TSTP Solution File: SYO441^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO441^1 : 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 : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:04:27 EDT 2024
% Result : Theorem 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO441^1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % 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
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 20 08:57:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 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
% 0.13/0.37 % (6288)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)
% 0.13/0.37 % (6286)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.37 % (6287)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)
% 0.13/0.37 % (6289)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37 % (6291)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)
% 0.13/0.37 % (6292)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.37 % (6289)Instruction limit reached!
% 0.13/0.37 % (6289)------------------------------
% 0.13/0.37 % (6289)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (6289)Termination reason: Unknown
% 0.13/0.37 % (6289)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (6289)Memory used [KB]: 1023
% 0.13/0.37 % (6289)Time elapsed: 0.003 s
% 0.13/0.37 % (6289)Instructions burned: 2 (million)
% 0.13/0.37 % (6289)------------------------------
% 0.13/0.37 % (6289)------------------------------
% 0.13/0.37 % (6287)Instruction limit reached!
% 0.13/0.37 % (6287)------------------------------
% 0.13/0.37 % (6287)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (6287)Termination reason: Unknown
% 0.13/0.37 % (6287)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (6287)Memory used [KB]: 1023
% 0.13/0.37 % (6287)Time elapsed: 0.004 s
% 0.13/0.37 % (6287)Instructions burned: 4 (million)
% 0.13/0.37 % (6287)------------------------------
% 0.13/0.37 % (6287)------------------------------
% 0.13/0.37 % (6290)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)
% 0.20/0.38 % (6290)Instruction limit reached!
% 0.20/0.38 % (6290)------------------------------
% 0.20/0.38 % (6290)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (6290)Termination reason: Unknown
% 0.20/0.38 % (6290)Termination phase: shuffling
% 0.20/0.38
% 0.20/0.38 % (6290)Memory used [KB]: 1023
% 0.20/0.38 % (6290)Time elapsed: 0.003 s
% 0.20/0.38 % (6290)Instructions burned: 3 (million)
% 0.20/0.38 % (6290)------------------------------
% 0.20/0.38 % (6290)------------------------------
% 0.20/0.38 % (6291)Refutation not found, incomplete strategy
% 0.20/0.38 % (6291)------------------------------
% 0.20/0.38 % (6291)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (6291)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.38
% 0.20/0.38
% 0.20/0.38 % (6291)Memory used [KB]: 5628
% 0.20/0.38 % (6291)Time elapsed: 0.007 s
% 0.20/0.38 % (6291)Instructions burned: 9 (million)
% 0.20/0.38 % (6291)------------------------------
% 0.20/0.38 % (6291)------------------------------
% 0.20/0.38 % (6292)Instruction limit reached!
% 0.20/0.38 % (6292)------------------------------
% 0.20/0.38 % (6292)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (6292)Termination reason: Unknown
% 0.20/0.38 % (6292)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (6292)Memory used [KB]: 5628
% 0.20/0.38 % (6292)Time elapsed: 0.011 s
% 0.20/0.38 % (6292)Instructions burned: 18 (million)
% 0.20/0.38 % (6292)------------------------------
% 0.20/0.38 % (6292)------------------------------
% 0.20/0.38 % (6293)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)
% 0.20/0.38 % (6288)Instruction limit reached!
% 0.20/0.38 % (6288)------------------------------
% 0.20/0.38 % (6288)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (6288)Termination reason: Unknown
% 0.20/0.38 % (6288)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (6288)Memory used [KB]: 5628
% 0.20/0.38 % (6288)Time elapsed: 0.015 s
% 0.20/0.38 % (6288)Instructions burned: 27 (million)
% 0.20/0.38 % (6288)------------------------------
% 0.20/0.38 % (6288)------------------------------
% 0.20/0.39 % (6293)Instruction limit reached!
% 0.20/0.39 % (6293)------------------------------
% 0.20/0.39 % (6293)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (6293)Termination reason: Unknown
% 0.20/0.39 % (6293)Termination phase: shuffling
% 0.20/0.39
% 0.20/0.39 % (6293)Memory used [KB]: 1023
% 0.20/0.39 % (6293)Time elapsed: 0.004 s
% 0.20/0.39 % (6293)Instructions burned: 4 (million)
% 0.20/0.39 % (6293)------------------------------
% 0.20/0.39 % (6293)------------------------------
% 0.20/0.39 % (6294)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)
% 0.20/0.39 % (6297)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)
% 0.20/0.39 % (6296)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)
% 0.20/0.39 % (6295)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)
% 0.20/0.39 % (6296)Instruction limit reached!
% 0.20/0.39 % (6296)------------------------------
% 0.20/0.39 % (6296)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (6296)Termination reason: Unknown
% 0.20/0.39 % (6296)Termination phase: shuffling
% 0.20/0.39
% 0.20/0.39 % (6296)Memory used [KB]: 1023
% 0.20/0.39 % (6296)Time elapsed: 0.004 s
% 0.20/0.39 % (6296)Instructions burned: 4 (million)
% 0.20/0.39 % (6296)------------------------------
% 0.20/0.39 % (6296)------------------------------
% 0.20/0.39 % (6298)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.40 % (6295)Instruction limit reached!
% 0.20/0.40 % (6295)------------------------------
% 0.20/0.40 % (6295)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (6295)Termination reason: Unknown
% 0.20/0.40 % (6295)Termination phase: Saturation
% 0.20/0.40 % (6299)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.40
% 0.20/0.40 % (6295)Memory used [KB]: 5628
% 0.20/0.40 % (6295)Time elapsed: 0.009 s
% 0.20/0.40 % (6295)Instructions burned: 15 (million)
% 0.20/0.40 % (6295)------------------------------
% 0.20/0.40 % (6295)------------------------------
% 0.20/0.40 % (6298)Instruction limit reached!
% 0.20/0.40 % (6298)------------------------------
% 0.20/0.40 % (6298)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (6298)Termination reason: Unknown
% 0.20/0.40 % (6298)Termination phase: Function definition elimination
% 0.20/0.40
% 0.20/0.40 % (6298)Memory used [KB]: 1023
% 0.20/0.40 % (6298)Time elapsed: 0.006 s
% 0.20/0.40 % (6298)Instructions burned: 8 (million)
% 0.20/0.40 % (6298)------------------------------
% 0.20/0.40 % (6298)------------------------------
% 0.20/0.40 % (6300)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)
% 0.20/0.40 % (6300)Instruction limit reached!
