,plain,(
% 0.16/0.41 ((!! @ $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)))))))) = $true)),
% 0.16/0.41 inference(beta_eta_normalization,[],[f148])).
% 0.16/0.41 thf(f148,plain,(
% 0.16/0.41 (((^[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)))) = $true)),
% 0.16/0.41 inference(definition_unfolding,[],[f111,f120,f141,f128,f141,f128,f128])).
% 0.16/0.41 thf(f111,plain,(
% 0.16/0.41 ((ivalid @ (iimplies @ (iatom @ p9) @ (iimplies @ (iatom @ p9) @ (iatom @ p8)))) = $true)),
% 0.16/0.41 inference(cnf_transformation,[],[f41])).
% 0.16/0.41 thf(f41,plain,(
% 0.16/0.41 ((ivalid @ (iimplies @ (iatom @ p9) @ (iimplies @ (iatom @ p9) @ (iatom @ p8)))) = $true)),
% 0.16/0.41 inference(fool_elimination,[],[f40])).
% 0.16/0.41 thf(f40,plain,(
% 0.16/0.41 (ivalid @ (iimplies @ (iatom @ p9) @ (iimplies @ (iatom @ p9) @ (iatom @ p8))))),
% 0.16/0.41 inference(rectify,[],[f31])).
% 0.16/0.41 thf(f31,axiom,(
% 0.16/0.41 (ivalid @ (iimplies @ (iatom @ p9) @ (iimplies @ (iatom @ p9) @ (iatom @ p8))))),
% 0.16/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10)).
% 0.16/0.41 thf(f532,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p9 @ X0) = $true)) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f529])).
% 0.16/0.41 thf(f529,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($false = $true) | ((p9 @ X0) = $true)) )),
% 0.16/0.41 inference(superposition,[],[f528,f260])).
% 0.16/0.41 thf(f260,plain,(
% 0.16/0.41 ( ! [X1 : $i] : (((p10 @ X1) = $true)) )),
% 0.16/0.41 inference(pi_clausification,[],[f259])).
% 0.16/0.41 thf(f259,plain,(
% 0.16/0.41 ((!! @ $i @ p10) = $true)),
% 0.16/0.41 inference(beta_eta_normalization,[],[f156])).
% 0.16/0.41 thf(f156,plain,(
% 0.16/0.41 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: (Y0)) @ p10)))),
% 0.16/0.41 inference(definition_unfolding,[],[f134,f120,f128])).
% 0.16/0.41 thf(f134,plain,(
% 0.16/0.41 ((ivalid @ (iatom @ p10)) = $true)),
% 0.16/0.41 inference(cnf_transformation,[],[f87])).
% 0.16/0.41 thf(f87,plain,(
% 0.16/0.41 ((ivalid @ (iatom @ p10)) = $true)),
% 0.16/0.41 inference(fool_elimination,[],[f86])).
% 0.16/0.41 thf(f86,plain,(
% 0.16/0.41 (ivalid @ (iatom @ p10))),
% 0.16/0.41 inference(rectify,[],[f22])).
% 0.16/0.41 thf(f22,axiom,(
% 0.16/0.41 (ivalid @ (iatom @ p10))),
% 0.16/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1)).
% 0.16/0.41 thf(f528,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p10 @ (sK4 @ X0)) = $false) | ((p9 @ X0) = $true)) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f525])).
% 0.16/0.41 thf(f525,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p9 @ X0) = $true) | ($false = $true) | ((p10 @ (sK4 @ X0)) = $false)) )),
% 0.16/0.41 inference(superposition,[],[f514,f260])).
% 0.16/0.41 thf(f514,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (($false = (p10 @ (sK6 @ X0))) | ((p10 @ (sK4 @ X0)) = $false) | ((p9 @ X0) = $true)) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f509])).
% 0.16/0.41 thf(f509,plain,(
% 0.16/0.41 ( ! [X0 : $i] : (((p10 @ (sK4 @ X0)) = $false) | ($false = $true) | ($false = (p10 @ (sK6 @ X0))) | ((p9 @ X0) = $true)) )),
% 0.16/0.41 inference(superposition,[],[f119,f503])).
% 0.16/0.41 thf(f503,plain,(
% 0.16/0.41 ( ! [X0 : $i,X1 : $i] : (($false = (irel @ X1 @ X0)) | ($false = (p10 @ (sK6 @ X0))) | ((p9 @ X0) = $true) | ((p10 @ (sK4 @ X1)) = $false)) )),
% 0.16/0.41 inference(trivial_inequality_removal,[],[f499])).
% 0.16/0.41 thf(f499,plain,(
% 0.16/0.41 ( ! [X0 : $i,X1 : $i] : (($false = (p10 @ (sK6 @ X0))) | ($false = $true) | ((p10 @ (sK4 @ X1)) = $false) | ((p9 @ X0) = $true) | ($false = (irel @ X1 @ X0))) )),
% 0.16/0.41 inference(superposition,[],[f119,f225])).
% 0.16/0.41 thf(f225,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((irel @ X1 @ X2) = $false) | ($false = (p10 @ (sK6 @ X2))) | ((p10 @ (sK4 @ X1)) = $false) | ((p9 @ X3) = $true)) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f222])).
% 0.16/0.41 thf(f222,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p10 @ (sK6 @ X2))) | ((p10 @ (sK4 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = ((irel @ X2 @ X3) => (p9 @ X3)))) )),
% 0.16/0.41 inference(binary_proxy_clausification,[],[f221])).
