TSTP Solution File: SYO430^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO430^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:04:24 EDT 2024
% Result : Theorem 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO430^1 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 08:50:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.39 % (23634)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.39 % (23635)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)
% 0.21/0.39 % (23637)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.39 % (23636)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)
% 0.21/0.39 % (23638)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)
% 0.21/0.39 % (23639)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)
% 0.21/0.39 % (23640)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.39 % (23637)Instruction limit reached!
% 0.21/0.39 % (23637)------------------------------
% 0.21/0.39 % (23637)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (23637)Termination reason: Unknown
% 0.21/0.39 % (23637)Termination phase: shuffling
% 0.21/0.39 % (23638)Instruction limit reached!
% 0.21/0.39 % (23638)------------------------------
% 0.21/0.39 % (23638)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39
% 0.21/0.39 % (23637)Memory used [KB]: 1023
% 0.21/0.39 % (23637)Time elapsed: 0.004 s
% 0.21/0.39 % (23637)Instructions burned: 2 (million)
% 0.21/0.39 % (23637)------------------------------
% 0.21/0.39 % (23637)------------------------------
% 0.21/0.39 % (23638)Termination reason: Unknown
% 0.21/0.39 % (23638)Termination phase: shuffling
% 0.21/0.39
% 0.21/0.39 % (23638)Memory used [KB]: 1023
% 0.21/0.39 % (23638)Time elapsed: 0.004 s
% 0.21/0.39 % (23638)Instructions burned: 2 (million)
% 0.21/0.39 % (23638)------------------------------
% 0.21/0.39 % (23638)------------------------------
% 0.21/0.39 % (23641)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)
% 0.21/0.40 % (23635)Instruction limit reached!
% 0.21/0.40 % (23635)------------------------------
% 0.21/0.40 % (23635)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (23635)Termination reason: Unknown
% 0.21/0.40 % (23635)Termination phase: shuffling
% 0.21/0.40
% 0.21/0.40 % (23635)Memory used [KB]: 1023
% 0.21/0.40 % (23635)Time elapsed: 0.006 s
% 0.21/0.40 % (23635)Instructions burned: 4 (million)
% 0.21/0.40 % (23635)------------------------------
% 0.21/0.40 % (23635)------------------------------
% 0.21/0.40 % (23641)Instruction limit reached!
% 0.21/0.40 % (23641)------------------------------
% 0.21/0.40 % (23641)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (23641)Termination reason: Unknown
% 0.21/0.40 % (23641)Termination phase: shuffling
% 0.21/0.40
% 0.21/0.40 % (23641)Memory used [KB]: 1023
% 0.21/0.40 % (23641)Time elapsed: 0.005 s
% 0.21/0.40 % (23641)Instructions burned: 3 (million)
% 0.21/0.40 % (23641)------------------------------
% 0.21/0.40 % (23641)------------------------------
% 0.21/0.40 % (23639)Refutation not found, incomplete strategy
% 0.21/0.40 % (23639)------------------------------
% 0.21/0.40 % (23639)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (23639)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.40
% 0.21/0.40
% 0.21/0.40 % (23639)Memory used [KB]: 5628
% 0.21/0.40 % (23639)Time elapsed: 0.011 s
% 0.21/0.40 % (23639)Instructions burned: 9 (million)
% 0.21/0.40 % (23639)------------------------------
% 0.21/0.40 % (23639)------------------------------
% 0.21/0.41 % (23640)Instruction limit reached!
% 0.21/0.41 % (23640)------------------------------
% 0.21/0.41 % (23640)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (23640)Termination reason: Unknown
% 0.21/0.41 % (23640)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (23640)Memory used [KB]: 5628
% 0.21/0.41 % (23640)Time elapsed: 0.018 s
% 0.21/0.41 % (23640)Instructions burned: 18 (million)
% 0.21/0.41 % (23640)------------------------------
% 0.21/0.41 % (23640)------------------------------
% 0.21/0.41 % (23636)Instruction limit reached!