% 0.20/0.40 % (6300)------------------------------
% 0.20/0.40 % (6300)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (6300)Termination reason: Unknown
% 0.20/0.40 % (6300)Termination phase: shuffling
% 0.20/0.40
% 0.20/0.40 % (6300)Memory used [KB]: 1023
% 0.20/0.40 % (6300)Time elapsed: 0.004 s
% 0.20/0.40 % (6300)Instructions burned: 4 (million)
% 0.20/0.40 % (6300)------------------------------
% 0.20/0.40 % (6300)------------------------------
% 0.20/0.41 % (6294)Instruction limit reached!
% 0.20/0.41 % (6294)------------------------------
% 0.20/0.41 % (6294)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (6294)Termination reason: Unknown
% 0.20/0.41 % (6294)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (6294)Memory used [KB]: 5756
% 0.20/0.41 % (6294)Time elapsed: 0.021 s
% 0.20/0.41 % (6294)Instructions burned: 38 (million)
% 0.20/0.41 % (6294)------------------------------
% 0.20/0.41 % (6294)------------------------------
% 0.20/0.41 % (6301)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)
% 0.20/0.41 % (6299)Instruction limit reached!
% 0.20/0.41 % (6299)------------------------------
% 0.20/0.41 % (6299)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (6299)Termination reason: Unknown
% 0.20/0.41 % (6299)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (6299)Memory used [KB]: 5756
% 0.20/0.41 % (6299)Time elapsed: 0.011 s
% 0.20/0.41 % (6299)Instructions burned: 16 (million)
% 0.20/0.41 % (6299)------------------------------
% 0.20/0.41 % (6299)------------------------------
% 0.20/0.41 % (6301)Instruction limit reached!
% 0.20/0.41 % (6301)------------------------------
% 0.20/0.41 % (6301)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (6301)Termination reason: Unknown
% 0.20/0.41 % (6301)Termination phase: Property scanning
% 0.20/0.41
% 0.20/0.41 % (6301)Memory used [KB]: 1023
% 0.20/0.41 % (6301)Time elapsed: 0.004 s
% 0.20/0.41 % (6301)Instructions burned: 4 (million)
% 0.20/0.41 % (6301)------------------------------
% 0.20/0.41 % (6301)------------------------------
% 0.20/0.41 % (6302)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)
% 0.20/0.41 % (6303)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)
% 0.20/0.42 % (6303)Instruction limit reached!
% 0.20/0.42 % (6303)------------------------------
% 0.20/0.42 % (6303)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (6303)Termination reason: Unknown
% 0.20/0.42 % (6303)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (6303)Memory used [KB]: 1023
% 0.20/0.42 % (6303)Time elapsed: 0.004 s
% 0.20/0.42 % (6303)Instructions burned: 4 (million)
% 0.20/0.42 % (6303)------------------------------
% 0.20/0.42 % (6303)------------------------------
% 0.20/0.42 % (6304)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.42 % (6302)Instruction limit reached!
% 0.20/0.42 % (6302)------------------------------
% 0.20/0.42 % (6302)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (6302)Termination reason: Unknown
% 0.20/0.42 % (6302)Termination phase: Property scanning
% 0.20/0.42
% 0.20/0.42 % (6302)Memory used [KB]: 1151
% 0.20/0.42 % (6302)Time elapsed: 0.006 s
% 0.20/0.42 % (6302)Instructions burned: 8 (million)
% 0.20/0.42 % (6302)------------------------------
% 0.20/0.42 % (6302)------------------------------
% 0.20/0.42 % (6304)Instruction limit reached!
% 0.20/0.42 % (6304)------------------------------
% 0.20/0.42 % (6304)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (6304)Termination reason: Unknown
% 0.20/0.42 % (6304)Termination phase: Property scanning
% 0.20/0.42
% 0.20/0.42 % (6304)Memory used [KB]: 1023
% 0.20/0.42 % (6304)Time elapsed: 0.004 s
% 0.20/0.42 % (6304)Instructions burned: 4 (million)
% 0.20/0.42 % (6304)------------------------------
% 0.20/0.42 % (6304)------------------------------
% 0.20/0.42 % (6305)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)
% 0.20/0.42 % (6306)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.20/0.42 % (6307)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.43 % (6307)Instruction limit reached!
% 0.20/0.43 % (6307)------------------------------
% 0.20/0.43 % (6307)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (6307)Termination reason: Unknown
% 0.20/0.43 % (6307)Termination phase: Property scanning
% 0.20/0.43
% 0.20/0.43 % (6307)Memory used [KB]: 1023
% 0.20/0.43 % (6307)Time elapsed: 0.005 s
% 0.20/0.43 % (6307)Instructions burned: 6 (million)
% 0.20/0.43 % (6307)------------------------------
% 0.20/0.43 % (6307)------------------------------
% 0.20/0.43 % (6306)Refutation not found, incomplete strategy
% 0.20/0.43 % (6306)------------------------------
% 0.20/0.43 % (6306)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (6306)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 % (6306)Memory used [KB]: 5628
% 0.20/0.43 % (6306)Time elapsed: 0.007 s
% 0.20/0.43 % (6306)Instructions burned: 9 (million)
% 0.20/0.43 % (6306)------------------------------
% 0.20/0.43 % (6306)------------------------------
% 0.20/0.43 % (6308)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)
% 0.20/0.43 % (6305)Instruction limit reached!
% 0.20/0.43 % (6305)------------------------------
% 0.20/0.43 % (6305)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (6305)Termination reason: Unknown
% 0.20/0.43 % (6305)Termination phase: Saturation
% 0.20/0.43
% 0.20/0.43 % (6305)Memory used [KB]: 5628
% 0.20/0.43 % (6305)Time elapsed: 0.013 s
% 0.20/0.43 % (6305)Instructions burned: 18 (million)
% 0.20/0.43 % (6305)------------------------------
% 0.20/0.43 % (6305)------------------------------
% 0.20/0.43 % (6309)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)
% 0.20/0.43 % (6310)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.20/0.43 % (6297)First to succeed.