% 0.16/0.41 thf(f221,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ (sK6 @ X2)) => (p10 @ (sK6 @ X2))) = $false) | ($true = ((irel @ X2 @ X3) => (p9 @ X3))) | ((irel @ X1 @ X2) = $false) | ((p10 @ (sK4 @ X1)) = $false)) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f220])).
% 0.16/0.41 thf(f220,plain,(
% 0.16/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))) @ X3) = $true) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ (sK6 @ X2)) => (p10 @ (sK6 @ X2))) = $false) | ((p10 @ (sK4 @ X1)) = $false)) )),
% 0.16/0.41 inference(pi_clausification,[],[f219])).
% 0.16/0.41 thf(f219,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))))) | (((irel @ X2 @ (sK6 @ X2)) => (p10 @ (sK6 @ X2))) = $false) | ((p10 @ (sK4 @ X1)) = $false)) )),
% 0.16/0.41 inference(beta_eta_normalization,[],[f218])).
% 0.16/0.41 thf(f218,plain,(
% 0.16/0.41 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))))) | ((p10 @ (sK4 @ X1)) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))) @ (sK6 @ X2)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.41 inference(sigma_clausification,[],[f217])).
% 0.16/0.42 thf(f217,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))))) | ((p10 @ (sK4 @ X1)) = $false)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f216])).
% 0.16/0.42 thf(f216,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))) = $true) | ((irel @ X1 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))))) | ((p10 @ (sK4 @ X1)) = $false)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f215])).
% 0.16/0.42 thf(f215,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0)))))) = $true) | ((p10 @ (sK4 @ X1)) = $false)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f214])).
% 0.16/0.42 thf(f214,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0)))))))) | ((p10 @ (sK4 @ X1)) = $false)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f213])).
% 0.16/0.42 thf(f213,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((p10 @ (sK4 @ X1)) = $false) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1)))))))) @ X2) = $true)) )),
% 0.16/0.42 inference(pi_clausification,[],[f198])).
% 0.16/0.42 thf(f198,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((p10 @ (sK4 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1))))))))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f197])).
% 0.16/0.42 thf(f197,plain,(
% 0.16/0.42 ( ! [X1 : $i] : ((((irel @ X1 @ (sK4 @ X1)) => (p10 @ (sK4 @ X1))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1))))))))) = $true)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f196])).
% 0.16/0.42 thf(f196,plain,(
% 0.16/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p10 @ Y0))) @ (sK4 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1))))))))) = $true)) )),
% 0.16/0.42 inference(sigma_clausification,[],[f195])).
% 0.16/0.42 thf(f195,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p10 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1))))))))) = $true)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f194])).
% 0.16/0.42 thf(f194,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p10 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1))))))))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f193])).
% 0.16/0.42 thf(f193,plain,(
% 0.16/0.42 ( ! [X1 : $i] : ((((!! @ $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)))))) = $true)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f192])).
% 0.16/0.42 thf(f192,plain,(
% 0.16/0.42 ( ! [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)) )),
% 0.16/0.42 inference(pi_clausification,[],[f191])).
% 0.16/0.42 thf(f191,plain,(
% 0.16/0.42 ((!! @ $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)))))))) = $true)),
% 0.16/0.42 inference(beta_eta_normalization,[],[f155])).
% 0.16/0.42 thf(f155,plain,(
% 0.16/0.42 (((^[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)),
% 0.16/0.42 inference(definition_unfolding,[],[f133,f120,f141,f128,f141,f128,f128])).
% 0.16/0.42 thf(f133,plain,(
% 0.16/0.42 ((ivalid @ (iimplies @ (iatom @ p10) @ (iimplies @ (iatom @ p10) @ (iatom @ p9)))) = $true)),
% 0.16/0.42 inference(cnf_transformation,[],[f37])).
% 0.16/0.42 thf(f37,plain,(
% 0.16/0.42 ((ivalid @ (iimplies @ (iatom @ p10) @ (iimplies @ (iatom @ p10) @ (iatom @ p9)))) = $true)),
% 0.16/0.42 inference(fool_elimination,[],[f36])).
% 0.16/0.42 thf(f36,plain,(
% 0.16/0.42 (ivalid @ (iimplies @ (iatom @ p10) @ (iimplies @ (iatom @ p10) @ (iatom @ p9))))),
% 0.16/0.42 inference(rectify,[],[f32])).
% 0.16/0.42 thf(f32,axiom,(
% 0.16/0.42 (ivalid @ (iimplies @ (iatom @ p10) @ (iimplies @ (iatom @ p10) @ (iatom @ p9))))),
% 0.16/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom11)).
% 0.16/0.42 thf(f658,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (((p8 @ (sK22 @ X0)) = $false) | ((p7 @ X0) = $true)) )),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f655])).
% 0.16/0.42 thf(f655,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (((p8 @ (sK22 @ X0)) = $false) | ((p7 @ X0) = $true) | ($false = $true)) )),
% 0.16/0.42 inference(superposition,[],[f653,f600])).
% 0.16/0.42 thf(f653,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (($false = (p8 @ (sK24 @ X0))) | ((p8 @ (sK22 @ X0)) = $false) | ((p7 @ X0) = $true)) )),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f649])).