% 0.21/0.41 % (23636)------------------------------
% 0.21/0.41 % (23636)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (23636)Termination reason: Unknown
% 0.21/0.41 % (23636)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (23636)Memory used [KB]: 5628
% 0.21/0.41 % (23636)Time elapsed: 0.024 s
% 0.21/0.41 % (23636)Instructions burned: 27 (million)
% 0.21/0.41 % (23636)------------------------------
% 0.21/0.41 % (23636)------------------------------
% 0.21/0.42 % (23642)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)
% 0.21/0.42 % (23643)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)
% 0.21/0.42 % (23644)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)
% 0.21/0.42 % (23645)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)
% 0.21/0.42 % (23644)Instruction limit reached!
% 0.21/0.42 % (23644)------------------------------
% 0.21/0.42 % (23644)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (23644)Termination reason: Unknown
% 0.21/0.42 % (23644)Termination phase: shuffling
% 0.21/0.42
% 0.21/0.42 % (23644)Memory used [KB]: 1023
% 0.21/0.42 % (23644)Time elapsed: 0.005 s
% 0.21/0.42 % (23644)Instructions burned: 3 (million)
% 0.21/0.42 % (23644)------------------------------
% 0.21/0.42 % (23644)------------------------------
% 0.21/0.43 % (23646)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.43 % (23643)Instruction limit reached!
% 0.21/0.43 % (23643)------------------------------
% 0.21/0.43 % (23643)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (23643)Termination reason: Unknown
% 0.21/0.43 % (23643)Termination phase: Saturation
% 0.21/0.43
% 0.21/0.43 % (23643)Memory used [KB]: 5628
% 0.21/0.43 % (23643)Time elapsed: 0.015 s
% 0.21/0.43 % (23643)Instructions burned: 15 (million)
% 0.21/0.43 % (23643)------------------------------
% 0.21/0.43 % (23643)------------------------------
% 0.21/0.43 % (23646)Instruction limit reached!
% 0.21/0.43 % (23646)------------------------------
% 0.21/0.43 % (23646)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (23647)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.43 % (23646)Termination reason: Unknown
% 0.21/0.43 % (23646)Termination phase: Function definition elimination
% 0.21/0.43
% 0.21/0.43 % (23646)Memory used [KB]: 1023
% 0.21/0.43 % (23646)Time elapsed: 0.009 s
% 0.21/0.43 % (23646)Instructions burned: 8 (million)
% 0.21/0.43 % (23646)------------------------------
% 0.21/0.43 % (23646)------------------------------
% 0.21/0.44 % (23648)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)
% 0.21/0.44 % (23648)Instruction limit reached!
% 0.21/0.44 % (23648)------------------------------
% 0.21/0.44 % (23648)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (23648)Termination reason: Unknown
% 0.21/0.44 % (23648)Termination phase: shuffling
% 0.21/0.44
% 0.21/0.44 % (23648)Memory used [KB]: 1023
% 0.21/0.44 % (23648)Time elapsed: 0.004 s
% 0.21/0.44 % (23648)Instructions burned: 4 (million)
% 0.21/0.44 % (23648)------------------------------
% 0.21/0.44 % (23648)------------------------------
% 0.21/0.45 % (23649)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)
% 0.21/0.45 % (23649)Instruction limit reached!
% 0.21/0.45 % (23649)------------------------------
% 0.21/0.45 % (23649)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (23649)Termination reason: Unknown
% 0.21/0.45 % (23649)Termination phase: shuffling
% 0.21/0.45
% 0.21/0.45 % (23649)Memory used [KB]: 1023
% 0.21/0.45 % (23649)Time elapsed: 0.004 s
% 0.21/0.45 % (23649)Instructions burned: 3 (million)
% 0.21/0.45 % (23649)------------------------------
% 0.21/0.45 % (23649)------------------------------
% 0.21/0.45 % (23642)Instruction limit reached!
% 0.21/0.45 % (23642)------------------------------
% 0.21/0.45 % (23642)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (23642)Termination reason: Unknown
% 0.21/0.45 % (23642)Termination phase: Saturation
% 0.21/0.45
% 0.21/0.45 % (23642)Memory used [KB]: 5628
% 0.21/0.45 % (23642)Time elapsed: 0.031 s
% 0.21/0.45 % (23642)Instructions burned: 37 (million)
% 0.21/0.45 % (23642)------------------------------
% 0.21/0.45 % (23642)------------------------------
% 0.21/0.45 % (23647)Instruction limit reached!
