TSTP Solution File: SYO447^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO447^1 : 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 : n011.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 09:04:28 EDT 2024
% Result : Theorem 0.25s 0.49s
% Output : Refutation 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYO447^1 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.40 % Computer : n011.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8042.1875MB
% 0.15/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Mon May 20 09:37:23 EDT 2024
% 0.15/0.40 % CPUTime :
% 0.15/0.40 This is a TH0_THM_EQU_NAR problem
% 0.15/0.40 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % (15275)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.42 % (15277)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.15/0.42 % (15273)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.42 % (15276)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.42 % (15272)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.42 % (15278)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.42 % (15274)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.15/0.42 % (15279)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.42 % (15275)Instruction limit reached!
% 0.15/0.42 % (15275)------------------------------
% 0.15/0.42 % (15275)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (15275)Termination reason: Unknown
% 0.15/0.42 % (15275)Termination phase: shuffling
% 0.15/0.42
% 0.15/0.42 % (15276)Instruction limit reached!
% 0.15/0.42 % (15276)------------------------------
% 0.15/0.42 % (15276)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (15276)Termination reason: Unknown
% 0.15/0.42 % (15276)Termination phase: shuffling
% 0.15/0.42
% 0.15/0.42 % (15276)Memory used [KB]: 1023
% 0.15/0.42 % (15276)Time elapsed: 0.003 s
% 0.15/0.42 % (15276)Instructions burned: 2 (million)
% 0.15/0.42 % (15276)------------------------------
% 0.15/0.42 % (15276)------------------------------
% 0.15/0.42 % (15275)Memory used [KB]: 1023
% 0.15/0.42 % (15275)Time elapsed: 0.003 s
% 0.15/0.42 % (15275)Instructions burned: 2 (million)
% 0.15/0.42 % (15275)------------------------------
% 0.15/0.42 % (15275)------------------------------
% 0.15/0.42 % (15279)Instruction limit reached!
% 0.15/0.42 % (15279)------------------------------
% 0.15/0.42 % (15279)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (15279)Termination reason: Unknown
% 0.15/0.42 % (15279)Termination phase: shuffling
% 0.15/0.42
% 0.15/0.42 % (15279)Memory used [KB]: 1023
% 0.15/0.42 % (15279)Time elapsed: 0.003 s
% 0.15/0.42 % (15279)Instructions burned: 3 (million)
% 0.15/0.42 % (15279)------------------------------
% 0.15/0.42 % (15279)------------------------------
% 0.15/0.42 % (15273)Instruction limit reached!
% 0.15/0.42 % (15273)------------------------------
% 0.15/0.42 % (15273)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (15273)Termination reason: Unknown
% 0.15/0.42 % (15273)Termination phase: Property scanning
% 0.15/0.42
% 0.15/0.42 % (15273)Memory used [KB]: 1023
% 0.15/0.42 % (15273)Time elapsed: 0.005 s
% 0.15/0.42 % (15273)Instructions burned: 5 (million)
% 0.15/0.42 % (15273)------------------------------
% 0.15/0.42 % (15273)------------------------------
% 0.15/0.42 % (15277)Refutation not found, incomplete strategy
% 0.15/0.42 % (15277)------------------------------
% 0.15/0.42 % (15277)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (15277)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.42
% 0.15/0.42
% 0.15/0.42 % (15277)Memory used [KB]: 5628
% 0.15/0.42 % (15277)Time elapsed: 0.007 s
% 0.15/0.42 % (15277)Instructions burned: 9 (million)
% 0.15/0.42 % (15277)------------------------------
% 0.15/0.42 % (15277)------------------------------
% 0.15/0.43 % (15278)Instruction limit reached!
% 0.15/0.43 % (15278)------------------------------
% 0.15/0.43 % (15278)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.43 % (15278)Termination reason: Unknown
% 0.15/0.43 % (15278)Termination phase: Saturation
% 0.15/0.43
% 0.15/0.43 % (15278)Memory used [KB]: 5628
% 0.15/0.43 % (15278)Time elapsed: 0.011 s
% 0.15/0.43 % (15278)Instructions burned: 19 (million)
% 0.15/0.43 % (15278)------------------------------
% 0.15/0.43 % (15278)------------------------------
% 0.15/0.43 % (15274)Instruction limit reached!
% 0.15/0.43 % (15274)------------------------------
% 0.15/0.43 % (15274)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.43 % (15274)Termination reason: Unknown
% 0.15/0.43 % (15274)Termination phase: Saturation
% 0.15/0.43
% 0.15/0.43 % (15274)Memory used [KB]: 5756
% 0.15/0.43 % (15274)Time elapsed: 0.016 s
% 0.15/0.43 % (15274)Instructions burned: 28 (million)
% 0.15/0.43 % (15274)------------------------------
% 0.15/0.43 % (15274)------------------------------
% 0.15/0.44 % (15281)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)
% 0.15/0.44 % (15280)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)
% 0.15/0.44 % (15282)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)
% 0.15/0.44 % (15283)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)
% 0.15/0.44 % (15282)Instruction limit reached!
% 0.15/0.44 % (15282)------------------------------
% 0.15/0.44 % (15282)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.44 % (15282)Termination reason: Unknown
% 0.15/0.44 % (15282)Termination phase: shuffling
% 0.15/0.44
% 0.15/0.44 % (15282)Memory used [KB]: 1023
% 0.15/0.44 % (15282)Time elapsed: 0.003 s
% 0.15/0.44 % (15282)Instructions burned: 3 (million)
% 0.15/0.44 % (15282)------------------------------
% 0.15/0.44 % (15282)------------------------------
% 0.25/0.44 % (15284)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.25/0.44 % (15281)Instruction limit reached!
% 0.25/0.44 % (15281)------------------------------
% 0.25/0.44 % (15281)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.44 % (15281)Termination reason: Unknown
% 0.25/0.44 % (15281)Termination phase: Saturation
% 0.25/0.44
% 0.25/0.44 % (15281)Memory used [KB]: 5628
% 0.25/0.44 % (15281)Time elapsed: 0.009 s
% 0.25/0.44 % (15281)Instructions burned: 16 (million)
% 0.25/0.44 % (15281)------------------------------
% 0.25/0.44 % (15281)------------------------------
% 0.25/0.44 % (15285)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.25/0.44 % (15284)Instruction limit reached!
% 0.25/0.44 % (15284)------------------------------
% 0.25/0.44 % (15284)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.44 % (15284)Termination reason: Unknown
% 0.25/0.44 % (15284)Termination phase: Function definition elimination
% 0.25/0.44
% 0.25/0.44 % (15284)Memory used [KB]: 1023
% 0.25/0.44 % (15284)Time elapsed: 0.006 s
% 0.25/0.44 % (15284)Instructions burned: 8 (million)
% 0.25/0.44 % (15284)------------------------------
% 0.25/0.44 % (15284)------------------------------
% 0.25/0.45 % (15286)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.25/0.45 % (15286)Instruction limit reached!