% 0.16/0.42 thf(f649,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (($false = $true) | ((p7 @ X0) = $true) | ((p8 @ (sK22 @ X0)) = $false) | ($false = (p8 @ (sK24 @ X0)))) )),
% 0.16/0.42 inference(superposition,[],[f119,f646])).
% 0.16/0.42 thf(f646,plain,(
% 0.16/0.42 ( ! [X0 : $i,X1 : $i] : (($false = (irel @ X1 @ X0)) | ($false = (p8 @ (sK24 @ X0))) | ((p7 @ X0) = $true) | ((p8 @ (sK22 @ X1)) = $false)) )),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f639])).
% 0.16/0.42 thf(f639,plain,(
% 0.16/0.42 ( ! [X0 : $i,X1 : $i] : (((p8 @ (sK22 @ X1)) = $false) | ($false = $true) | ($false = (p8 @ (sK24 @ X0))) | ((p7 @ X0) = $true) | ($false = (irel @ X1 @ X0))) )),
% 0.16/0.42 inference(superposition,[],[f119,f416])).
% 0.16/0.42 thf(f416,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p7 @ X3) = $true) | ((p8 @ (sK24 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ((p8 @ (sK22 @ X1)) = $false)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f415])).
% 0.16/0.42 thf(f415,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p8 @ (sK22 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ X3) => (p7 @ X3)) = $true) | ((p8 @ (sK24 @ X2)) = $false)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f414])).
% 0.16/0.42 thf(f414,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p8 @ (sK24 @ X2)) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))) @ X3) = $true) | ((p8 @ (sK22 @ X1)) = $false)) )),
% 0.16/0.42 inference(pi_clausification,[],[f409])).
% 0.16/0.42 thf(f409,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((p8 @ (sK24 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ((p8 @ (sK22 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f408])).
% 0.16/0.42 thf(f408,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : ((((irel @ X2 @ (sK24 @ X2)) => (p8 @ (sK24 @ X2))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) = $true) | ((p8 @ (sK22 @ X1)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f407])).
% 0.16/0.42 thf(f407,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))) @ (sK24 @ X2)) = $false) | ((p8 @ (sK22 @ X1)) = $false)) )),
% 0.16/0.42 inference(sigma_clausification,[],[f406])).
% 0.16/0.42 thf(f406,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) = $true) | ((p8 @ (sK22 @ X1)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f405])).
% 0.16/0.42 thf(f405,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))))) = $true) | ((irel @ X1 @ X2) = $false) | ((p8 @ (sK22 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f394])).
% 0.16/0.42 thf(f394,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))))))) | ((irel @ X1 @ X2) = $false) | ((p8 @ (sK22 @ X1)) = $false)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f393])).
% 0.16/0.42 thf(f393,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK22 @ X1)) => (p8 @ (sK22 @ X1))) = $false) | ((irel @ X1 @ X2) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))))))) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f392])).
% 0.16/0.42 thf(f392,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))))))) = $true) | (((irel @ X1 @ (sK22 @ X1)) => (p8 @ (sK22 @ X1))) = $false)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f391])).
% 0.16/0.42 thf(f391,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))))))) @ X2) = $true) | (((irel @ X1 @ (sK22 @ X1)) => (p8 @ (sK22 @ X1))) = $false)) )),
% 0.16/0.42 inference(pi_clausification,[],[f390])).
% 0.16/0.42 thf(f390,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1))))))))) = $true) | (((irel @ X1 @ (sK22 @ X1)) => (p8 @ (sK22 @ X1))) = $false)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f389])).
% 0.16/0.42 thf(f389,plain,(
% 0.16/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0))) @ (sK22 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1))))))))) = $true)) )),
% 0.16/0.42 inference(sigma_clausification,[],[f388])).
% 0.16/0.42 thf(f388,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1))))))))) = $true)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f387])).
% 0.16/0.42 thf(f387,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1))))))))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f386])).
% 0.16/0.42 thf(f386,plain,(
% 0.16/0.42 ( ! [X1 : $i] : ((((!! @ $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)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f385])).
% 0.16/0.42 thf(f385,plain,(
% 0.16/0.42 ( ! [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) = $true)) )),
% 0.16/0.42 inference(pi_clausification,[],[f384])).
% 0.16/0.42 thf(f384,plain,(
% 0.16/0.42 ($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 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))))))))),
% 0.16/0.42 inference(beta_eta_normalization,[],[f147])).
% 0.16/0.42 thf(f147,plain,(
% 0.16/0.42 ($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)))))),
% 0.16/0.42 inference(definition_unfolding,[],[f107,f120,f141,f128,f141,f128,f128])).
% 0.16/0.42 thf(f107,plain,(
% 0.16/0.42 ((ivalid @ (iimplies @ (iatom @ p8) @ (iimplies @ (iatom @ p8) @ (iatom @ p7)))) = $true)),
% 0.16/0.42 inference(cnf_transformation,[],[f69])).
% 0.16/0.42 thf(f69,plain,(
% 0.16/0.42 ((ivalid @ (iimplies @ (iatom @ p8) @ (iimplies @ (iatom @ p8) @ (iatom @ p7)))) = $true)),
% 0.16/0.42 inference(fool_elimination,[],[f68])).
% 0.16/0.42 thf(f68,plain,(
% 0.16/0.42 (ivalid @ (iimplies @ (iatom @ p8) @ (iimplies @ (iatom @ p8) @ (iatom @ p7))))),
% 0.16/0.42 inference(rectify,[],[f30])).