% 0.21/0.45 % (23647)------------------------------
% 0.21/0.45 % (23647)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (23647)Termination reason: Unknown
% 0.21/0.45 % (23647)Termination phase: Saturation
% 0.21/0.45
% 0.21/0.45 % (23647)Memory used [KB]: 5884
% 0.21/0.45 % (23647)Time elapsed: 0.017 s
% 0.21/0.45 % (23647)Instructions burned: 16 (million)
% 0.21/0.45 % (23647)------------------------------
% 0.21/0.45 % (23647)------------------------------
% 0.21/0.45 % (23653)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.45 % (23652)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)
% 0.21/0.45 % (23653)Instruction limit reached!
% 0.21/0.45 % (23653)------------------------------
% 0.21/0.45 % (23653)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (23653)Termination reason: Unknown
% 0.21/0.45 % (23653)Termination phase: shuffling
% 0.21/0.45
% 0.21/0.45 % (23653)Memory used [KB]: 1023
% 0.21/0.45 % (23653)Time elapsed: 0.003 s
% 0.21/0.45 % (23653)Instructions burned: 4 (million)
% 0.21/0.45 % (23653)------------------------------
% 0.21/0.45 % (23653)------------------------------
% 0.21/0.46 % (23652)Instruction limit reached!
% 0.21/0.46 % (23652)------------------------------
% 0.21/0.46 % (23652)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (23652)Termination reason: Unknown
% 0.21/0.46 % (23652)Termination phase: Property scanning
% 0.21/0.46
% 0.21/0.46 % (23652)Memory used [KB]: 1023
% 0.21/0.46 % (23652)Time elapsed: 0.004 s
% 0.21/0.46 % (23652)Instructions burned: 4 (million)
% 0.21/0.46 % (23652)------------------------------
% 0.21/0.46 % (23652)------------------------------
% 0.21/0.46 % (23650)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)
% 0.21/0.46 % (23650)Instruction limit reached!
% 0.21/0.46 % (23650)------------------------------
% 0.21/0.46 % (23650)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (23650)Termination reason: Unknown
% 0.21/0.46 % (23650)Termination phase: Function definition elimination
% 0.21/0.46
% 0.21/0.46 % (23650)Memory used [KB]: 1023
% 0.21/0.46 % (23650)Time elapsed: 0.006 s
% 0.21/0.46 % (23650)Instructions burned: 8 (million)
% 0.21/0.46 % (23650)------------------------------
% 0.21/0.46 % (23650)------------------------------
% 0.21/0.46 % (23654)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)
% 0.21/0.46 % (23656)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.47 % (23655)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.47 % (23656)Instruction limit reached!
% 0.21/0.47 % (23656)------------------------------
% 0.21/0.47 % (23656)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (23656)Termination reason: Unknown
% 0.21/0.47 % (23656)Termination phase: Preprocessing 3
% 0.21/0.47
% 0.21/0.47 % (23656)Memory used [KB]: 1023
% 0.21/0.47 % (23656)Time elapsed: 0.004 s
% 0.21/0.47 % (23656)Instructions burned: 6 (million)
% 0.21/0.47 % (23656)------------------------------
% 0.21/0.47 % (23656)------------------------------
% 0.21/0.47 % (23657)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)
% 0.21/0.47 % (23658)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)
% 0.21/0.47 % (23655)Refutation not found, incomplete strategy
% 0.21/0.47 % (23655)------------------------------
% 0.21/0.47 % (23655)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (23655)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.47
% 0.21/0.47
% 0.21/0.47 % (23655)Memory used [KB]: 5628
% 0.21/0.47 % (23655)Time elapsed: 0.007 s
% 0.21/0.47 % (23655)Instructions burned: 9 (million)
% 0.21/0.47 % (23655)------------------------------
% 0.21/0.47 % (23655)------------------------------
% 0.21/0.47 % (23654)Instruction limit reached!