% 0.20/0.43 % (6308)Refutation not found, incomplete strategy
% 0.20/0.43 % (6308)------------------------------
% 0.20/0.43 % (6308)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (6308)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 % (6308)Memory used [KB]: 5628
% 0.20/0.44 % (6308)Time elapsed: 0.007 s
% 0.20/0.44 % (6308)Instructions burned: 9 (million)
% 0.20/0.44 % (6308)------------------------------
% 0.20/0.44 % (6308)------------------------------
% 0.20/0.44 % (6310)Instruction limit reached!
% 0.20/0.44 % (6310)------------------------------
% 0.20/0.44 % (6310)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (6310)Termination reason: Unknown
% 0.20/0.44 % (6310)Termination phase: Property scanning
% 0.20/0.44
% 0.20/0.44 % (6310)Memory used [KB]: 1023
% 0.20/0.44 % (6310)Time elapsed: 0.005 s
% 0.20/0.44 % (6310)Instructions burned: 7 (million)
% 0.20/0.44 % (6310)------------------------------
% 0.20/0.44 % (6310)------------------------------
% 0.20/0.44 % (6311)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)
% 0.20/0.44 % (6297)Refutation found. Thanks to Tanya!
% 0.20/0.44 % SZS status Theorem for theBenchmark
% 0.20/0.44 % SZS output start Proof for theBenchmark
% 0.20/0.44 thf(type_def_5, type, mu: $tType).
% 0.20/0.44 thf(func_def_0, type, mu: $tType).
% 0.20/0.44 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.20/0.44 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_15, type, mtrue: $i > $o).
% 0.20/0.44 thf(func_def_16, type, mfalse: $i > $o).
% 0.20/0.44 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.20/0.44 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.20/0.44 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.20/0.44 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.20/0.44 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.20/0.44 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_36, type, p: $i > $o).
% 0.20/0.44 thf(func_def_53, type, ph1: !>[X0: $tType]:(X0)).
% 0.20/0.44 thf(f819,plain,(
% 0.20/0.44 $false),
% 0.20/0.44 inference(avatar_sat_refutation,[],[f210,f266,f818])).
% 0.20/0.44 thf(f818,plain,(
% 0.20/0.44 ~spl0_1),
% 0.20/0.44 inference(avatar_contradiction_clause,[],[f817])).
% 0.20/0.44 thf(f817,plain,(
% 0.20/0.44 $false | ~spl0_1),
% 0.20/0.44 inference(trivial_inequality_removal,[],[f816])).
% 0.20/0.44 thf(f816,plain,(
% 0.20/0.44 ($true = $false) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f815])).
% 0.20/0.44 thf(f815,plain,(
% 0.20/0.44 ($true = (~ $true)) | ~spl0_1),
% 0.20/0.44 inference(forward_demodulation,[],[f808,f774])).
% 0.20/0.44 thf(f774,plain,(
% 0.20/0.44 ($true = (rel_s5 @ sK6 @ sK4)) | ~spl0_1),
% 0.20/0.44 inference(trivial_inequality_removal,[],[f761])).
% 0.20/0.44 thf(f761,plain,(
% 0.20/0.44 ($true = $false) | ($true = (rel_s5 @ sK6 @ sK4)) | ~spl0_1),
% 0.20/0.44 inference(superposition,[],[f175,f600])).
% 0.20/0.44 thf(f600,plain,(
% 0.20/0.44 ($true = (rel_s5 @ sK4 @ sK6)) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f591])).
% 0.20/0.44 thf(f591,plain,(
% 0.20/0.44 (($true => (rel_s5 @ sK4 @ sK6)) = $true) | ~spl0_1),
% 0.20/0.44 inference(superposition,[],[f424,f540])).
% 0.20/0.44 thf(f540,plain,(
% 0.20/0.44 ($true = (rel_s5 @ sK4 @ sK5)) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f530])).
% 0.20/0.44 thf(f530,plain,(
% 0.20/0.44 (($true => (rel_s5 @ sK4 @ sK5)) = $true) | ~spl0_1),
% 0.20/0.44 inference(superposition,[],[f321,f498])).
% 0.20/0.44 thf(f498,plain,(
% 0.20/0.44 ($true = (rel_s5 @ sK4 @ sK3)) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f489])).
% 0.20/0.44 thf(f489,plain,(
% 0.20/0.44 ($true = ($true => (rel_s5 @ sK4 @ sK3))) | ~spl0_1),
% 0.20/0.44 inference(superposition,[],[f298,f359])).
% 0.20/0.44 thf(f359,plain,(
% 0.20/0.44 ($true = (rel_s5 @ sK4 @ sK2)) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f357])).
% 0.20/0.44 thf(f357,plain,(
% 0.20/0.44 ($true = ($true => (rel_s5 @ sK4 @ sK2))) | ~spl0_1),
% 0.20/0.44 inference(superposition,[],[f174,f340])).
% 0.20/0.44 thf(f340,plain,(
% 0.20/0.44 ($true = (rel_s5 @ sK2 @ sK4)) | ~spl0_1),
% 0.20/0.44 inference(not_proxy_clausification,[],[f337])).
% 0.20/0.44 thf(f337,plain,(
% 0.20/0.44 ($false = (~ (rel_s5 @ sK2 @ sK4))) | ~spl0_1),
% 0.20/0.44 inference(binary_proxy_clausification,[],[f279])).
% 0.20/0.44 thf(f279,plain,(
% 0.20/0.44 ($false = ((~ (rel_s5 @ sK2 @ sK4)) | (p @ sK4))) | ~spl0_1),
% 0.20/0.44 inference(beta_eta_normalization,[],[f278])).
% 0.20/0.44 thf(f278,plain,(
% 0.20/0.44 ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))) @ sK4)) | ~spl0_1),
% 0.20/0.44 inference(sigma_clausification,[],[f272])).
% 0.20/0.44 thf(f272,plain,(
% 0.20/0.44 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0)))) = $false) | ~spl0_1),
% 0.20/0.44 inference(binary_proxy_clausification,[],[f269])).
% 0.20/0.44 thf(f269,plain,(
% 0.20/0.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0)))))) | ~spl0_1),
% 0.20/0.44 inference(not_proxy_clausification,[],[f206])).