% 0.16/0.42 thf(f30,axiom,(
% 0.16/0.42 (ivalid @ (iimplies @ (iatom @ p8) @ (iimplies @ (iatom @ p8) @ (iatom @ p7))))),
% 0.16/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9)).
% 0.16/0.42 thf(f702,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (((p7 @ (sK28 @ X0)) = $false) | ($true = (p6 @ X0))) )),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f700])).
% 0.16/0.42 thf(f700,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (((p7 @ (sK28 @ X0)) = $false) | ($true = (p6 @ X0)) | ($false = $true)) )),
% 0.16/0.42 inference(superposition,[],[f662,f697])).
% 0.16/0.42 thf(f697,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (((p7 @ (sK30 @ X0)) = $false) | ((p7 @ (sK28 @ X0)) = $false) | ($true = (p6 @ X0))) )),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f691])).
% 0.16/0.42 thf(f691,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (((p7 @ (sK28 @ X0)) = $false) | ($false = $true) | ((p7 @ (sK30 @ X0)) = $false) | ($true = (p6 @ X0))) )),
% 0.16/0.42 inference(superposition,[],[f689,f119])).
% 0.16/0.42 thf(f689,plain,(
% 0.16/0.42 ( ! [X0 : $i,X1 : $i] : (($false = (irel @ X1 @ X0)) | ($false = (p7 @ (sK28 @ X1))) | ($true = (p6 @ X0)) | ((p7 @ (sK30 @ X0)) = $false)) )),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f681])).
% 0.16/0.42 thf(f681,plain,(
% 0.16/0.42 ( ! [X0 : $i,X1 : $i] : (((p7 @ (sK30 @ X0)) = $false) | ($true = (p6 @ X0)) | ($false = (p7 @ (sK28 @ X1))) | ($false = $true) | ($false = (irel @ X1 @ X0))) )),
% 0.16/0.42 inference(superposition,[],[f478,f119])).
% 0.16/0.42 thf(f478,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p7 @ (sK30 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ((p6 @ X3) = $true) | ($false = (p7 @ (sK28 @ X1)))) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f475])).
% 0.16/0.42 thf(f475,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p7 @ (sK30 @ X2)) = $false) | (((irel @ X2 @ X3) => (p6 @ X3)) = $true) | ((irel @ X1 @ X2) = $false) | ($false = (p7 @ (sK28 @ X1)))) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f474])).
% 0.16/0.42 thf(f474,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | (((irel @ X2 @ (sK30 @ X2)) => (p7 @ (sK30 @ X2))) = $false) | (((irel @ X2 @ X3) => (p6 @ X3)) = $true) | ($false = (p7 @ (sK28 @ X1)))) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f473])).
% 0.16/0.42 thf(f473,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0))) @ X3) = $true) | ($false = (p7 @ (sK28 @ X1))) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ (sK30 @ X2)) => (p7 @ (sK30 @ X2))) = $false)) )),
% 0.16/0.42 inference(pi_clausification,[],[f472])).
% 0.16/0.42 thf(f472,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (p7 @ (sK28 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) = $true) | (((irel @ X2 @ (sK30 @ X2)) => (p7 @ (sK30 @ X2))) = $false)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f471])).
% 0.16/0.42 thf(f471,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))) @ (sK30 @ X2))) | ($false = (p7 @ (sK28 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.42 inference(sigma_clausification,[],[f470])).
% 0.16/0.42 thf(f470,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (p7 @ (sK28 @ X1))) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) = $true)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f469])).
% 0.16/0.42 thf(f469,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (p7 @ (sK28 @ X1))) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f468])).
% 0.16/0.42 thf(f468,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (p7 @ (sK28 @ X1))) | ((irel @ X1 @ X2) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f456])).
% 0.16/0.42 thf(f456,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (p7 @ (sK28 @ X1))) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))))))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f455])).
% 0.16/0.42 thf(f455,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK28 @ X1)) => (p7 @ (sK28 @ X1))) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))))))) = $true)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f454])).
% 0.16/0.42 thf(f454,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))))))) @ X2) = $true) | (((irel @ X1 @ (sK28 @ X1)) => (p7 @ (sK28 @ X1))) = $false)) )),
% 0.16/0.42 inference(pi_clausification,[],[f453])).
% 0.16/0.42 thf(f453,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1))))))))) = $true) | (((irel @ X1 @ (sK28 @ X1)) => (p7 @ (sK28 @ X1))) = $false)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f452])).
% 0.16/0.42 thf(f452,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0))) @ (sK28 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1))))))))) = $true)) )),
% 0.16/0.42 inference(sigma_clausification,[],[f451])).
% 0.16/0.42 thf(f451,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1))))))))) = $true)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f450])).
% 0.16/0.42 thf(f450,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1))))))))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f449])).
% 0.16/0.42 thf(f449,plain,(
% 0.16/0.42 ( ! [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)))))))) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f448])).
% 0.16/0.42 thf(f448,plain,(
% 0.16/0.42 ( ! [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 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1))))))) @ X1))) )),
% 0.16/0.42 inference(pi_clausification,[],[f447])).
% 0.16/0.42 thf(f447,plain,(
% 0.16/0.42 ($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)))))))))),
% 0.16/0.42 inference(beta_eta_normalization,[],[f152])).