% 0.21/0.47 % (23654)------------------------------
% 0.21/0.47 % (23654)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (23654)Termination reason: Unknown
% 0.21/0.47 % (23654)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (23654)Memory used [KB]: 5628
% 0.21/0.47 % (23654)Time elapsed: 0.012 s
% 0.21/0.47 % (23654)Instructions burned: 18 (million)
% 0.21/0.47 % (23654)------------------------------
% 0.21/0.47 % (23654)------------------------------
% 0.21/0.47 % (23657)Refutation not found, incomplete strategy
% 0.21/0.47 % (23657)------------------------------
% 0.21/0.47 % (23657)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (23657)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.47
% 0.21/0.47
% 0.21/0.47 % (23657)Memory used [KB]: 5628
% 0.21/0.47 % (23657)Time elapsed: 0.007 s
% 0.21/0.47 % (23657)Instructions burned: 9 (million)
% 0.21/0.47 % (23657)------------------------------
% 0.21/0.47 % (23657)------------------------------
% 0.21/0.47 % (23659)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.21/0.48 % (23645)First to succeed.
% 0.21/0.48 % (23659)Instruction limit reached!
% 0.21/0.48 % (23659)------------------------------
% 0.21/0.48 % (23659)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48 % (23659)Termination reason: Unknown
% 0.21/0.48 % (23659)Termination phase: Property scanning
% 0.21/0.48
% 0.21/0.48 % (23659)Memory used [KB]: 1023
% 0.21/0.48 % (23659)Time elapsed: 0.004 s
% 0.21/0.48 % (23659)Instructions burned: 6 (million)
% 0.21/0.48 % (23659)------------------------------
% 0.21/0.48 % (23659)------------------------------
% 0.21/0.48 % (23658)Instruction limit reached!
% 0.21/0.48 % (23658)------------------------------
% 0.21/0.48 % (23658)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48 % (23658)Termination reason: Unknown
% 0.21/0.48 % (23658)Termination phase: Saturation
% 0.21/0.48
% 0.21/0.48 % (23658)Memory used [KB]: 5628
% 0.21/0.48 % (23658)Time elapsed: 0.014 s
% 0.21/0.48 % (23658)Instructions burned: 22 (million)
% 0.21/0.48 % (23658)------------------------------
% 0.21/0.48 % (23658)------------------------------
% 0.21/0.48 % (23660)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)
% 0.21/0.48 % (23645)Refutation found. Thanks to Tanya!
% 0.21/0.48 % SZS status Theorem for theBenchmark
% 0.21/0.48 % SZS output start Proof for theBenchmark
% 0.21/0.48 thf(type_def_5, type, mu: $tType).
% 0.21/0.48 thf(func_def_0, type, mu: $tType).
% 0.21/0.48 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.21/0.48 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.48 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.21/0.48 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.48 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.48 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.48 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.48 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.48 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.48 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.48 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.48 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.48 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.48 thf(func_def_15, type, mtrue: $i > $o).
% 0.21/0.48 thf(func_def_16, type, mfalse: $i > $o).
% 0.21/0.48 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.48 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.48 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.21/0.48 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.21/0.48 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.21/0.48 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.21/0.48 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.21/0.48 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.21/0.48 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.21/0.48 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.21/0.48 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.21/0.48 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.21/0.48 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.21/0.48 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.21/0.48 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.21/0.48 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.21/0.48 thf(func_def_33, type, rel_b: $i > $i > $o).
% 0.21/0.48 thf(func_def_34, type, mbox_b: ($i > $o) > $i > $o).
% 0.21/0.48 thf(func_def_35, type, mdia_b: ($i > $o) > $i > $o).
% 0.21/0.48 thf(func_def_36, type, p: $i > $o).
% 0.21/0.48 thf(func_def_53, type, ph1: !>[X0: $tType]:(X0)).
% 0.21/0.48 thf(f474,plain,(
% 0.21/0.48 $false),
% 0.21/0.48 inference(avatar_sat_refutation,[],[f188,f378,f473])).
% 0.21/0.48 thf(f473,plain,(
% 0.21/0.48 ~spl0_1),
% 0.21/0.48 inference(avatar_contradiction_clause,[],[f472])).
% 0.21/0.48 thf(f472,plain,(
% 0.21/0.48 $false | ~spl0_1),
% 0.21/0.48 inference(trivial_inequality_removal,[],[f471])).