% 0.20/0.44 thf(f206,plain,(
% 0.20/0.44 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))))) | ~spl0_1),
% 0.20/0.44 inference(avatar_component_clause,[],[f205])).
% 0.20/0.44 thf(f205,plain,(
% 0.20/0.44 spl0_1 <=> ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0)))))))),
% 0.20/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.20/0.44 thf(f174,plain,(
% 0.20/0.44 ( ! [X2 : $i,X1 : $i] : (($true = ((rel_s5 @ X2 @ X1) => (rel_s5 @ X1 @ X2)))) )),
% 0.20/0.44 inference(beta_eta_normalization,[],[f173])).
% 0.20/0.44 thf(f173,plain,(
% 0.20/0.44 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((rel_s5 @ Y0 @ X1) => (rel_s5 @ X1 @ Y0))) @ X2))) )),
% 0.20/0.44 inference(pi_clausification,[],[f172])).
% 0.20/0.44 thf(f172,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((rel_s5 @ Y0 @ X1) => (rel_s5 @ X1 @ Y0)))))) )),
% 0.20/0.44 inference(beta_eta_normalization,[],[f171])).
% 0.20/0.44 thf(f171,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y1 @ Y0) => (rel_s5 @ Y0 @ Y1))))) @ X1))) )),
% 0.20/0.44 inference(pi_clausification,[],[f167])).
% 0.20/0.44 thf(f167,plain,(
% 0.20/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y1 @ Y0) => (rel_s5 @ Y0 @ Y1)))))))),
% 0.20/0.44 inference(beta_eta_normalization,[],[f161])).
% 0.20/0.44 thf(f161,plain,(
% 0.20/0.44 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))) @ rel_s5))),
% 0.20/0.44 inference(definition_unfolding,[],[f135,f120])).
% 0.20/0.44 thf(f120,plain,(
% 0.20/0.44 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.20/0.44 inference(cnf_transformation,[],[f49])).
% 0.20/0.44 thf(f49,plain,(
% 0.20/0.44 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.20/0.44 inference(fool_elimination,[],[f48])).
% 0.20/0.44 thf(f48,plain,(
% 0.20/0.44 (msymmetric = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)))))),
% 0.20/0.44 inference(rectify,[],[f19])).
% 0.20/0.44 thf(f19,axiom,(
% 0.20/0.44 (msymmetric = (^[X6 : $i > $i > $o] : (! [X8,X9] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))))),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric)).
% 0.20/0.44 thf(f135,plain,(
% 0.20/0.44 ((msymmetric @ rel_s5) = $true)),
% 0.20/0.44 inference(cnf_transformation,[],[f106])).
% 0.20/0.44 thf(f106,plain,(
% 0.20/0.44 ((msymmetric @ rel_s5) = $true)),
% 0.20/0.44 inference(fool_elimination,[],[f105])).
% 0.20/0.44 thf(f105,plain,(
% 0.20/0.44 (msymmetric @ rel_s5)),
% 0.20/0.44 inference(rectify,[],[f36])).
% 0.20/0.44 thf(f36,axiom,(
% 0.20/0.44 (msymmetric @ rel_s5)),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3)).
% 0.20/0.44 thf(f298,plain,(
% 0.20/0.44 ( ! [X0 : $i] : (($true = ((rel_s5 @ X0 @ sK2) => (rel_s5 @ X0 @ sK3)))) ) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f289])).
% 0.20/0.44 thf(f289,plain,(
% 0.20/0.44 ( ! [X0 : $i] : (($true = (($true & (rel_s5 @ X0 @ sK2)) => (rel_s5 @ X0 @ sK3)))) ) | ~spl0_1),
% 0.20/0.44 inference(superposition,[],[f185,f284])).
% 0.20/0.44 thf(f284,plain,(
% 0.20/0.44 ($true = (rel_s5 @ sK2 @ sK3)) | ~spl0_1),
% 0.20/0.44 inference(not_proxy_clausification,[],[f281])).
% 0.20/0.44 thf(f281,plain,(
% 0.20/0.44 ($false = (~ (rel_s5 @ sK2 @ sK3))) | ~spl0_1),
% 0.20/0.44 inference(binary_proxy_clausification,[],[f277])).
% 0.20/0.44 thf(f277,plain,(
% 0.20/0.44 ($false = ((~ (rel_s5 @ sK2 @ sK3)) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))))) | ~spl0_1),
% 0.20/0.44 inference(beta_eta_normalization,[],[f276])).
% 0.20/0.44 thf(f276,plain,(
% 0.20/0.44 ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3))))))))))))) @ sK3)) | ~spl0_1),
% 0.20/0.44 inference(sigma_clausification,[],[f275])).
% 0.20/0.44 thf(f275,plain,(
% 0.20/0.44 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3))))))))))))))) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f274])).
% 0.20/0.44 thf(f274,plain,(
% 0.20/0.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))) | $false)) | ~spl0_1),
% 0.20/0.44 inference(backward_demodulation,[],[f269,f272])).
% 0.20/0.44 thf(f185,plain,(
% 0.20/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((rel_s5 @ X1 @ X2) & (rel_s5 @ X3 @ X1)) => (rel_s5 @ X3 @ X2)))) )),
% 0.20/0.44 inference(beta_eta_normalization,[],[f184])).
% 0.20/0.44 thf(f184,plain,(
% 0.20/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((rel_s5 @ X1 @ X2) & (rel_s5 @ Y0 @ X1)) => (rel_s5 @ Y0 @ X2))) @ X3))) )),
% 0.20/0.44 inference(pi_clausification,[],[f183])).
% 0.20/0.44 thf(f183,plain,(
% 0.20/0.44 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s5 @ X1 @ X2) & (rel_s5 @ Y0 @ X1)) => (rel_s5 @ Y0 @ X2)))))) )),
% 0.20/0.44 inference(beta_eta_normalization,[],[f182])).
% 0.20/0.44 thf(f182,plain,(
% 0.20/0.44 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ X1 @ Y0) & (rel_s5 @ Y1 @ X1)) => (rel_s5 @ Y1 @ Y0))))) @ X2))) )),
% 0.20/0.44 inference(pi_clausification,[],[f181])).