% 0.25/0.45 % (15286)------------------------------
% 0.25/0.45 % (15286)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.45 % (15286)Termination reason: Unknown
% 0.25/0.45 % (15286)Termination phase: shuffling
% 0.25/0.45
% 0.25/0.45 % (15286)Memory used [KB]: 1023
% 0.25/0.45 % (15286)Time elapsed: 0.003 s
% 0.25/0.45 % (15286)Instructions burned: 3 (million)
% 0.25/0.45 % (15286)------------------------------
% 0.25/0.45 % (15286)------------------------------
% 0.25/0.45 % (15287)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.25/0.45 % (15287)Instruction limit reached!
% 0.25/0.45 % (15287)------------------------------
% 0.25/0.45 % (15287)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.45 % (15287)Termination reason: Unknown
% 0.25/0.45 % (15287)Termination phase: shuffling
% 0.25/0.45
% 0.25/0.45 % (15287)Memory used [KB]: 1023
% 0.25/0.45 % (15287)Time elapsed: 0.003 s
% 0.25/0.45 % (15287)Instructions burned: 3 (million)
% 0.25/0.45 % (15287)------------------------------
% 0.25/0.45 % (15287)------------------------------
% 0.25/0.45 % (15285)Instruction limit reached!
% 0.25/0.45 % (15285)------------------------------
% 0.25/0.45 % (15285)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.45 % (15285)Termination reason: Unknown
% 0.25/0.45 % (15285)Termination phase: Saturation
% 0.25/0.45
% 0.25/0.45 % (15285)Memory used [KB]: 5756
% 0.25/0.45 % (15285)Time elapsed: 0.011 s
% 0.25/0.45 % (15285)Instructions burned: 16 (million)
% 0.25/0.45 % (15285)------------------------------
% 0.25/0.45 % (15285)------------------------------
% 0.25/0.45 % (15280)Instruction limit reached!
% 0.25/0.45 % (15280)------------------------------
% 0.25/0.45 % (15280)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.45 % (15280)Termination reason: Unknown
% 0.25/0.45 % (15280)Termination phase: Saturation
% 0.25/0.45
% 0.25/0.45 % (15280)Memory used [KB]: 5756
% 0.25/0.45 % (15280)Time elapsed: 0.020 s
% 0.25/0.45 % (15280)Instructions burned: 38 (million)
% 0.25/0.45 % (15280)------------------------------
% 0.25/0.45 % (15280)------------------------------
% 0.25/0.46 % (15288)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.25/0.46 % (15289)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.25/0.46 % (15289)Instruction limit reached!
% 0.25/0.46 % (15289)------------------------------
% 0.25/0.46 % (15289)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.46 % (15289)Termination reason: Unknown
% 0.25/0.46 % (15289)Termination phase: Property scanning
% 0.25/0.46
% 0.25/0.46 % (15289)Memory used [KB]: 1023
% 0.25/0.46 % (15289)Time elapsed: 0.004 s
% 0.25/0.46 % (15289)Instructions burned: 4 (million)
% 0.25/0.46 % (15289)------------------------------
% 0.25/0.46 % (15289)------------------------------
% 0.25/0.46 % (15288)Instruction limit reached!
% 0.25/0.46 % (15288)------------------------------
% 0.25/0.46 % (15288)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.46 % (15288)Termination reason: Unknown
% 0.25/0.46 % (15288)Termination phase: Function definition elimination
% 0.25/0.46
% 0.25/0.46 % (15288)Memory used [KB]: 1023
% 0.25/0.46 % (15288)Time elapsed: 0.006 s
% 0.25/0.46 % (15288)Instructions burned: 8 (million)
% 0.25/0.46 % (15288)------------------------------
% 0.25/0.46 % (15288)------------------------------
% 0.25/0.47 % (15290)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.25/0.47 % (15292)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.25/0.47 % (15291)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.25/0.47 % (15290)Instruction limit reached!
% 0.25/0.47 % (15290)------------------------------
% 0.25/0.47 % (15290)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.47 % (15290)Termination reason: Unknown
% 0.25/0.47 % (15290)Termination phase: shuffling
% 0.25/0.47
% 0.25/0.47 % (15290)Memory used [KB]: 1023
% 0.25/0.47 % (15290)Time elapsed: 0.004 s
% 0.25/0.47 % (15290)Instructions burned: 4 (million)
% 0.25/0.47 % (15290)------------------------------
% 0.25/0.47 % (15290)------------------------------
% 0.25/0.47 % (15293)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.25/0.47 % (15293)Instruction limit reached!
% 0.25/0.47 % (15293)------------------------------
% 0.25/0.47 % (15293)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.47 % (15293)Termination reason: Unknown
% 0.25/0.47 % (15293)Termination phase: Function definition elimination
% 0.25/0.47
% 0.25/0.47 % (15293)Memory used [KB]: 1023
% 0.25/0.47 % (15293)Time elapsed: 0.005 s
% 0.25/0.47 % (15293)Instructions burned: 7 (million)
% 0.25/0.47 % (15293)------------------------------
% 0.25/0.47 % (15293)------------------------------
% 0.25/0.47 % (15292)Refutation not found, incomplete strategy
% 0.25/0.47 % (15292)------------------------------
% 0.25/0.47 % (15292)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.47 % (15292)Termination reason: Refutation not found, incomplete strategy
% 0.25/0.47
% 0.25/0.47
% 0.25/0.47 % (15292)Memory used [KB]: 5628
% 0.25/0.47 % (15292)Time elapsed: 0.028 s
% 0.25/0.47 % (15292)Instructions burned: 10 (million)
% 0.25/0.47 % (15292)------------------------------
% 0.25/0.47 % (15292)------------------------------
% 0.25/0.48 % (15294)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.25/0.48 % (15295)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.25/0.48 % (15291)Instruction limit reached!
% 0.25/0.48 % (15291)------------------------------
% 0.25/0.48 % (15291)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.48 % (15291)Termination reason: Unknown
% 0.25/0.48 % (15291)Termination phase: Saturation
% 0.25/0.48
% 0.25/0.48 % (15291)Memory used [KB]: 5628
% 0.25/0.48 % (15291)Time elapsed: 0.033 s
% 0.25/0.48 % (15291)Instructions burned: 18 (million)
% 0.25/0.48 % (15291)------------------------------
% 0.25/0.48 % (15291)------------------------------
% 0.25/0.48 % (15283)First to succeed.
% 0.25/0.48 % (15294)Refutation not found, incomplete strategy
% 0.25/0.48 % (15294)------------------------------
% 0.25/0.48 % (15294)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.48 % (15294)Termination reason: Refutation not found, incomplete strategy
% 0.25/0.48
% 0.25/0.48
% 0.25/0.48 % (15294)Memory used [KB]: 5628
% 0.25/0.48 % (15294)Time elapsed: 0.007 s
% 0.25/0.48 % (15294)Instructions burned: 9 (million)
% 0.25/0.48 % (15294)------------------------------
% 0.25/0.48 % (15294)------------------------------
% 0.25/0.48 % (15296)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.25/0.48 % (15296)Instruction limit reached!