% 0.16/0.42 thf(f152,plain,(
% 0.16/0.42 (((^[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)))) = $true)),
% 0.16/0.42 inference(definition_unfolding,[],[f116,f120,f141,f128,f141,f128,f128])).
% 0.16/0.42 thf(f116,plain,(
% 0.16/0.42 ((ivalid @ (iimplies @ (iatom @ p7) @ (iimplies @ (iatom @ p7) @ (iatom @ p6)))) = $true)),
% 0.16/0.42 inference(cnf_transformation,[],[f63])).
% 0.16/0.42 thf(f63,plain,(
% 0.16/0.42 ((ivalid @ (iimplies @ (iatom @ p7) @ (iimplies @ (iatom @ p7) @ (iatom @ p6)))) = $true)),
% 0.16/0.42 inference(fool_elimination,[],[f62])).
% 0.16/0.42 thf(f62,plain,(
% 0.16/0.42 (ivalid @ (iimplies @ (iatom @ p7) @ (iimplies @ (iatom @ p7) @ (iatom @ p6))))),
% 0.16/0.42 inference(rectify,[],[f29])).
% 0.16/0.42 thf(f29,axiom,(
% 0.16/0.42 (ivalid @ (iimplies @ (iatom @ p7) @ (iimplies @ (iatom @ p7) @ (iatom @ p6))))),
% 0.16/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8)).
% 0.16/0.42 thf(f800,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (((p5 @ (sK11 @ X0)) = $false) | ($true = (p4 @ X0))) )),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f797])).
% 0.16/0.42 thf(f797,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (($true = (p4 @ X0)) | ((p5 @ (sK11 @ X0)) = $false) | ($false = $true)) )),
% 0.16/0.42 inference(superposition,[],[f714,f566])).
% 0.16/0.42 thf(f566,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (((p5 @ (sK13 @ X0)) = $false) | ($true = (p4 @ X0)) | ((p5 @ (sK11 @ X0)) = $false)) )),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f561])).
% 0.16/0.42 thf(f561,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (($false = $true) | ((p5 @ (sK11 @ X0)) = $false) | ($true = (p4 @ X0)) | ((p5 @ (sK13 @ X0)) = $false)) )),
% 0.16/0.42 inference(superposition,[],[f119,f557])).
% 0.16/0.42 thf(f557,plain,(
% 0.16/0.42 ( ! [X0 : $i,X1 : $i] : (($false = (irel @ X1 @ X0)) | ((p5 @ (sK13 @ X0)) = $false) | ((p5 @ (sK11 @ X1)) = $false) | ($true = (p4 @ X0))) )),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f551])).
% 0.16/0.42 thf(f551,plain,(
% 0.16/0.42 ( ! [X0 : $i,X1 : $i] : (((p5 @ (sK13 @ X0)) = $false) | ((p5 @ (sK11 @ X1)) = $false) | ($true = (p4 @ X0)) | ($false = (irel @ X1 @ X0)) | ($false = $true)) )),
% 0.16/0.42 inference(superposition,[],[f119,f293])).
% 0.16/0.42 thf(f293,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((irel @ X1 @ X2) = $false) | ((p4 @ X3) = $true) | ((p5 @ (sK13 @ X2)) = $false) | ((p5 @ (sK11 @ X1)) = $false)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f290])).
% 0.16/0.42 thf(f290,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p5 @ (sK13 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ((p5 @ (sK11 @ X1)) = $false) | (((irel @ X2 @ X3) => (p4 @ X3)) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f289])).
% 0.16/0.42 thf(f289,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ (sK13 @ X2)) => (p5 @ (sK13 @ X2))) = $false) | ((irel @ X1 @ X2) = $false) | ((p5 @ (sK11 @ X1)) = $false) | (((irel @ X2 @ X3) => (p4 @ X3)) = $true)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f288])).
% 0.16/0.42 thf(f288,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))) @ (sK13 @ X2)) = $false) | ((p5 @ (sK11 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ X3) => (p4 @ X3)) = $true)) )),
% 0.16/0.42 inference(sigma_clausification,[],[f287])).
% 0.16/0.42 thf(f287,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p5 @ (sK11 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))) = $false) | (((irel @ X2 @ X3) => (p4 @ X3)) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f286])).
% 0.16/0.42 thf(f286,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))) = $true) | ((p5 @ (sK11 @ X1)) = $false) | (((irel @ X2 @ X3) => (p4 @ X3)) = $true)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f285])).
% 0.16/0.42 thf(f285,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p5 @ (sK11 @ X1)) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))) @ X3) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))) = $true)) )),
% 0.16/0.42 inference(pi_clausification,[],[f272])).
% 0.16/0.42 thf(f272,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false) | ((p5 @ (sK11 @ X1)) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f271])).
% 0.16/0.42 thf(f271,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK11 @ X1)) => (p5 @ (sK11 @ X1))) = $false) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f270])).
% 0.16/0.42 thf(f270,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))))) = $true) | (((irel @ X1 @ (sK11 @ X1)) => (p5 @ (sK11 @ X1))) = $false)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f269])).
% 0.16/0.42 thf(f269,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))))) = $true) | (((irel @ X1 @ (sK11 @ X1)) => (p5 @ (sK11 @ X1))) = $false)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f268])).
% 0.16/0.42 thf(f268,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))))) = $true) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0))) @ (sK11 @ X1)) = $false)) )),
% 0.16/0.42 inference(sigma_clausification,[],[f267])).
% 0.16/0.42 thf(f267,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0)))) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))))) = $true)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f266])).