% 0.20/0.44 thf(f181,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ X1 @ Y0) & (rel_s5 @ Y1 @ X1)) => (rel_s5 @ Y1 @ Y0)))))) = $true)) )),
% 0.20/0.44 inference(beta_eta_normalization,[],[f180])).
% 0.20/0.44 thf(f180,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y0 @ Y1) & (rel_s5 @ Y2 @ Y0)) => (rel_s5 @ Y2 @ Y1))))))) @ X1))) )),
% 0.20/0.44 inference(pi_clausification,[],[f168])).
% 0.20/0.44 thf(f168,plain,(
% 0.20/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y0 @ Y1) & (rel_s5 @ Y2 @ Y0)) => (rel_s5 @ Y2 @ Y1)))))))))),
% 0.20/0.44 inference(beta_eta_normalization,[],[f160])).
% 0.20/0.44 thf(f160,plain,(
% 0.20/0.44 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) @ rel_s5))),
% 0.20/0.44 inference(definition_unfolding,[],[f125,f130])).
% 0.20/0.44 thf(f130,plain,(
% 0.20/0.44 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))))),
% 0.20/0.44 inference(cnf_transformation,[],[f43])).
% 0.20/0.44 thf(f43,plain,(
% 0.20/0.44 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))))),
% 0.20/0.44 inference(fool_elimination,[],[f42])).
% 0.20/0.44 thf(f42,plain,(
% 0.20/0.44 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X3) & (X0 @ X3 @ X2)) => (X0 @ X1 @ X2)))) = mtransitive)),
% 0.20/0.44 inference(rectify,[],[f21])).
% 0.20/0.44 thf(f21,axiom,(
% 0.20/0.44 ((^[X6 : $i > $i > $o] : (! [X8,X10,X9] : (((X6 @ X8 @ X9) & (X6 @ X9 @ X10)) => (X6 @ X8 @ X10)))) = mtransitive)),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive)).
% 0.20/0.44 thf(f125,plain,(
% 0.20/0.44 ((mtransitive @ rel_s5) = $true)),
% 0.20/0.44 inference(cnf_transformation,[],[f110])).
% 0.20/0.44 thf(f110,plain,(
% 0.20/0.44 ((mtransitive @ rel_s5) = $true)),
% 0.20/0.44 inference(fool_elimination,[],[f109])).
% 0.20/0.44 thf(f109,plain,(
% 0.20/0.44 (mtransitive @ rel_s5)),
% 0.20/0.44 inference(rectify,[],[f35])).
% 0.20/0.44 thf(f35,axiom,(
% 0.20/0.44 (mtransitive @ rel_s5)),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 0.20/0.44 thf(f321,plain,(
% 0.20/0.44 ( ! [X0 : $i] : (($true = ((rel_s5 @ X0 @ sK3) => (rel_s5 @ X0 @ sK5)))) ) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f316])).
% 0.20/0.44 thf(f316,plain,(
% 0.20/0.44 ( ! [X0 : $i] : (($true = (($true & (rel_s5 @ X0 @ sK3)) => (rel_s5 @ X0 @ sK5)))) ) | ~spl0_1),
% 0.20/0.44 inference(superposition,[],[f185,f313])).
% 0.20/0.44 thf(f313,plain,(
% 0.20/0.44 ($true = (rel_s5 @ sK3 @ sK5)) | ~spl0_1),
% 0.20/0.44 inference(not_proxy_clausification,[],[f302])).
% 0.20/0.44 thf(f302,plain,(
% 0.20/0.44 ($false = (~ (rel_s5 @ sK3 @ sK5))) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f301])).
% 0.20/0.44 thf(f301,plain,(
% 0.20/0.44 ($false = ((~ (rel_s5 @ sK3 @ sK5)) | $false)) | ~spl0_1),
% 0.20/0.44 inference(backward_demodulation,[],[f288,f299])).
% 0.20/0.44 thf(f299,plain,(
% 0.20/0.44 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))) = $false) | ~spl0_1),
% 0.20/0.44 inference(binary_proxy_clausification,[],[f288])).
% 0.20/0.44 thf(f288,plain,(
% 0.20/0.44 ($false = ((~ (rel_s5 @ sK3 @ sK5)) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))))) | ~spl0_1),
% 0.20/0.44 inference(beta_eta_normalization,[],[f287])).
% 0.20/0.44 thf(f287,plain,(
% 0.20/0.44 ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))))) @ sK5)) | ~spl0_1),
% 0.20/0.44 inference(sigma_clausification,[],[f283])).
% 0.20/0.44 thf(f283,plain,(
% 0.20/0.44 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))))))) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f282])).
% 0.20/0.44 thf(f282,plain,(
% 0.20/0.44 ($false = ($false | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))))) | ~spl0_1),
% 0.20/0.44 inference(backward_demodulation,[],[f277,f281])).
% 0.20/0.44 thf(f424,plain,(
% 0.20/0.44 ( ! [X0 : $i] : (($true = ((rel_s5 @ X0 @ sK5) => (rel_s5 @ X0 @ sK6)))) ) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f419])).
% 0.20/0.44 thf(f419,plain,(
% 0.20/0.44 ( ! [X0 : $i] : (($true = (($true & (rel_s5 @ X0 @ sK5)) => (rel_s5 @ X0 @ sK6)))) ) | ~spl0_1),
% 0.20/0.44 inference(superposition,[],[f185,f415])).
% 0.20/0.44 thf(f415,plain,(
% 0.20/0.44 ($true = (rel_s5 @ sK5 @ sK6)) | ~spl0_1),
% 0.20/0.44 inference(not_proxy_clausification,[],[f402])).
% 0.20/0.44 thf(f402,plain,(
% 0.20/0.44 ($false = (~ (rel_s5 @ sK5 @ sK6))) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f401])).
% 0.20/0.44 thf(f401,plain,(
% 0.20/0.44 ($false = ((~ (rel_s5 @ sK5 @ sK6)) | $false)) | ~spl0_1),
% 0.20/0.44 inference(backward_demodulation,[],[f388,f399])).
% 0.20/0.44 thf(f399,plain,(
% 0.20/0.44 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK6 @ Y0)) | (p @ Y0)))))) | ~spl0_1),
% 0.20/0.44 inference(binary_proxy_clausification,[],[f388])).