% 0.25/0.48 % (15296)------------------------------
% 0.25/0.48 % (15296)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.48 % (15296)Termination reason: Unknown
% 0.25/0.48 % (15296)Termination phase: Property scanning
% 0.25/0.48
% 0.25/0.48 % (15296)Memory used [KB]: 1023
% 0.25/0.48 % (15296)Time elapsed: 0.005 s
% 0.25/0.48 % (15296)Instructions burned: 6 (million)
% 0.25/0.48 % (15296)------------------------------
% 0.25/0.48 % (15296)------------------------------
% 0.25/0.49 % (15297)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.25/0.49 % (15298)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.25/0.49 % (15295)Instruction limit reached!
% 0.25/0.49 % (15295)------------------------------
% 0.25/0.49 % (15295)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.49 % (15295)Termination reason: Unknown
% 0.25/0.49 % (15295)Termination phase: Saturation
% 0.25/0.49
% 0.25/0.49 % (15295)Memory used [KB]: 5628
% 0.25/0.49 % (15295)Time elapsed: 0.014 s
% 0.25/0.49 % (15295)Instructions burned: 22 (million)
% 0.25/0.49 % (15295)------------------------------
% 0.25/0.49 % (15295)------------------------------
% 0.25/0.49 % (15283)Refutation found. Thanks to Tanya!
% 0.25/0.49 % SZS status Theorem for theBenchmark
% 0.25/0.49 % SZS output start Proof for theBenchmark
% 0.25/0.49 thf(type_def_5, type, mu: $tType).
% 0.25/0.49 thf(func_def_0, type, mu: $tType).
% 0.25/0.49 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.25/0.49 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.25/0.49 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.25/0.49 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.25/0.49 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.25/0.49 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.25/0.49 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.25/0.49 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.25/0.49 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.25/0.49 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.25/0.49 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.25/0.49 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.25/0.49 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.25/0.49 thf(func_def_15, type, mtrue: $i > $o).
% 0.25/0.49 thf(func_def_16, type, mfalse: $i > $o).
% 0.25/0.49 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.25/0.49 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.25/0.49 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.25/0.49 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.25/0.49 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.25/0.49 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.25/0.49 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.25/0.49 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.25/0.49 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.25/0.49 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.25/0.49 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.25/0.49 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.25/0.49 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.25/0.49 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.25/0.49 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.25/0.49 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.25/0.49 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.25/0.49 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.25/0.49 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.25/0.49 thf(func_def_36, type, p: $i > $o).
% 0.25/0.49 thf(func_def_37, type, q: $i > $o).
% 0.25/0.49 thf(func_def_54, type, ph1: !>[X0: $tType]:(X0)).
% 0.25/0.49 thf(f593,plain,(
% 0.25/0.49 $false),
% 0.25/0.49 inference(avatar_sat_refutation,[],[f211,f281,f357,f388,f592])).
% 0.25/0.49 thf(f592,plain,(
% 0.25/0.49 ~spl0_1),
% 0.25/0.49 inference(avatar_contradiction_clause,[],[f591])).
% 0.25/0.49 thf(f591,plain,(
% 0.25/0.49 $false | ~spl0_1),
% 0.25/0.49 inference(trivial_inequality_removal,[],[f590])).
% 0.25/0.49 thf(f590,plain,(
% 0.25/0.49 ($false = $true) | ~spl0_1),
% 0.25/0.49 inference(forward_demodulation,[],[f587,f572])).
% 0.25/0.49 thf(f572,plain,(
% 0.25/0.49 ($false = (rel_s5 @ sK2 @ sK6)) | ~spl0_1),
% 0.25/0.49 inference(not_proxy_clausification,[],[f540])).
% 0.25/0.49 thf(f540,plain,(
% 0.25/0.49 ($true = (~ (rel_s5 @ sK2 @ sK6))) | ~spl0_1),
% 0.25/0.49 inference(boolean_simplification,[],[f539])).
% 0.25/0.49 thf(f539,plain,(
% 0.25/0.49 (((~ (rel_s5 @ sK2 @ sK6)) | $false) = $true) | ~spl0_1),
% 0.25/0.49 inference(superposition,[],[f422,f532])).
% 0.25/0.49 thf(f532,plain,(
% 0.25/0.49 ((q @ sK6) = $false) | ~spl0_1),
% 0.25/0.49 inference(binary_proxy_clausification,[],[f517])).
% 0.25/0.49 thf(f517,plain,(
% 0.25/0.49 (((~ (rel_s5 @ sK5 @ sK6)) | (q @ sK6)) = $false) | ~spl0_1),
% 0.25/0.49 inference(beta_eta_normalization,[],[f515])).
% 0.25/0.49 thf(f515,plain,(
% 0.25/0.49 (((^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (q @ Y0))) @ sK6) = $false) | ~spl0_1),
% 0.25/0.49 inference(sigma_clausification,[],[f499])).
% 0.25/0.49 thf(f499,plain,(
% 0.25/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (q @ Y0)))) = $false) | ~spl0_1),
% 0.25/0.49 inference(not_proxy_clausification,[],[f462])).
% 0.25/0.49 thf(f462,plain,(
% 0.25/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (q @ Y0))))) = $true) | ~spl0_1),
% 0.25/0.49 inference(boolean_simplification,[],[f461])).
% 0.25/0.49 thf(f461,plain,(
% 0.25/0.49 (($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (q @ Y0)))))) = $true) | ~spl0_1),
% 0.25/0.49 inference(forward_demodulation,[],[f460,f455])).
% 0.25/0.49 thf(f455,plain,(
% 0.25/0.49 ($false = (~ (rel_s5 @ sK2 @ sK5))) | ~spl0_1),
% 0.25/0.49 inference(binary_proxy_clausification,[],[f453])).
% 0.25/0.49 thf(f453,plain,(
% 0.25/0.49 ($false = ((~ (rel_s5 @ sK2 @ sK5)) | (~ (p @ sK5)))) | ~spl0_1),
% 0.25/0.49 inference(beta_eta_normalization,[],[f452])).
% 0.25/0.49 thf(f452,plain,(
% 0.25/0.49 ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))) @ sK5)) | ~spl0_1),
% 0.25/0.49 inference(sigma_clausification,[],[f409])).
% 0.25/0.49 thf(f409,plain,(
% 0.25/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))) = $false) | ~spl0_1),
% 0.25/0.49 inference(binary_proxy_clausification,[],[f405])).
% 0.25/0.49 thf(f405,plain,(
% 0.25/0.49 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))) = $false) | ~spl0_1),
% 0.25/0.49 inference(binary_proxy_clausification,[],[f402])).
% 0.25/0.49 thf(f402,plain,(
% 0.25/0.49 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))) = $false) | ~spl0_1),
% 0.25/0.49 inference(not_proxy_clausification,[],[f207])).
% 0.25/0.49 thf(f207,plain,(
% 0.25/0.49 ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))))) | ~spl0_1),
% 0.25/0.49 inference(avatar_component_clause,[],[f206])).
% 0.25/0.49 thf(f206,plain,(
% 0.25/0.49 spl0_1 <=> ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))))))),
% 0.25/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.25/0.49 thf(f460,plain,(
% 0.25/0.49 (((~ (rel_s5 @ sK2 @ sK5)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (q @ Y0)))))) = $true) | ~spl0_1),
% 0.25/0.49 inference(boolean_simplification,[],[f459])).