% 0.16/0.42 thf(f266,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $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))))))) = $true)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f265])).
% 0.16/0.42 thf(f265,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0))))) = $true) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))))))) @ X2) = $true)) )),
% 0.16/0.42 inference(pi_clausification,[],[f264])).
% 0.16/0.42 thf(f264,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((!! @ $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))))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f263])).
% 0.16/0.42 thf(f263,plain,(
% 0.16/0.42 ( ! [X1 : $i] : ((((!! @ $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)))))) = $true)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f262])).
% 0.16/0.42 thf(f262,plain,(
% 0.16/0.42 ( ! [X1 : $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))))))) @ X1) = $true)) )),
% 0.16/0.42 inference(pi_clausification,[],[f261])).
% 0.16/0.42 thf(f261,plain,(
% 0.16/0.42 ((!! @ $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)))))))) = $true)),
% 0.16/0.42 inference(beta_eta_normalization,[],[f145])).
% 0.16/0.42 thf(f145,plain,(
% 0.16/0.42 (((^[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)))) = $true)),
% 0.16/0.42 inference(definition_unfolding,[],[f103,f120,f141,f128,f141,f128,f128])).
% 0.16/0.42 thf(f103,plain,(
% 0.16/0.42 ((ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4)))) = $true)),
% 0.16/0.42 inference(cnf_transformation,[],[f57])).
% 0.16/0.42 thf(f57,plain,(
% 0.16/0.42 ((ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4)))) = $true)),
% 0.16/0.42 inference(fool_elimination,[],[f56])).
% 0.16/0.42 thf(f56,plain,(
% 0.16/0.42 (ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4))))),
% 0.16/0.42 inference(rectify,[],[f27])).
% 0.16/0.42 thf(f27,axiom,(
% 0.16/0.42 (ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4))))),
% 0.16/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6)).
% 0.16/0.42 thf(f824,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (((p2 @ (sK7 @ X0)) = $false) | ((p1 @ X0) = $true)) )),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f821])).
% 0.16/0.42 thf(f821,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (($false = $true) | ((p2 @ (sK7 @ X0)) = $false) | ((p1 @ X0) = $true)) )),
% 0.16/0.42 inference(superposition,[],[f820,f548])).
% 0.16/0.42 thf(f548,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (($false = (p2 @ (sK9 @ X0))) | ((p1 @ X0) = $true) | ((p2 @ (sK7 @ X0)) = $false)) )),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f541])).
% 0.16/0.42 thf(f541,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (((p2 @ (sK7 @ X0)) = $false) | ($false = (p2 @ (sK9 @ X0))) | ($false = $true) | ((p1 @ X0) = $true)) )),
% 0.16/0.42 inference(superposition,[],[f523,f119])).
% 0.16/0.42 thf(f523,plain,(
% 0.16/0.42 ( ! [X0 : $i,X1 : $i] : (($false = (irel @ X1 @ X0)) | ((p2 @ (sK7 @ X1)) = $false) | ($false = (p2 @ (sK9 @ X0))) | ((p1 @ X0) = $true)) )),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f515])).
% 0.16/0.42 thf(f515,plain,(
% 0.16/0.42 ( ! [X0 : $i,X1 : $i] : (((p2 @ (sK7 @ X1)) = $false) | ($false = (irel @ X1 @ X0)) | ($false = (p2 @ (sK9 @ X0))) | ((p1 @ X0) = $true) | ($false = $true)) )),
% 0.16/0.42 inference(superposition,[],[f255,f119])).
% 0.16/0.42 thf(f255,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p2 @ (sK9 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ((p2 @ (sK7 @ X1)) = $false) | ((p1 @ X3) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f254])).
% 0.16/0.42 thf(f254,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p1 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ((p2 @ (sK7 @ X1)) = $false) | ((irel @ X2 @ X3) = $false) | (((irel @ X2 @ (sK9 @ X2)) => (p2 @ (sK9 @ X2))) = $false)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f253])).
% 0.16/0.42 thf(f253,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ X3) => (p1 @ X3)) = $true) | ((irel @ X1 @ X2) = $false) | ((p2 @ (sK7 @ X1)) = $false) | (((irel @ X2 @ (sK9 @ X2)) => (p2 @ (sK9 @ X2))) = $false)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f252])).
% 0.16/0.42 thf(f252,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ X3) => (p1 @ X3)) = $true) | ((p2 @ (sK7 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))) @ (sK9 @ X2)) = $false)) )),
% 0.16/0.42 inference(sigma_clausification,[],[f251])).
% 0.16/0.42 thf(f251,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $false) | (((irel @ X2 @ X3) => (p1 @ X3)) = $true) | ((irel @ X1 @ X2) = $false) | ((p2 @ (sK7 @ X1)) = $false)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f250])).
% 0.16/0.42 thf(f250,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p2 @ (sK7 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))))) | (((irel @ X2 @ X3) => (p1 @ X3)) = $true)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f249])).
% 0.16/0.42 thf(f249,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))) @ X3) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))))) | ((p2 @ (sK7 @ X1)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.42 inference(pi_clausification,[],[f248])).
% 0.16/0.42 thf(f248,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))))) | ((p2 @ (sK7 @ X1)) = $false)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f247])).
% 0.16/0.42 thf(f247,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((p2 @ (sK7 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f235])).
% 0.16/0.42 thf(f235,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((p2 @ (sK7 @ X1)) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f234])).