% 0.20/0.44 thf(f388,plain,(
% 0.20/0.44 (((~ (rel_s5 @ sK5 @ sK6)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK6 @ Y0)) | (p @ Y0)))))) = $false) | ~spl0_1),
% 0.20/0.44 inference(beta_eta_normalization,[],[f387])).
% 0.20/0.44 thf(f387,plain,(
% 0.20/0.44 ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))) @ sK6)) | ~spl0_1),
% 0.20/0.44 inference(sigma_clausification,[],[f299])).
% 0.20/0.44 thf(f175,plain,(
% 0.20/0.44 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s5 @ X2 @ X1)) | ((rel_s5 @ X1 @ X2) = $true)) )),
% 0.20/0.44 inference(binary_proxy_clausification,[],[f174])).
% 0.20/0.44 thf(f808,plain,(
% 0.20/0.44 ($true = (~ (rel_s5 @ sK6 @ sK4))) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f798])).
% 0.20/0.44 thf(f798,plain,(
% 0.20/0.44 ($true = ((~ (rel_s5 @ sK6 @ sK4)) | $false)) | ~spl0_1),
% 0.20/0.44 inference(superposition,[],[f776,f339])).
% 0.20/0.44 thf(f339,plain,(
% 0.20/0.44 ($false = (p @ sK4)) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f338])).
% 0.20/0.44 thf(f338,plain,(
% 0.20/0.44 ($false = ($false | (p @ sK4))) | ~spl0_1),
% 0.20/0.44 inference(backward_demodulation,[],[f279,f337])).
% 0.20/0.44 thf(f776,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK6 @ X1)) | (p @ X1)))) ) | ~spl0_1),
% 0.20/0.44 inference(beta_eta_normalization,[],[f775])).
% 0.20/0.44 thf(f775,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK6 @ Y0)) | (p @ Y0))) @ X1))) ) | ~spl0_1),
% 0.20/0.44 inference(pi_clausification,[],[f756])).
% 0.20/0.44 thf(f756,plain,(
% 0.20/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK6 @ Y0)) | (p @ Y0))))) | ~spl0_1),
% 0.20/0.44 inference(not_proxy_clausification,[],[f399])).
% 0.20/0.44 thf(f266,plain,(
% 0.20/0.44 ~spl0_2),
% 0.20/0.44 inference(avatar_contradiction_clause,[],[f265])).
% 0.20/0.44 thf(f265,plain,(
% 0.20/0.44 $false | ~spl0_2),
% 0.20/0.44 inference(trivial_inequality_removal,[],[f264])).
% 0.20/0.44 thf(f264,plain,(
% 0.20/0.44 ($true = $false) | ~spl0_2),
% 0.20/0.44 inference(boolean_simplification,[],[f263])).
% 0.20/0.44 thf(f263,plain,(
% 0.20/0.44 ($true = (~ $true)) | ~spl0_2),
% 0.20/0.44 inference(forward_demodulation,[],[f256,f170])).
% 0.20/0.44 thf(f170,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = (rel_s5 @ X1 @ X1))) )),
% 0.20/0.44 inference(beta_eta_normalization,[],[f169])).
% 0.20/0.44 thf(f169,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (rel_s5 @ Y0 @ Y0)) @ X1))) )),
% 0.20/0.44 inference(pi_clausification,[],[f166])).
% 0.20/0.44 thf(f166,plain,(
% 0.20/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: (rel_s5 @ Y0 @ Y0))))),
% 0.20/0.44 inference(beta_eta_normalization,[],[f159])).
% 0.20/0.44 thf(f159,plain,(
% 0.20/0.44 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s5))),
% 0.20/0.44 inference(definition_unfolding,[],[f123,f121])).
% 0.20/0.44 thf(f121,plain,(
% 0.20/0.44 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.20/0.44 inference(cnf_transformation,[],[f91])).
% 0.20/0.44 thf(f91,plain,(
% 0.20/0.44 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.20/0.44 inference(fool_elimination,[],[f90])).
% 0.20/0.44 thf(f90,plain,(
% 0.20/0.44 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))))),
% 0.20/0.44 inference(rectify,[],[f18])).
% 0.20/0.44 thf(f18,axiom,(
% 0.20/0.44 (mreflexive = (^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))))),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
% 0.20/0.44 thf(f123,plain,(
% 0.20/0.44 ((mreflexive @ rel_s5) = $true)),
% 0.20/0.44 inference(cnf_transformation,[],[f102])).
% 0.20/0.44 thf(f102,plain,(
% 0.20/0.44 ((mreflexive @ rel_s5) = $true)),
% 0.20/0.44 inference(fool_elimination,[],[f101])).
% 0.20/0.44 thf(f101,plain,(
% 0.20/0.44 (mreflexive @ rel_s5)),
% 0.20/0.44 inference(rectify,[],[f34])).
% 0.20/0.44 thf(f34,axiom,(
% 0.20/0.44 (mreflexive @ rel_s5)),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 0.20/0.44 thf(f256,plain,(
% 0.20/0.44 ($true = (~ (rel_s5 @ sK2 @ sK2))) | ~spl0_2),
% 0.20/0.44 inference(boolean_simplification,[],[f255])).
% 0.20/0.44 thf(f255,plain,(
% 0.20/0.44 ($true = ((~ (rel_s5 @ sK2 @ sK2)) | $false)) | ~spl0_2),
% 0.20/0.44 inference(boolean_simplification,[],[f253])).
% 0.20/0.44 thf(f253,plain,(
% 0.20/0.44 ($true = ((~ (rel_s5 @ sK2 @ sK2)) | (~ $true))) | ~spl0_2),
% 0.20/0.44 inference(superposition,[],[f250,f220])).
% 0.20/0.44 thf(f220,plain,(
% 0.20/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))) | ~spl0_2),
% 0.20/0.44 inference(not_proxy_clausification,[],[f219])).
% 0.20/0.44 thf(f219,plain,(
% 0.20/0.44 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0)))))) | ~spl0_2),
% 0.20/0.44 inference(boolean_simplification,[],[f218])).
% 0.20/0.44 thf(f218,plain,(
% 0.20/0.44 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))) | $false) = $false) | ~spl0_2),
% 0.20/0.44 inference(backward_demodulation,[],[f213,f216])).