% 0.21/0.48 thf(f471,plain,(
% 0.21/0.48 ($true = $false) | ~spl0_1),
% 0.21/0.48 inference(boolean_simplification,[],[f470])).
% 0.21/0.48 thf(f470,plain,(
% 0.21/0.48 ((~ $true) = $true) | ~spl0_1),
% 0.21/0.48 inference(backward_demodulation,[],[f460,f468])).
% 0.21/0.48 thf(f468,plain,(
% 0.21/0.48 ($true = (rel_b @ sK8 @ sK2)) | ~spl0_1),
% 0.21/0.48 inference(boolean_simplification,[],[f464])).
% 0.21/0.48 thf(f464,plain,(
% 0.21/0.48 ($true = ($true => (rel_b @ sK8 @ sK2))) | ~spl0_1),
% 0.21/0.48 inference(superposition,[],[f167,f446])).
% 0.21/0.48 thf(f446,plain,(
% 0.21/0.48 ((rel_b @ sK2 @ sK8) = $true) | ~spl0_1),
% 0.21/0.48 inference(not_proxy_clausification,[],[f419])).
% 0.21/0.48 thf(f419,plain,(
% 0.21/0.48 ((~ (rel_b @ sK2 @ sK8)) = $false) | ~spl0_1),
% 0.21/0.48 inference(binary_proxy_clausification,[],[f412])).
% 0.21/0.48 thf(f412,plain,(
% 0.21/0.48 ($false = ((~ (rel_b @ sK2 @ sK8)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK8 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2))))))))))))))) | ~spl0_1),
% 0.21/0.48 inference(beta_eta_normalization,[],[f411])).
% 0.21/0.48 thf(f411,plain,(
% 0.21/0.48 ($false = ((^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3))))))))))))))) @ sK8)) | ~spl0_1),
% 0.21/0.48 inference(sigma_clausification,[],[f385])).
% 0.21/0.48 thf(f385,plain,(
% 0.21/0.48 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) = $false) | ~spl0_1),
% 0.21/0.48 inference(binary_proxy_clausification,[],[f381])).
% 0.21/0.48 thf(f381,plain,(
% 0.21/0.48 (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))))) = $false) | ~spl0_1),
% 0.21/0.48 inference(not_proxy_clausification,[],[f184])).
% 0.21/0.48 thf(f184,plain,(
% 0.21/0.48 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))))))) | ~spl0_1),
% 0.21/0.48 inference(avatar_component_clause,[],[f183])).
% 0.21/0.48 thf(f183,plain,(
% 0.21/0.48 spl0_1 <=> ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1))))))))))))),
% 0.21/0.48 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.21/0.48 thf(f167,plain,(
% 0.21/0.48 ( ! [X2 : $i,X1 : $i] : (($true = ((rel_b @ X2 @ X1) => (rel_b @ X1 @ X2)))) )),
% 0.21/0.48 inference(beta_eta_normalization,[],[f166])).
% 0.21/0.48 thf(f166,plain,(
% 0.21/0.48 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((rel_b @ Y0 @ X1) => (rel_b @ X1 @ Y0))) @ X2) = $true)) )),
% 0.21/0.48 inference(pi_clausification,[],[f165])).
% 0.21/0.48 thf(f165,plain,(
% 0.21/0.48 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((rel_b @ Y0 @ X1) => (rel_b @ X1 @ Y0)))) = $true)) )),
% 0.21/0.48 inference(beta_eta_normalization,[],[f164])).
% 0.21/0.48 thf(f164,plain,(
% 0.21/0.48 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_b @ Y1 @ Y0) => (rel_b @ Y0 @ Y1))))) @ X1))) )),
% 0.21/0.48 inference(pi_clausification,[],[f157])).
% 0.21/0.48 thf(f157,plain,(
% 0.21/0.48 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_b @ Y1 @ Y0) => (rel_b @ Y0 @ Y1)))))) = $true)),
% 0.21/0.48 inference(beta_eta_normalization,[],[f154])).
% 0.21/0.48 thf(f154,plain,(
% 0.21/0.48 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))) @ rel_b))),
% 0.21/0.48 inference(definition_unfolding,[],[f109,f125])).
% 0.21/0.48 thf(f125,plain,(
% 0.21/0.48 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.21/0.48 inference(cnf_transformation,[],[f56])).