% 0.25/0.49 thf(f459,plain,(
% 0.25/0.49 ($true = ((~ (rel_s5 @ sK2 @ sK5)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (q @ Y0))))) | $false))) | ~spl0_1),
% 0.25/0.49 inference(superposition,[],[f420,f457])).
% 0.25/0.49 thf(f457,plain,(
% 0.25/0.49 ((~ (p @ sK5)) = $false) | ~spl0_1),
% 0.25/0.49 inference(boolean_simplification,[],[f456])).
% 0.25/0.49 thf(f456,plain,(
% 0.25/0.49 (($false | (~ (p @ sK5))) = $false) | ~spl0_1),
% 0.25/0.49 inference(backward_demodulation,[],[f453,f455])).
% 0.25/0.49 thf(f420,plain,(
% 0.25/0.49 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK2 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (q @ Y0))))) | (~ (p @ X1)))))) ) | ~spl0_1),
% 0.25/0.49 inference(beta_eta_normalization,[],[f419])).
% 0.25/0.49 thf(f419,plain,(
% 0.25/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0))))) @ X1) = $true)) ) | ~spl0_1),
% 0.25/0.49 inference(pi_clausification,[],[f413])).
% 0.25/0.49 thf(f413,plain,(
% 0.25/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0)))))) = $true) | ~spl0_1),
% 0.25/0.49 inference(not_proxy_clausification,[],[f408])).
% 0.25/0.49 thf(f408,plain,(
% 0.25/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0))))))) = $false) | ~spl0_1),
% 0.25/0.49 inference(boolean_simplification,[],[f407])).
% 0.25/0.49 thf(f407,plain,(
% 0.25/0.49 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0))))))) | $false) = $false) | ~spl0_1),
% 0.25/0.49 inference(backward_demodulation,[],[f402,f405])).
% 0.25/0.49 thf(f422,plain,(
% 0.25/0.49 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK2 @ X1)) | (q @ X1)))) ) | ~spl0_1),
% 0.25/0.49 inference(beta_eta_normalization,[],[f421])).
% 0.25/0.49 thf(f421,plain,(
% 0.25/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))) @ X1) = $true)) ) | ~spl0_1),
% 0.25/0.49 inference(pi_clausification,[],[f416])).
% 0.25/0.49 thf(f416,plain,(
% 0.25/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0)))) = $true) | ~spl0_1),
% 0.25/0.49 inference(not_proxy_clausification,[],[f412])).
% 0.25/0.49 thf(f412,plain,(
% 0.25/0.49 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0)))))) | ~spl0_1),
% 0.25/0.49 inference(boolean_simplification,[],[f411])).
% 0.25/0.49 thf(f411,plain,(
% 0.25/0.49 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))) | $false) = $false) | ~spl0_1),
% 0.25/0.49 inference(backward_demodulation,[],[f405,f409])).
% 0.25/0.49 thf(f587,plain,(
% 0.25/0.49 ((rel_s5 @ sK2 @ sK6) = $true) | ~spl0_1),
% 0.25/0.49 inference(boolean_simplification,[],[f584])).
% 0.25/0.49 thf(f584,plain,(
% 0.25/0.49 (($true => (rel_s5 @ sK2 @ sK6)) = $true) | ~spl0_1),
% 0.25/0.49 inference(superposition,[],[f493,f536])).
% 0.25/0.49 thf(f536,plain,(
% 0.25/0.49 ((rel_s5 @ sK5 @ sK6) = $true) | ~spl0_1),
% 0.25/0.49 inference(not_proxy_clausification,[],[f535])).
% 0.25/0.49 thf(f535,plain,(
% 0.25/0.49 ($false = (~ (rel_s5 @ sK5 @ sK6))) | ~spl0_1),
% 0.25/0.49 inference(boolean_simplification,[],[f534])).
% 0.25/0.49 thf(f534,plain,(
% 0.25/0.49 (((~ (rel_s5 @ sK5 @ sK6)) | $false) = $false) | ~spl0_1),
% 0.25/0.49 inference(backward_demodulation,[],[f517,f532])).
% 0.25/0.49 thf(f493,plain,(
% 0.25/0.49 ( ! [X0 : $i] : ((((rel_s5 @ sK5 @ X0) => (rel_s5 @ sK2 @ X0)) = $true)) ) | ~spl0_1),
% 0.25/0.49 inference(boolean_simplification,[],[f482])).
% 0.25/0.49 thf(f482,plain,(
% 0.25/0.49 ( ! [X0 : $i] : (((((rel_s5 @ sK5 @ X0) & $true) => (rel_s5 @ sK2 @ X0)) = $true)) ) | ~spl0_1),
% 0.25/0.49 inference(superposition,[],[f186,f470])).
% 0.25/0.49 thf(f470,plain,(
% 0.25/0.49 ((rel_s5 @ sK2 @ sK5) = $true) | ~spl0_1),
% 0.25/0.49 inference(not_proxy_clausification,[],[f455])).
% 0.25/0.49 thf(f186,plain,(
% 0.25/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((rel_s5 @ X2 @ X1) & (rel_s5 @ X3 @ X2)) => (rel_s5 @ X3 @ X1)))) )),
% 0.25/0.49 inference(beta_eta_normalization,[],[f185])).
% 0.25/0.49 thf(f185,plain,(
% 0.25/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((rel_s5 @ X2 @ X1) & (rel_s5 @ Y0 @ X2)) => (rel_s5 @ Y0 @ X1))) @ X3) = $true)) )),
% 0.25/0.49 inference(pi_clausification,[],[f184])).
% 0.25/0.49 thf(f184,plain,(
% 0.25/0.49 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s5 @ X2 @ X1) & (rel_s5 @ Y0 @ X2)) => (rel_s5 @ Y0 @ X1)))))) )),
% 0.25/0.49 inference(beta_eta_normalization,[],[f183])).
% 0.25/0.49 thf(f183,plain,(
% 0.25/0.49 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y0 @ X1) & (rel_s5 @ Y1 @ Y0)) => (rel_s5 @ Y1 @ X1))))) @ X2) = $true)) )),
% 0.25/0.49 inference(pi_clausification,[],[f182])).
% 0.25/0.49 thf(f182,plain,(
% 0.25/0.49 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y0 @ X1) & (rel_s5 @ Y1 @ Y0)) => (rel_s5 @ Y1 @ X1)))))))) )),
% 0.25/0.49 inference(beta_eta_normalization,[],[f181])).
% 0.25/0.49 thf(f181,plain,(
% 0.25/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y1 @ Y0) & (rel_s5 @ Y2 @ Y1)) => (rel_s5 @ Y2 @ Y0))))))) @ X1) = $true)) )),
% 0.25/0.49 inference(pi_clausification,[],[f164])).
% 0.25/0.49 thf(f164,plain,(
% 0.25/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y1 @ Y0) & (rel_s5 @ Y2 @ Y1)) => (rel_s5 @ Y2 @ Y0)))))))) = $true)),
% 0.25/0.49 inference(beta_eta_normalization,[],[f161])).