% 0.20/0.44 thf(f216,plain,(
% 0.20/0.44 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | ~spl0_2),
% 0.20/0.44 inference(binary_proxy_clausification,[],[f213])).
% 0.20/0.44 thf(f213,plain,(
% 0.20/0.44 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3))))))))))))))))) | ~spl0_2),
% 0.20/0.44 inference(not_proxy_clausification,[],[f209])).
% 0.20/0.44 thf(f209,plain,(
% 0.20/0.44 ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))))) | ~spl0_2),
% 0.20/0.44 inference(avatar_component_clause,[],[f208])).
% 0.20/0.44 thf(f208,plain,(
% 0.20/0.44 spl0_2 <=> ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3))))))))))))))))))),
% 0.20/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.20/0.44 thf(f250,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK2 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (p @ Y0)))))))) ) | ~spl0_2),
% 0.20/0.44 inference(beta_eta_normalization,[],[f248])).
% 0.20/0.44 thf(f248,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))) @ X1))) ) | ~spl0_2),
% 0.20/0.44 inference(pi_clausification,[],[f247])).
% 0.20/0.44 thf(f247,plain,(
% 0.20/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))))) | ~spl0_2),
% 0.20/0.44 inference(boolean_simplification,[],[f246])).
% 0.20/0.44 thf(f246,plain,(
% 0.20/0.44 ($true = ($false | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))))) | ~spl0_2),
% 0.20/0.44 inference(boolean_simplification,[],[f245])).
% 0.20/0.44 thf(f245,plain,(
% 0.20/0.44 ($true = ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))))) | ~spl0_2),
% 0.20/0.44 inference(superposition,[],[f242,f170])).
% 0.20/0.44 thf(f242,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK2 @ X1)) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))))))) ) | ~spl0_2),
% 0.20/0.44 inference(beta_eta_normalization,[],[f240])).
% 0.20/0.44 thf(f240,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))))) @ X1))) ) | ~spl0_2),
% 0.20/0.44 inference(pi_clausification,[],[f239])).
% 0.20/0.44 thf(f239,plain,(
% 0.20/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))))))) | ~spl0_2),
% 0.20/0.44 inference(boolean_simplification,[],[f238])).
% 0.20/0.44 thf(f238,plain,(
% 0.20/0.44 ($true = ($false | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))))) | ~spl0_2),
% 0.20/0.44 inference(boolean_simplification,[],[f237])).
% 0.20/0.44 thf(f237,plain,(
% 0.20/0.44 ($true = ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))))) | ~spl0_2),
% 0.20/0.44 inference(superposition,[],[f235,f170])).
% 0.20/0.44 thf(f235,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK2 @ X1)) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))))))))) ) | ~spl0_2),
% 0.20/0.44 inference(beta_eta_normalization,[],[f234])).
% 0.20/0.44 thf(f234,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3))))))))))))) @ X1))) ) | ~spl0_2),
% 0.20/0.44 inference(pi_clausification,[],[f231])).
% 0.20/0.44 thf(f231,plain,(
% 0.20/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3))))))))))))))) | ~spl0_2),
% 0.20/0.44 inference(not_proxy_clausification,[],[f216])).
% 0.20/0.44 thf(f210,plain,(
% 0.20/0.44 spl0_1 | spl0_2),
% 0.20/0.44 inference(avatar_split_clause,[],[f203,f208,f205])).
% 0.20/0.44 thf(f203,plain,(
% 0.20/0.44 ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))))) | ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0)))))))),
% 0.20/0.44 inference(binary_proxy_clausification,[],[f200])).
% 0.20/0.44 thf(f200,plain,(
% 0.20/0.44 ($true = ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))))))),
% 0.20/0.44 inference(not_proxy_clausification,[],[f199])).
% 0.20/0.44 thf(f199,plain,(
% 0.20/0.44 ((~ ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3))))))))))))))))))) = $false)),
% 0.20/0.44 inference(beta_eta_normalization,[],[f198])).
% 0.20/0.44 thf(f198,plain,(
% 0.20/0.44 ($false = ((^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))))) @ sK2))),
% 0.20/0.44 inference(sigma_clausification,[],[f195])).
% 0.20/0.44 thf(f195,plain,(
% 0.20/0.44 ($false = (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4))))))))))))))))))))))),
% 0.20/0.44 inference(not_proxy_clausification,[],[f165])).
% 0.20/0.44 thf(f165,plain,(
% 0.20/0.44 ((~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))))))) = $true)),
% 0.20/0.44 inference(boolean_simplification,[],[f164])).
% 0.20/0.44 thf(f164,plain,(
% 0.20/0.44 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))))))))),
% 0.20/0.44 inference(boolean_simplification,[],[f163])).
% 0.20/0.44 thf(f163,plain,(
% 0.20/0.44 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))))))))))),
% 0.20/0.44 inference(boolean_simplification,[],[f162])).
% 0.20/0.44 thf(f162,plain,(
% 0.20/0.44 ((~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))))))))))) = $true)),
% 0.20/0.44 inference(beta_eta_normalization,[],[f158])).
% 0.20/0.44 thf(f158,plain,(
% 0.20/0.44 ($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]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p)))))),
% 0.20/0.44 inference(definition_unfolding,[],[f114,f137,f151,f157,f157,f157,f132,f132])).
% 0.20/0.44 thf(f132,plain,(
% 0.20/0.44 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.44 inference(cnf_transformation,[],[f41])).
% 0.20/0.44 thf(f41,plain,(
% 0.20/0.44 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.44 inference(fool_elimination,[],[f40])).
% 0.20/0.44 thf(f40,plain,(
% 0.20/0.44 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s5 @ X1 @ X2)))) = mbox_s5)),
% 0.20/0.44 inference(rectify,[],[f32])).
% 0.20/0.44 thf(f32,axiom,(
% 0.20/0.44 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_s5 @ X2 @ X7)))) = mbox_s5)),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s5)).
% 0.20/0.44 thf(f157,plain,(
% 0.20/0.44 (mdia_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.20/0.44 inference(definition_unfolding,[],[f122,f133,f132,f133])).
% 0.20/0.44 thf(f133,plain,(
% 0.20/0.44 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.44 inference(cnf_transformation,[],[f87])).
% 0.20/0.44 thf(f87,plain,(
% 0.20/0.44 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.44 inference(fool_elimination,[],[f86])).