% 0.16/0.42 thf(f234,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK7 @ X1)) => (p2 @ (sK7 @ X1))) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))))) = $true)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f233])).
% 0.16/0.42 thf(f233,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK7 @ X1)) => (p2 @ (sK7 @ X1))) = $false) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))))))) @ X2) = $true)) )),
% 0.16/0.42 inference(pi_clausification,[],[f232])).
% 0.16/0.42 thf(f232,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1))))))))) = $true) | (((irel @ X1 @ (sK7 @ X1)) => (p2 @ (sK7 @ X1))) = $false)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f231])).
% 0.16/0.42 thf(f231,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0))) @ (sK7 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1))))))))) = $true)) )),
% 0.16/0.42 inference(sigma_clausification,[],[f230])).
% 0.16/0.42 thf(f230,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1))))))))) = $true)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f229])).
% 0.16/0.42 thf(f229,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1))))))))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f228])).
% 0.16/0.42 thf(f228,plain,(
% 0.16/0.42 ( ! [X1 : $i] : ((((!! @ $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)))))) = $true)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f227])).
% 0.16/0.42 thf(f227,plain,(
% 0.16/0.42 ( ! [X1 : $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))))))) @ X1) = $true)) )),
% 0.16/0.42 inference(pi_clausification,[],[f226])).
% 0.16/0.42 thf(f226,plain,(
% 0.16/0.42 ((!! @ $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)))))))) = $true)),
% 0.16/0.42 inference(beta_eta_normalization,[],[f151])).
% 0.16/0.42 thf(f151,plain,(
% 0.16/0.42 (((^[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)))) = $true)),
% 0.16/0.42 inference(definition_unfolding,[],[f115,f120,f141,f128,f141,f128,f128])).
% 0.16/0.42 thf(f115,plain,(
% 0.16/0.42 ((ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1)))) = $true)),
% 0.16/0.42 inference(cnf_transformation,[],[f99])).
% 0.16/0.42 thf(f99,plain,(
% 0.16/0.42 ((ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1)))) = $true)),
% 0.16/0.42 inference(fool_elimination,[],[f98])).
% 0.16/0.42 thf(f98,plain,(
% 0.16/0.42 (ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1))))),
% 0.16/0.42 inference(rectify,[],[f24])).
% 0.16/0.42 thf(f24,axiom,(
% 0.16/0.42 (ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1))))),
% 0.16/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3)).
% 0.16/0.42 thf(f913,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (((p1 @ (sK19 @ X0)) = $false) | ($true = (p0 @ X0))) )),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f910])).
% 0.16/0.42 thf(f910,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (((p1 @ (sK19 @ X0)) = $false) | ($false = $true) | ($true = (p0 @ X0))) )),
% 0.16/0.42 inference(superposition,[],[f828,f635])).
% 0.16/0.42 thf(f635,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (((p1 @ (sK21 @ X0)) = $false) | ($true = (p0 @ X0)) | ((p1 @ (sK19 @ X0)) = $false)) )),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f629])).
% 0.16/0.42 thf(f629,plain,(
% 0.16/0.42 ( ! [X0 : $i] : (($true = (p0 @ X0)) | ((p1 @ (sK21 @ X0)) = $false) | ((p1 @ (sK19 @ X0)) = $false) | ($false = $true)) )),
% 0.16/0.42 inference(superposition,[],[f628,f119])).
% 0.16/0.42 thf(f628,plain,(
% 0.16/0.42 ( ! [X0 : $i,X1 : $i] : (($false = (irel @ X1 @ X0)) | ($true = (p0 @ X0)) | ($false = (p1 @ (sK19 @ X1))) | ((p1 @ (sK21 @ X0)) = $false)) )),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f619])).
% 0.16/0.42 thf(f619,plain,(
% 0.16/0.42 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ($false = (irel @ X1 @ X0)) | ($true = (p0 @ X0)) | ($false = (p1 @ (sK19 @ X1))) | ((p1 @ (sK21 @ X0)) = $false)) )),
% 0.16/0.42 inference(superposition,[],[f383,f119])).
% 0.16/0.42 thf(f383,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ($false = (p1 @ (sK21 @ X2))) | ((p0 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ($false = (p1 @ (sK19 @ X1)))) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f380])).
% 0.16/0.42 thf(f380,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p1 @ (sK21 @ X2))) | ((irel @ X1 @ X2) = $false) | ($false = (p1 @ (sK19 @ X1))) | ($true = ((irel @ X2 @ X3) => (p0 @ X3)))) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f379])).
% 0.16/0.42 thf(f379,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | (((irel @ X2 @ (sK21 @ X2)) => (p1 @ (sK21 @ X2))) = $false) | ($false = (p1 @ (sK19 @ X1))) | ($true = ((irel @ X2 @ X3) => (p0 @ X3)))) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f378])).
% 0.16/0.42 thf(f378,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((irel @ X2 @ X3) => (p0 @ X3))) | ($false = (p1 @ (sK19 @ X1))) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))) @ (sK21 @ X2)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.42 inference(sigma_clausification,[],[f377])).
% 0.16/0.42 thf(f377,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) = $false) | ($false = (p1 @ (sK19 @ X1))) | ((irel @ X1 @ X2) = $false) | ($true = ((irel @ X2 @ X3) => (p0 @ X3)))) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f376])).