% 0.25/0.49 thf(f161,plain,(
% 0.25/0.49 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) @ rel_s5) = $true)),
% 0.25/0.49 inference(definition_unfolding,[],[f147,f118])).
% 0.25/0.49 thf(f118,plain,(
% 0.25/0.49 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.25/0.49 inference(cnf_transformation,[],[f73])).
% 0.25/0.49 thf(f73,plain,(
% 0.25/0.49 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.25/0.49 inference(fool_elimination,[],[f72])).
% 0.25/0.49 thf(f72,plain,(
% 0.25/0.49 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)))) = mtransitive)),
% 0.25/0.49 inference(rectify,[],[f21])).
% 0.25/0.49 thf(f21,axiom,(
% 0.25/0.49 ((^[X6 : $i > $i > $o] : (! [X8,X9,X10] : (((X6 @ X8 @ X9) & (X6 @ X9 @ X10)) => (X6 @ X8 @ X10)))) = mtransitive)),
% 0.25/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive)).
% 0.25/0.49 thf(f147,plain,(
% 0.25/0.49 ((mtransitive @ rel_s5) = $true)),
% 0.25/0.49 inference(cnf_transformation,[],[f91])).
% 0.25/0.49 thf(f91,plain,(
% 0.25/0.49 ((mtransitive @ rel_s5) = $true)),
% 0.25/0.49 inference(fool_elimination,[],[f90])).
% 0.25/0.49 thf(f90,plain,(
% 0.25/0.49 (mtransitive @ rel_s5)),
% 0.25/0.49 inference(rectify,[],[f35])).
% 0.25/0.49 thf(f35,axiom,(
% 0.25/0.49 (mtransitive @ rel_s5)),
% 0.25/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 0.25/0.49 thf(f388,plain,(
% 0.25/0.49 ~spl0_2 | ~spl0_4),
% 0.25/0.49 inference(avatar_contradiction_clause,[],[f387])).
% 0.25/0.49 thf(f387,plain,(
% 0.25/0.49 $false | (~spl0_2 | ~spl0_4)),
% 0.25/0.49 inference(trivial_inequality_removal,[],[f386])).
% 0.25/0.49 thf(f386,plain,(
% 0.25/0.49 ($false = $true) | (~spl0_2 | ~spl0_4)),
% 0.25/0.49 inference(boolean_simplification,[],[f385])).
% 0.25/0.49 thf(f385,plain,(
% 0.25/0.49 ((~ $true) = $true) | (~spl0_2 | ~spl0_4)),
% 0.25/0.49 inference(forward_demodulation,[],[f376,f234])).
% 0.25/0.49 thf(f234,plain,(
% 0.25/0.49 ((p @ sK3) = $true) | ~spl0_2),
% 0.25/0.49 inference(not_proxy_clausification,[],[f230])).
% 0.25/0.49 thf(f230,plain,(
% 0.25/0.49 ($false = (~ (p @ sK3))) | ~spl0_2),
% 0.25/0.49 inference(binary_proxy_clausification,[],[f226])).
% 0.25/0.49 thf(f226,plain,(
% 0.25/0.49 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (q @ Y0))))) | (~ (p @ sK3))) = $false) | ~spl0_2),
% 0.25/0.49 inference(boolean_simplification,[],[f225])).
% 0.25/0.49 thf(f225,plain,(
% 0.25/0.49 (($false | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (q @ Y0))))) | (~ (p @ sK3)))) = $false) | ~spl0_2),
% 0.25/0.49 inference(backward_demodulation,[],[f222,f224])).
% 0.25/0.49 thf(f224,plain,(
% 0.25/0.49 ($false = (~ (rel_s5 @ sK2 @ sK3))) | ~spl0_2),
% 0.25/0.49 inference(binary_proxy_clausification,[],[f222])).
% 0.25/0.49 thf(f222,plain,(
% 0.25/0.49 ($false = ((~ (rel_s5 @ sK2 @ sK3)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (q @ Y0))))) | (~ (p @ sK3))))) | ~spl0_2),
% 0.25/0.49 inference(beta_eta_normalization,[],[f221])).
% 0.25/0.49 thf(f221,plain,(
% 0.25/0.49 (((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0))))) @ sK3) = $false) | ~spl0_2),
% 0.25/0.49 inference(sigma_clausification,[],[f220])).
% 0.25/0.49 thf(f220,plain,(
% 0.25/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0)))))) = $false) | ~spl0_2),
% 0.25/0.49 inference(boolean_simplification,[],[f219])).
% 0.25/0.49 thf(f219,plain,(
% 0.25/0.49 (($false | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0))))))) = $false) | ~spl0_2),
% 0.25/0.49 inference(backward_demodulation,[],[f214,f218])).
% 0.25/0.49 thf(f218,plain,(
% 0.25/0.49 ($false = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))))) | ~spl0_2),
% 0.25/0.49 inference(binary_proxy_clausification,[],[f214])).
% 0.25/0.49 thf(f214,plain,(
% 0.25/0.49 ($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0)))))))) | ~spl0_2),
% 0.25/0.49 inference(not_proxy_clausification,[],[f210])).
% 0.25/0.49 thf(f210,plain,(
% 0.25/0.49 ($true = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0))))))))) | ~spl0_2),
% 0.25/0.49 inference(avatar_component_clause,[],[f209])).
% 0.25/0.49 thf(f209,plain,(
% 0.25/0.49 spl0_2 <=> ($true = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0)))))))))),
% 0.25/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.25/0.49 thf(f376,plain,(
% 0.25/0.49 ($true = (~ (p @ sK3))) | (~spl0_2 | ~spl0_4)),
% 0.25/0.49 inference(boolean_simplification,[],[f375])).
% 0.25/0.49 thf(f375,plain,(
% 0.25/0.49 (($false | (~ (p @ sK3))) = $true) | (~spl0_2 | ~spl0_4)),
% 0.25/0.49 inference(boolean_simplification,[],[f374])).
% 0.25/0.49 thf(f374,plain,(
% 0.25/0.49 (((~ $true) | (~ (p @ sK3))) = $true) | (~spl0_2 | ~spl0_4)),
% 0.25/0.49 inference(superposition,[],[f361,f227])).
% 0.25/0.49 thf(f227,plain,(
% 0.25/0.49 ((rel_s5 @ sK2 @ sK3) = $true) | ~spl0_2),
% 0.25/0.49 inference(not_proxy_clausification,[],[f224])).
% 0.25/0.49 thf(f361,plain,(
% 0.25/0.49 ( ! [X1 : $i] : ((((~ (rel_s5 @ sK2 @ X1)) | (~ (p @ X1))) = $true)) ) | ~spl0_4),
% 0.25/0.49 inference(beta_eta_normalization,[],[f360])).
% 0.25/0.49 thf(f360,plain,(
% 0.25/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))) @ X1) = $true)) ) | ~spl0_4),
% 0.25/0.49 inference(pi_clausification,[],[f280])).