% 0.20/0.44 thf(f86,plain,(
% 0.20/0.44 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.20/0.44 inference(rectify,[],[f3])).
% 0.20/0.44 thf(f3,axiom,(
% 0.20/0.44 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.20/0.44 thf(f122,plain,(
% 0.20/0.44 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.20/0.44 inference(cnf_transformation,[],[f54])).
% 0.20/0.44 thf(f54,plain,(
% 0.20/0.44 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.20/0.44 inference(fool_elimination,[],[f53])).
% 0.20/0.44 thf(f53,plain,(
% 0.20/0.44 (mdia_s5 = (^[X0 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X0)))))),
% 0.20/0.44 inference(rectify,[],[f33])).
% 0.20/0.44 thf(f33,axiom,(
% 0.20/0.44 (mdia_s5 = (^[X3 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X3)))))),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s5)).
% 0.20/0.44 thf(f151,plain,(
% 0.20/0.44 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.20/0.44 inference(definition_unfolding,[],[f143,f148,f149,f149])).
% 0.20/0.44 thf(f149,plain,(
% 0.20/0.44 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.20/0.44 inference(definition_unfolding,[],[f142,f116,f133])).
% 0.20/0.44 thf(f116,plain,(
% 0.20/0.44 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.44 inference(cnf_transformation,[],[f85])).
% 0.20/0.44 thf(f85,plain,(
% 0.20/0.44 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.44 inference(fool_elimination,[],[f84])).
% 0.20/0.44 thf(f84,plain,(
% 0.20/0.44 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.20/0.44 inference(rectify,[],[f4])).
% 0.20/0.44 thf(f4,axiom,(
% 0.20/0.44 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.20/0.44 thf(f142,plain,(
% 0.20/0.44 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.44 inference(cnf_transformation,[],[f65])).
% 0.20/0.44 thf(f65,plain,(
% 0.20/0.44 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.44 inference(fool_elimination,[],[f64])).
% 0.20/0.44 thf(f64,plain,(
% 0.20/0.44 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.20/0.44 inference(rectify,[],[f6])).
% 0.20/0.44 thf(f6,axiom,(
% 0.20/0.44 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.20/0.44 thf(f148,plain,(
% 0.20/0.44 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.20/0.44 inference(definition_unfolding,[],[f118,f133,f116,f133,f133])).
% 0.20/0.44 thf(f118,plain,(
% 0.20/0.44 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.44 inference(cnf_transformation,[],[f52])).
% 0.20/0.44 thf(f52,plain,(
% 0.20/0.44 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.44 inference(fool_elimination,[],[f51])).
% 0.20/0.44 thf(f51,plain,(
% 0.20/0.44 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.20/0.44 inference(rectify,[],[f5])).
% 0.20/0.44 thf(f5,axiom,(
% 0.20/0.44 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.20/0.44 thf(f143,plain,(
% 0.20/0.44 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.20/0.44 inference(cnf_transformation,[],[f73])).
% 0.20/0.44 thf(f73,plain,(
% 0.20/0.44 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.20/0.44 inference(fool_elimination,[],[f72])).
% 0.20/0.44 thf(f72,plain,(
% 0.20/0.44 (mequiv = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))))),
% 0.20/0.44 inference(rectify,[],[f8])).
% 0.20/0.44 thf(f8,axiom,(
% 0.20/0.44 (mequiv = (^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))))),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
% 0.20/0.44 thf(f137,plain,(
% 0.20/0.44 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.44 inference(cnf_transformation,[],[f98])).
% 0.20/0.44 thf(f98,plain,(
% 0.20/0.44 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.44 inference(fool_elimination,[],[f97])).
% 0.20/0.44 thf(f97,plain,(
% 0.20/0.44 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.20/0.44 inference(rectify,[],[f28])).
% 0.20/0.44 thf(f28,axiom,(
% 0.20/0.44 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.20/0.44 thf(f114,plain,(
% 0.20/0.44 ($true = (~ (mvalid @ (mequiv @ (mdia_s5 @ (mdia_s5 @ (mdia_s5 @ (mbox_s5 @ p)))) @ (mbox_s5 @ p)))))),
% 0.20/0.44 inference(cnf_transformation,[],[f77])).
% 0.20/0.44 thf(f77,plain,(
% 0.20/0.44 ($true = (~ (mvalid @ (mequiv @ (mdia_s5 @ (mdia_s5 @ (mdia_s5 @ (mbox_s5 @ p)))) @ (mbox_s5 @ p)))))),
% 0.20/0.44 inference(fool_elimination,[],[f76])).
% 0.20/0.44 thf(f76,plain,(
% 0.20/0.44 ~(mvalid @ (mequiv @ (mdia_s5 @ (mdia_s5 @ (mdia_s5 @ (mbox_s5 @ p)))) @ (mbox_s5 @ p)))),
% 0.20/0.44 inference(rectify,[],[f38])).
% 0.20/0.44 thf(f38,negated_conjecture,(
% 0.20/0.44 ~(mvalid @ (mequiv @ (mdia_s5 @ (mdia_s5 @ (mdia_s5 @ (mbox_s5 @ p)))) @ (mbox_s5 @ p)))),
% 0.20/0.44 inference(negated_conjecture,[],[f37])).
% 0.20/0.44 thf(f37,conjecture,(
% 0.20/0.44 (mvalid @ (mequiv @ (mdia_s5 @ (mdia_s5 @ (mdia_s5 @ (mbox_s5 @ p)))) @ (mbox_s5 @ p)))),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.20/0.44 % SZS output end Proof for theBenchmark
% 0.20/0.44 % (6297)------------------------------
% 0.20/0.44 % (6297)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (6297)Termination reason: Refutation
% 0.20/0.44
% 0.20/0.44 % (6297)Memory used [KB]: 6140
% 0.20/0.44 % (6297)Time elapsed: 0.072 s
% 0.20/0.44 % (6297)Instructions burned: 88 (million)
% 0.20/0.44 % (6297)------------------------------
% 0.20/0.44 % (6297)------------------------------
% 0.20/0.44 % (6285)Success in time 0.086 s
% 0.20/0.44 % Vampire---4.8 exiting
%------------------------------------------------------------------------------