% 0.21/0.48 thf(f56,plain,(
% 0.21/0.48 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.21/0.48 inference(fool_elimination,[],[f55])).
% 0.21/0.48 thf(f55,plain,(
% 0.21/0.48 ((^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)))) = msymmetric)),
% 0.21/0.48 inference(rectify,[],[f19])).
% 0.21/0.48 thf(f19,axiom,(
% 0.21/0.48 ((^[X6 : $i > $i > $o] : (! [X8,X9] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))) = msymmetric)),
% 0.21/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)).
% 0.21/0.48 thf(f109,plain,(
% 0.21/0.48 ((msymmetric @ rel_b) = $true)),
% 0.21/0.48 inference(cnf_transformation,[],[f48])).
% 0.21/0.48 thf(f48,plain,(
% 0.21/0.48 ((msymmetric @ rel_b) = $true)),
% 0.21/0.48 inference(fool_elimination,[],[f47])).
% 0.21/0.48 thf(f47,plain,(
% 0.21/0.48 (msymmetric @ rel_b)),
% 0.21/0.48 inference(rectify,[],[f35])).
% 0.21/0.48 thf(f35,axiom,(
% 0.21/0.48 (msymmetric @ rel_b)),
% 0.21/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 0.21/0.48 thf(f460,plain,(
% 0.21/0.48 ((~ (rel_b @ sK8 @ sK2)) = $true) | ~spl0_1),
% 0.21/0.48 inference(boolean_simplification,[],[f459])).
% 0.21/0.48 thf(f459,plain,(
% 0.21/0.48 (((~ (rel_b @ sK8 @ sK2)) | $false) = $true) | ~spl0_1),
% 0.21/0.48 inference(boolean_simplification,[],[f454])).
% 0.21/0.48 thf(f454,plain,(
% 0.21/0.48 ($true = ((~ (rel_b @ sK8 @ sK2)) | (~ $true))) | ~spl0_1),
% 0.21/0.48 inference(superposition,[],[f445,f388])).
% 0.21/0.48 thf(f388,plain,(
% 0.21/0.48 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))) = $true) | ~spl0_1),
% 0.21/0.48 inference(not_proxy_clausification,[],[f387])).
% 0.21/0.48 thf(f387,plain,(
% 0.21/0.48 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))))) | ~spl0_1),
% 0.21/0.49 inference(boolean_simplification,[],[f386])).
% 0.21/0.49 thf(f386,plain,(
% 0.21/0.49 (($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))))) = $false) | ~spl0_1),
% 0.21/0.49 inference(backward_demodulation,[],[f381,f385])).
% 0.21/0.49 thf(f445,plain,(
% 0.21/0.49 ( ! [X1 : $i] : ((((~ (rel_b @ sK8 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))))) = $true)) ) | ~spl0_1),
% 0.21/0.49 inference(beta_eta_normalization,[],[f444])).
% 0.21/0.49 thf(f444,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_b @ sK8 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2))))))))))) @ X1))) ) | ~spl0_1),
% 0.21/0.49 inference(pi_clausification,[],[f429])).
% 0.21/0.49 thf(f429,plain,(
% 0.21/0.49 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK8 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2))))))))))))) | ~spl0_1),
% 0.21/0.49 inference(not_proxy_clausification,[],[f421])).
% 0.21/0.49 thf(f421,plain,(
% 0.21/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK8 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2))))))))))))) = $false) | ~spl0_1),
% 0.21/0.49 inference(boolean_simplification,[],[f420])).
% 0.21/0.49 thf(f420,plain,(
% 0.21/0.49 ($false = ($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK8 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2))))))))))))))) | ~spl0_1),
% 0.21/0.49 inference(backward_demodulation,[],[f412,f419])).
% 0.21/0.49 thf(f378,plain,(
% 0.21/0.49 ~spl0_2),
% 0.21/0.49 inference(avatar_contradiction_clause,[],[f377])).
% 0.21/0.49 thf(f377,plain,(
% 0.21/0.49 $false | ~spl0_2),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f376])).
% 0.21/0.49 thf(f376,plain,(
% 0.21/0.49 ($true = $false) | ~spl0_2),
% 0.21/0.49 inference(boolean_simplification,[],[f375])).