% 0.25/0.49 thf(f280,plain,(
% 0.25/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))) = $true) | ~spl0_4),
% 0.25/0.49 inference(avatar_component_clause,[],[f279])).
% 0.25/0.49 thf(f279,plain,(
% 0.25/0.49 spl0_4 <=> ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))) = $true)),
% 0.25/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.25/0.49 thf(f357,plain,(
% 0.25/0.49 ~spl0_2 | ~spl0_3),
% 0.25/0.49 inference(avatar_contradiction_clause,[],[f356])).
% 0.25/0.49 thf(f356,plain,(
% 0.25/0.49 $false | (~spl0_2 | ~spl0_3)),
% 0.25/0.49 inference(trivial_inequality_removal,[],[f355])).
% 0.25/0.49 thf(f355,plain,(
% 0.25/0.49 ($false = $true) | (~spl0_2 | ~spl0_3)),
% 0.25/0.49 inference(boolean_simplification,[],[f354])).
% 0.25/0.49 thf(f354,plain,(
% 0.25/0.49 ((~ $true) = $true) | (~spl0_2 | ~spl0_3)),
% 0.25/0.49 inference(backward_demodulation,[],[f308,f353])).
% 0.25/0.49 thf(f353,plain,(
% 0.25/0.49 ((rel_s5 @ sK3 @ sK4) = $true) | (~spl0_2 | ~spl0_3)),
% 0.25/0.49 inference(boolean_simplification,[],[f346])).
% 0.25/0.49 thf(f346,plain,(
% 0.25/0.49 (($true => (rel_s5 @ sK3 @ sK4)) = $true) | (~spl0_2 | ~spl0_3)),
% 0.25/0.49 inference(superposition,[],[f175,f327])).
% 0.25/0.49 thf(f327,plain,(
% 0.25/0.49 ((rel_s5 @ sK4 @ sK3) = $true) | (~spl0_2 | ~spl0_3)),
% 0.25/0.49 inference(boolean_simplification,[],[f319])).
% 0.25/0.49 thf(f319,plain,(
% 0.25/0.49 (($true => (rel_s5 @ sK4 @ sK3)) = $true) | (~spl0_2 | ~spl0_3)),
% 0.25/0.49 inference(superposition,[],[f248,f316])).
% 0.25/0.49 thf(f316,plain,(
% 0.25/0.49 ((rel_s5 @ sK4 @ sK2) = $true) | ~spl0_3),
% 0.25/0.49 inference(boolean_simplification,[],[f312])).
% 0.25/0.49 thf(f312,plain,(
% 0.25/0.49 (($true => (rel_s5 @ sK4 @ sK2)) = $true) | ~spl0_3),
% 0.25/0.49 inference(superposition,[],[f175,f304])).
% 0.25/0.49 thf(f304,plain,(
% 0.25/0.49 ($true = (rel_s5 @ sK2 @ sK4)) | ~spl0_3),
% 0.25/0.49 inference(not_proxy_clausification,[],[f303])).
% 0.25/0.49 thf(f303,plain,(
% 0.25/0.49 ((~ (rel_s5 @ sK2 @ sK4)) = $false) | ~spl0_3),
% 0.25/0.49 inference(boolean_simplification,[],[f302])).
% 0.25/0.49 thf(f302,plain,(
% 0.25/0.49 (((~ (rel_s5 @ sK2 @ sK4)) | $false) = $false) | ~spl0_3),
% 0.25/0.49 inference(backward_demodulation,[],[f299,f300])).
% 0.25/0.49 thf(f300,plain,(
% 0.25/0.49 ($false = (q @ sK4)) | ~spl0_3),
% 0.25/0.49 inference(binary_proxy_clausification,[],[f299])).
% 0.25/0.49 thf(f299,plain,(
% 0.25/0.49 ($false = ((~ (rel_s5 @ sK2 @ sK4)) | (q @ sK4))) | ~spl0_3),
% 0.25/0.49 inference(beta_eta_normalization,[],[f298])).
% 0.25/0.49 thf(f298,plain,(
% 0.25/0.49 (((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))) @ sK4) = $false) | ~spl0_3),
% 0.25/0.49 inference(sigma_clausification,[],[f286])).
% 0.25/0.49 thf(f286,plain,(
% 0.25/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0)))) = $false) | ~spl0_3),
% 0.25/0.49 inference(not_proxy_clausification,[],[f277])).
% 0.25/0.49 thf(f277,plain,(
% 0.25/0.49 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0)))))) | ~spl0_3),
% 0.25/0.49 inference(avatar_component_clause,[],[f276])).
% 0.25/0.49 thf(f276,plain,(
% 0.25/0.49 spl0_3 <=> ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))))),
% 0.25/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.25/0.49 thf(f248,plain,(
% 0.25/0.49 ( ! [X0 : $i] : (($true = ((rel_s5 @ X0 @ sK2) => (rel_s5 @ X0 @ sK3)))) ) | ~spl0_2),
% 0.25/0.49 inference(boolean_simplification,[],[f242])).
% 0.25/0.49 thf(f242,plain,(
% 0.25/0.49 ( ! [X0 : $i] : (((($true & (rel_s5 @ X0 @ sK2)) => (rel_s5 @ X0 @ sK3)) = $true)) ) | ~spl0_2),
% 0.25/0.49 inference(superposition,[],[f186,f227])).
% 0.25/0.49 thf(f175,plain,(
% 0.25/0.49 ( ! [X2 : $i,X1 : $i] : ((((rel_s5 @ X1 @ X2) => (rel_s5 @ X2 @ X1)) = $true)) )),
% 0.25/0.49 inference(beta_eta_normalization,[],[f174])).
% 0.25/0.49 thf(f174,plain,(
% 0.25/0.49 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((rel_s5 @ X1 @ Y0) => (rel_s5 @ Y0 @ X1))) @ X2))) )),
% 0.25/0.49 inference(pi_clausification,[],[f173])).
% 0.25/0.49 thf(f173,plain,(
% 0.25/0.49 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((rel_s5 @ X1 @ Y0) => (rel_s5 @ Y0 @ X1)))) = $true)) )),
% 0.25/0.49 inference(beta_eta_normalization,[],[f172])).
% 0.25/0.49 thf(f172,plain,(
% 0.25/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0))))) @ X1) = $true)) )),
% 0.25/0.49 inference(pi_clausification,[],[f162])).
% 0.25/0.49 thf(f162,plain,(
% 0.25/0.49 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0)))))))),
% 0.25/0.49 inference(beta_eta_normalization,[],[f160])).
% 0.25/0.49 thf(f160,plain,(
% 0.25/0.49 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ rel_s5) = $true)),
% 0.25/0.49 inference(definition_unfolding,[],[f141,f142])).
% 0.25/0.49 thf(f142,plain,(
% 0.25/0.49 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.25/0.49 inference(cnf_transformation,[],[f81])).
% 0.25/0.49 thf(f81,plain,(
% 0.25/0.49 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.25/0.49 inference(fool_elimination,[],[f80])).
% 0.25/0.49 thf(f80,plain,(
% 0.25/0.49 (msymmetric = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))))),
% 0.25/0.49 inference(rectify,[],[f19])).