% 0.16/0.42 thf(f376,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))))) | ($true = ((irel @ X2 @ X3) => (p0 @ X3))) | ($false = (p1 @ (sK19 @ X1)))) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f375])).
% 0.16/0.42 thf(f375,plain,(
% 0.16/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))))) | ((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0))) @ X3) = $true) | ($false = (p1 @ (sK19 @ X1)))) )),
% 0.16/0.42 inference(pi_clausification,[],[f374])).
% 0.16/0.42 thf(f374,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))))) | ($false = (p1 @ (sK19 @ X1))) | ((irel @ X1 @ X2) = $false)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f373])).
% 0.16/0.42 thf(f373,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))))) = $true) | ((irel @ X1 @ X2) = $false) | ($false = (p1 @ (sK19 @ X1)))) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f360])).
% 0.16/0.42 thf(f360,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (p1 @ (sK19 @ X1))) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f359])).
% 0.16/0.42 thf(f359,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ X1 @ (sK19 @ X1)) => (p1 @ (sK19 @ X1)))) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))))) = $true)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f358])).
% 0.16/0.42 thf(f358,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))) @ (sK19 @ X1))) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))))) = $true)) )),
% 0.16/0.42 inference(sigma_clausification,[],[f357])).
% 0.16/0.42 thf(f357,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0)))) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))))) = $true)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f356])).
% 0.16/0.42 thf(f356,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))))))) @ X2) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0)))) = $false)) )),
% 0.16/0.42 inference(pi_clausification,[],[f355])).
% 0.16/0.42 thf(f355,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((!! @ $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)))) = $false)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f354])).
% 0.16/0.42 thf(f354,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))))))) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f353])).
% 0.16/0.42 thf(f353,plain,(
% 0.16/0.42 ( ! [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)))))))) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f352])).
% 0.16/0.42 thf(f352,plain,(
% 0.16/0.42 ( ! [X1 : $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))))))) @ X1) = $true)) )),
% 0.16/0.42 inference(pi_clausification,[],[f351])).
% 0.16/0.42 thf(f351,plain,(
% 0.16/0.42 ((!! @ $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)),
% 0.16/0.42 inference(beta_eta_normalization,[],[f153])).
% 0.16/0.42 thf(f153,plain,(
% 0.16/0.42 (((^[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)),
% 0.16/0.42 inference(definition_unfolding,[],[f118,f120,f141,f128,f141,f128,f128])).
% 0.16/0.42 thf(f118,plain,(
% 0.16/0.42 ((ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0)))) = $true)),
% 0.16/0.42 inference(cnf_transformation,[],[f45])).
% 0.16/0.42 thf(f45,plain,(
% 0.16/0.42 ((ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0)))) = $true)),
% 0.16/0.42 inference(fool_elimination,[],[f44])).
% 0.16/0.42 thf(f44,plain,(
% 0.16/0.42 (ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0))))),
% 0.16/0.42 inference(rectify,[],[f23])).
% 0.16/0.42 thf(f23,axiom,(
% 0.16/0.42 (ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0))))),
% 0.16/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2)).
% 0.16/0.42 thf(f258,plain,(
% 0.16/0.42 ((p0 @ sK10) = $false)),
% 0.16/0.42 inference(sigma_clausification,[],[f257])).
% 0.16/0.42 thf(f257,plain,(
% 0.16/0.42 ($true != (!! @ $i @ p0))),
% 0.16/0.42 inference(beta_eta_normalization,[],[f149])).
% 0.16/0.42 thf(f149,plain,(
% 0.16/0.42 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: (Y0)) @ p0)))),
% 0.16/0.42 inference(definition_unfolding,[],[f112,f120,f128])).
% 0.16/0.42 thf(f112,plain,(
% 0.16/0.42 ((ivalid @ (iatom @ p0)) != $true)),
% 0.16/0.42 inference(cnf_transformation,[],[f100])).
% 0.16/0.42 thf(f100,plain,(
% 0.16/0.42 ((ivalid @ (iatom @ p0)) != $true)),
% 0.16/0.42 inference(flattening,[],[f67])).
% 0.16/0.42 thf(f67,plain,(
% 0.16/0.42 ~((ivalid @ (iatom @ p0)) = $true)),
% 0.16/0.42 inference(fool_elimination,[],[f66])).
% 0.16/0.42 thf(f66,plain,(
% 0.16/0.42 ~(ivalid @ (iatom @ p0))),
% 0.16/0.42 inference(rectify,[],[f34])).
% 0.16/0.42 thf(f34,negated_conjecture,(
% 0.16/0.42 ~(ivalid @ (iatom @ p0))),
% 0.16/0.42 inference(negated_conjecture,[],[f33])).
% 0.16/0.42 thf(f33,conjecture,(
% 0.16/0.42 (ivalid @ (iatom @ p0))),
% 0.16/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 0.16/0.42 % SZS output end Proof for theBenchmark
% 0.16/0.42 % (24026)------------------------------
% 0.16/0.42 % (24026)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (24026)Termination reason: Refutation
% 0.16/0.42
% 0.16/0.42 % (24026)Memory used [KB]: 6268
% 0.16/0.42 % (24026)Time elapsed: 0.082 s
% 0.16/0.42 % (24026)Instructions burned: 140 (million)
% 0.16/0.42 % (24026)------------------------------
% 0.16/0.42 % (24026)------------------------------
% 0.16/0.42 % (24025)Success in time 0.081 s
% 0.16/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------