% 0.21/0.49 thf(f375,plain,(
% 0.21/0.49 ((~ $true) = $true) | ~spl0_2),
% 0.21/0.49 inference(forward_demodulation,[],[f370,f361])).
% 0.21/0.49 thf(f361,plain,(
% 0.21/0.49 ($true = (rel_b @ sK6 @ sK3)) | ~spl0_2),
% 0.21/0.49 inference(boolean_simplification,[],[f359])).
% 0.21/0.49 thf(f359,plain,(
% 0.21/0.49 ($true = ($true => (rel_b @ sK6 @ sK3))) | ~spl0_2),
% 0.21/0.49 inference(superposition,[],[f167,f346])).
% 0.21/0.49 thf(f346,plain,(
% 0.21/0.49 ($true = (rel_b @ sK3 @ sK6)) | ~spl0_2),
% 0.21/0.49 inference(not_proxy_clausification,[],[f343])).
% 0.21/0.49 thf(f343,plain,(
% 0.21/0.49 ((~ (rel_b @ sK3 @ sK6)) = $false) | ~spl0_2),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f335])).
% 0.21/0.49 thf(f335,plain,(
% 0.21/0.49 ($false = ((~ (rel_b @ sK3 @ sK6)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK6 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1))))))))))) | ~spl0_2),
% 0.21/0.49 inference(beta_eta_normalization,[],[f333])).
% 0.21/0.49 thf(f333,plain,(
% 0.21/0.49 (((^[Y0 : $i]: ((~ (rel_b @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2))))))))))) @ sK6) = $false) | ~spl0_2),
% 0.21/0.49 inference(sigma_clausification,[],[f321])).
% 0.21/0.49 thf(f321,plain,(
% 0.21/0.49 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2))))))))))))) | ~spl0_2),
% 0.21/0.49 inference(not_proxy_clausification,[],[f222])).
% 0.21/0.49 thf(f222,plain,(
% 0.21/0.49 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2)))))))))))))) | ~spl0_2),
% 0.21/0.49 inference(boolean_simplification,[],[f221])).
% 0.21/0.49 thf(f221,plain,(
% 0.21/0.49 (($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2)))))))))))))) = $true) | ~spl0_2),
% 0.21/0.49 inference(boolean_simplification,[],[f216])).
% 0.21/0.49 thf(f216,plain,(
% 0.21/0.49 ($true = ((~ $true) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2))))))))))))))) | ~spl0_2),
% 0.21/0.49 inference(superposition,[],[f208,f209])).
% 0.21/0.49 thf(f209,plain,(
% 0.21/0.49 ($true = (rel_b @ sK2 @ sK3)) | ~spl0_2),
% 0.21/0.49 inference(not_proxy_clausification,[],[f206])).
% 0.21/0.49 thf(f206,plain,(
% 0.21/0.49 ((~ (rel_b @ sK2 @ sK3)) = $false) | ~spl0_2),
% 0.21/0.49 inference(boolean_simplification,[],[f205])).
% 0.21/0.49 thf(f205,plain,(
% 0.21/0.49 (((~ (rel_b @ sK2 @ sK3)) | $false) = $false) | ~spl0_2),
% 0.21/0.49 inference(backward_demodulation,[],[f199,f203])).
% 0.21/0.49 thf(f203,plain,(
% 0.21/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK3 @ Y0)) | (p @ Y0))))) = $false) | ~spl0_2),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f199])).
% 0.21/0.49 thf(f199,plain,(
% 0.21/0.49 (((~ (rel_b @ sK2 @ sK3)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK3 @ Y0)) | (p @ Y0)))))) = $false) | ~spl0_2),
% 0.21/0.49 inference(beta_eta_normalization,[],[f198])).
% 0.21/0.49 thf(f198,plain,(
% 0.21/0.49 ($false = ((^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1))))))) @ sK3)) | ~spl0_2),
% 0.21/0.49 inference(sigma_clausification,[],[f195])).
% 0.21/0.49 thf(f195,plain,(
% 0.21/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))) = $false) | ~spl0_2),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f191])).