% 0.25/0.49 thf(f19,axiom,(
% 0.25/0.49 (msymmetric = (^[X6 : $i > $i > $o] : (! [X9,X8] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))))),
% 0.25/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric)).
% 0.25/0.49 thf(f141,plain,(
% 0.25/0.49 ((msymmetric @ rel_s5) = $true)),
% 0.25/0.49 inference(cnf_transformation,[],[f75])).
% 0.25/0.49 thf(f75,plain,(
% 0.25/0.49 ((msymmetric @ rel_s5) = $true)),
% 0.25/0.49 inference(fool_elimination,[],[f74])).
% 0.25/0.49 thf(f74,plain,(
% 0.25/0.49 (msymmetric @ rel_s5)),
% 0.25/0.49 inference(rectify,[],[f36])).
% 0.25/0.49 thf(f36,axiom,(
% 0.25/0.49 (msymmetric @ rel_s5)),
% 0.25/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3)).
% 0.25/0.49 thf(f308,plain,(
% 0.25/0.49 ((~ (rel_s5 @ sK3 @ sK4)) = $true) | (~spl0_2 | ~spl0_3)),
% 0.25/0.49 inference(boolean_simplification,[],[f307])).
% 0.25/0.49 thf(f307,plain,(
% 0.25/0.49 (((~ (rel_s5 @ sK3 @ sK4)) | $false) = $true) | (~spl0_2 | ~spl0_3)),
% 0.25/0.49 inference(superposition,[],[f241,f300])).
% 0.25/0.49 thf(f241,plain,(
% 0.25/0.49 ( ! [X1 : $i] : ((((~ (rel_s5 @ sK3 @ X1)) | (q @ X1)) = $true)) ) | ~spl0_2),
% 0.25/0.49 inference(beta_eta_normalization,[],[f240])).
% 0.25/0.49 thf(f240,plain,(
% 0.25/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (q @ Y0))) @ X1) = $true)) ) | ~spl0_2),
% 0.25/0.49 inference(pi_clausification,[],[f237])).
% 0.25/0.49 thf(f237,plain,(
% 0.25/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (q @ Y0)))) = $true) | ~spl0_2),
% 0.25/0.49 inference(not_proxy_clausification,[],[f233])).
% 0.25/0.49 thf(f233,plain,(
% 0.25/0.49 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (q @ Y0)))))) | ~spl0_2),
% 0.25/0.49 inference(boolean_simplification,[],[f232])).
% 0.25/0.49 thf(f232,plain,(
% 0.25/0.49 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (q @ Y0))))) | $false) = $false) | ~spl0_2),
% 0.25/0.49 inference(backward_demodulation,[],[f226,f230])).
% 0.25/0.49 thf(f281,plain,(
% 0.25/0.49 spl0_3 | spl0_4 | ~spl0_2),
% 0.25/0.49 inference(avatar_split_clause,[],[f274,f209,f279,f276])).
% 0.25/0.49 thf(f274,plain,(
% 0.25/0.49 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))) = $true) | ~spl0_2),
% 0.25/0.49 inference(binary_proxy_clausification,[],[f258])).
% 0.25/0.49 thf(f258,plain,(
% 0.25/0.49 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))) = $true) | ~spl0_2),
% 0.25/0.49 inference(not_proxy_clausification,[],[f218])).
% 0.25/0.49 thf(f211,plain,(
% 0.25/0.49 spl0_1 | spl0_2),
% 0.25/0.49 inference(avatar_split_clause,[],[f204,f209,f206])).
% 0.25/0.49 thf(f204,plain,(
% 0.25/0.49 ($true = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0))))))))) | ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))))))),
% 0.25/0.49 inference(binary_proxy_clausification,[],[f201])).
% 0.25/0.49 thf(f201,plain,(
% 0.25/0.49 (((~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0)))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))))) = $true)),
% 0.25/0.49 inference(not_proxy_clausification,[],[f200])).
% 0.25/0.49 thf(f200,plain,(
% 0.25/0.49 ($false = (~ ((~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0)))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (p @ Y0))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))))))))),
% 0.25/0.49 inference(beta_eta_normalization,[],[f199])).
% 0.25/0.49 thf(f199,plain,(
% 0.25/0.49 ($false = ((^[Y0 : $i]: (~ ((~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))) | (~ (p @ Y1)))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))) | (~ (p @ Y1))))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))))))) @ sK2))),
% 0.25/0.49 inference(sigma_clausification,[],[f196])).
% 0.25/0.49 thf(f196,plain,(
% 0.25/0.49 ($false = (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))) | (~ (p @ Y1)))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))) | (~ (p @ Y1))))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1)))))))))))))),
% 0.25/0.49 inference(not_proxy_clausification,[],[f169])).
% 0.25/0.49 thf(f169,plain,(
% 0.25/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))) | (~ (p @ Y1)))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))) | (~ (p @ Y1))))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))))))))) = $true)),
% 0.25/0.49 inference(boolean_simplification,[],[f168])).
% 0.25/0.49 thf(f168,plain,(
% 0.25/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))) | (~ (p @ Y1)))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))) | (~ (p @ Y1))))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))))))))) = $true)),
% 0.25/0.49 inference(boolean_simplification,[],[f167])).
% 0.25/0.49 thf(f167,plain,(
% 0.25/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))) | (~ (p @ Y1)))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))) | (~ (p @ Y1))))))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))))))))) = $true)),
% 0.25/0.49 inference(boolean_simplification,[],[f166])).
% 0.25/0.49 thf(f166,plain,(
% 0.25/0.49 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))) | (~ (p @ Y1)))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))) | (~ (p @ Y1))))))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))))))))))))),
% 0.25/0.49 inference(boolean_simplification,[],[f165])).
% 0.25/0.49 thf(f165,plain,(
% 0.25/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))) | (~ (p @ Y1)))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))) | (~ (p @ Y1))))))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))))))))))))) = $true)),
% 0.25/0.49 inference(beta_eta_normalization,[],[f158])).
% 0.25/0.49 thf(f158,plain,(
% 0.25/0.49 ((~ ((^[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]: ((Y5 @ Y6) | (Y4 @ 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]: ((Y5 @ Y6) | (Y4 @ 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]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[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)))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ q)) @ ((^[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 > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ p @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ q)))))) = $true)),
% 0.25/0.49 inference(definition_unfolding,[],[f114,f113,f151,f148,f157,f127,f157,f148,f127])).
% 0.25/0.49 thf(f127,plain,(
% 0.25/0.49 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.25/0.49 inference(cnf_transformation,[],[f49])).
% 0.25/0.49 thf(f49,plain,(
% 0.25/0.49 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.25/0.49 inference(fool_elimination,[],[f48])).
% 0.25/0.49 thf(f48,plain,(
% 0.25/0.49 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s5 @ X1 @ X2)))) = mbox_s5)),
% 0.25/0.49 inference(rectify,[],[f32])).
% 0.25/0.49 thf(f32,axiom,(
% 0.25/0.49 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_s5 @ X2 @ X7)))) = mbox_s5)),
% 0.25/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s5)).
% 0.25/0.49 thf(f157,plain,(
% 0.25/0.49 (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)))))),
% 0.25/0.49 inference(definition_unfolding,[],[f129,f123,f127,f123])).
% 0.25/0.49 thf(f123,plain,(
% 0.25/0.49 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.25/0.49 inference(cnf_transformation,[],[f83])).
% 0.25/0.49 thf(f83,plain,(
% 0.25/0.49 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.25/0.49 inference(fool_elimination,[],[f82])).
% 0.25/0.49 thf(f82,plain,(
% 0.25/0.49 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.25/0.49 inference(rectify,[],[f3])).
% 0.25/0.49 thf(f3,axiom,(
% 0.25/0.49 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.25/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.25/0.49 thf(f129,plain,(
% 0.25/0.49 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.25/0.49 inference(cnf_transformation,[],[f69])).
% 0.25/0.49 thf(f69,plain,(
% 0.25/0.49 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.25/0.49 inference(fool_elimination,[],[f68])).
% 0.25/0.49 thf(f68,plain,(
% 0.25/0.49 (mdia_s5 = (^[X0 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X0)))))),
% 0.25/0.49 inference(rectify,[],[f33])).
% 0.25/0.49 thf(f33,axiom,(
% 0.25/0.49 (mdia_s5 = (^[X3 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X3)))))),
% 0.25/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s5)).
% 0.25/0.49 thf(f148,plain,(
% 0.25/0.49 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.25/0.49 inference(definition_unfolding,[],[f130,f123,f145,f123,f123])).
% 0.25/0.49 thf(f145,plain,(
% 0.25/0.49 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.25/0.49 inference(cnf_transformation,[],[f45])).
% 0.25/0.49 thf(f45,plain,(
% 0.25/0.49 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.25/0.49 inference(fool_elimination,[],[f44])).
% 0.25/0.49 thf(f44,plain,(
% 0.25/0.49 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.25/0.49 inference(rectify,[],[f4])).
% 0.25/0.49 thf(f4,axiom,(
% 0.25/0.49 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.25/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.25/0.49 thf(f130,plain,(
% 0.25/0.49 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.25/0.49 inference(cnf_transformation,[],[f43])).
% 0.25/0.49 thf(f43,plain,(
% 0.25/0.49 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.25/0.49 inference(fool_elimination,[],[f42])).
% 0.25/0.49 thf(f42,plain,(
% 0.25/0.49 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.25/0.49 inference(rectify,[],[f5])).
% 0.25/0.49 thf(f5,axiom,(
% 0.25/0.49 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.25/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.25/0.49 thf(f151,plain,(
% 0.25/0.49 (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]: ((Y5 @ Y6) | (Y4 @ 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]: ((Y5 @ Y6) | (Y4 @ 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]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.25/0.49 inference(definition_unfolding,[],[f143,f148,f149,f149])).
% 0.25/0.49 thf(f149,plain,(
% 0.25/0.49 (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)))))),
% 0.25/0.49 inference(definition_unfolding,[],[f116,f145,f123])).
% 0.25/0.49 thf(f116,plain,(
% 0.25/0.49 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.25/0.49 inference(cnf_transformation,[],[f65])).
% 0.25/0.49 thf(f65,plain,(
% 0.25/0.49 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.25/0.49 inference(fool_elimination,[],[f64])).
% 0.25/0.49 thf(f64,plain,(
% 0.25/0.49 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.25/0.49 inference(rectify,[],[f6])).
% 0.25/0.49 thf(f6,axiom,(
% 0.25/0.49 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.25/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.25/0.49 thf(f143,plain,(
% 0.25/0.49 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.25/0.49 inference(cnf_transformation,[],[f85])).
% 0.25/0.49 thf(f85,plain,(
% 0.25/0.49 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.25/0.49 inference(fool_elimination,[],[f84])).
% 0.25/0.49 thf(f84,plain,(
% 0.25/0.49 ((^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))) = mequiv)),
% 0.25/0.49 inference(rectify,[],[f8])).
% 0.25/0.49 thf(f8,axiom,(
% 0.25/0.49 ((^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))) = mequiv)),
% 0.25/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
% 0.25/0.49 thf(f113,plain,(
% 0.25/0.49 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.25/0.49 inference(cnf_transformation,[],[f95])).
% 0.25/0.49 thf(f95,plain,(
% 0.25/0.49 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.25/0.49 inference(fool_elimination,[],[f94])).
% 0.25/0.49 thf(f94,plain,(
% 0.25/0.49 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.25/0.49 inference(rectify,[],[f28])).
% 0.25/0.49 thf(f28,axiom,(
% 0.25/0.49 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.25/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.25/0.49 thf(f114,plain,(
% 0.25/0.49 ((~ (mvalid @ (mequiv @ (mand @ (mdia_s5 @ p) @ (mbox_s5 @ q)) @ (mdia_s5 @ (mand @ p @ (mbox_s5 @ q)))))) = $true)),
% 0.25/0.49 inference(cnf_transformation,[],[f77])).
% 0.25/0.49 thf(f77,plain,(
% 0.25/0.49 ((~ (mvalid @ (mequiv @ (mand @ (mdia_s5 @ p) @ (mbox_s5 @ q)) @ (mdia_s5 @ (mand @ p @ (mbox_s5 @ q)))))) = $true)),
% 0.25/0.49 inference(fool_elimination,[],[f76])).
% 0.25/0.49 thf(f76,plain,(
% 0.25/0.49 ~(mvalid @ (mequiv @ (mand @ (mdia_s5 @ p) @ (mbox_s5 @ q)) @ (mdia_s5 @ (mand @ p @ (mbox_s5 @ q)))))),
% 0.25/0.49 inference(rectify,[],[f38])).
% 0.25/0.49 thf(f38,negated_conjecture,(
% 0.25/0.49 ~(mvalid @ (mequiv @ (mand @ (mdia_s5 @ p) @ (mbox_s5 @ q)) @ (mdia_s5 @ (mand @ p @ (mbox_s5 @ q)))))),
% 0.25/0.49 inference(negated_conjecture,[],[f37])).
% 0.25/0.49 thf(f37,conjecture,(
% 0.25/0.49 (mvalid @ (mequiv @ (mand @ (mdia_s5 @ p) @ (mbox_s5 @ q)) @ (mdia_s5 @ (mand @ p @ (mbox_s5 @ q)))))),
% 0.25/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.25/0.49 % SZS output end Proof for theBenchmark
% 0.25/0.49 % (15283)------------------------------
% 0.25/0.49 % (15283)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.49 % (15283)Termination reason: Refutation
% 0.25/0.49
% 0.25/0.49 % (15283)Memory used [KB]: 6140
% 0.25/0.49 % (15283)Time elapsed: 0.052 s
% 0.25/0.49 % (15283)Instructions burned: 74 (million)
% 0.25/0.49 % (15283)------------------------------
% 0.25/0.49 % (15283)------------------------------
% 0.25/0.49 % (15271)Success in time 0.083 s
% 0.25/0.49 % Vampire---4.8 exiting
%------------------------------------------------------------------------------