% 0.21/0.49 thf(f191,plain,(
% 0.21/0.49 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3))))))))))))))))))) | ~spl0_2),
% 0.21/0.49 inference(not_proxy_clausification,[],[f187])).
% 0.21/0.49 thf(f187,plain,(
% 0.21/0.49 ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3))))))))))))))))))) = $true) | ~spl0_2),
% 0.21/0.49 inference(avatar_component_clause,[],[f186])).
% 0.21/0.49 thf(f186,plain,(
% 0.21/0.49 spl0_2 <=> ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3))))))))))))))))))) = $true)),
% 0.21/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.21/0.49 thf(f208,plain,(
% 0.21/0.49 ( ! [X1 : $i] : ((((~ (rel_b @ sK2 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2)))))))))))))) = $true)) ) | ~spl0_2),
% 0.21/0.49 inference(beta_eta_normalization,[],[f207])).
% 0.21/0.49 thf(f207,plain,(
% 0.21/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3))))))))))))))) @ X1) = $true)) ) | ~spl0_2),
% 0.21/0.49 inference(pi_clausification,[],[f200])).
% 0.21/0.49 thf(f200,plain,(
% 0.21/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) = $true) | ~spl0_2),
% 0.21/0.49 inference(not_proxy_clausification,[],[f197])).
% 0.21/0.49 thf(f197,plain,(
% 0.21/0.49 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3)))))))))))))))))) | ~spl0_2),
% 0.21/0.49 inference(boolean_simplification,[],[f196])).
% 0.21/0.49 thf(f196,plain,(
% 0.21/0.49 (($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3)))))))))))))))))) = $false) | ~spl0_2),
% 0.21/0.49 inference(backward_demodulation,[],[f191,f195])).
% 0.21/0.49 thf(f370,plain,(
% 0.21/0.49 ((~ (rel_b @ sK6 @ sK3)) = $true) | ~spl0_2),
% 0.21/0.49 inference(boolean_simplification,[],[f369])).
% 0.21/0.49 thf(f369,plain,(
% 0.21/0.49 (((~ (rel_b @ sK6 @ sK3)) | $false) = $true) | ~spl0_2),
% 0.21/0.49 inference(boolean_simplification,[],[f366])).
% 0.21/0.49 thf(f366,plain,(
% 0.21/0.49 (((~ (rel_b @ sK6 @ sK3)) | (~ $true)) = $true) | ~spl0_2),
% 0.21/0.49 inference(superposition,[],[f357,f237])).
% 0.21/0.49 thf(f237,plain,(
% 0.21/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK3 @ Y0)) | (p @ Y0)))) = $true) | ~spl0_2),
% 0.21/0.49 inference(not_proxy_clausification,[],[f203])).
% 0.21/0.49 thf(f357,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = ((~ (rel_b @ sK6 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ X1 @ Y0)) | (p @ Y0)))))))) ) | ~spl0_2),
% 0.21/0.49 inference(beta_eta_normalization,[],[f356])).
% 0.21/0.49 thf(f356,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_b @ sK6 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1))))))) @ X1))) ) | ~spl0_2),
% 0.21/0.49 inference(pi_clausification,[],[f351])).
% 0.21/0.49 thf(f351,plain,(
% 0.21/0.49 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK6 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1))))))))) | ~spl0_2),
% 0.21/0.49 inference(not_proxy_clausification,[],[f345])).
% 0.21/0.49 thf(f345,plain,(
% 0.21/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK6 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1))))))))) = $false) | ~spl0_2),
% 0.21/0.49 inference(boolean_simplification,[],[f344])).
% 0.21/0.49 thf(f344,plain,(
% 0.21/0.49 (($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK6 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))))) = $false) | ~spl0_2),
% 0.21/0.49 inference(backward_demodulation,[],[f335,f343])).
% 0.21/0.49 thf(f188,plain,(
% 0.21/0.49 spl0_1 | spl0_2),
% 0.21/0.49 inference(avatar_split_clause,[],[f181,f186,f183])).
% 0.21/0.49 thf(f181,plain,(
% 0.21/0.49 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))))))) | ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3))))))))))))))))))) = $true)),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f178])).
% 0.21/0.49 thf(f178,plain,(
% 0.21/0.49 (((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3))))))))))))))))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))))))) = $true)),
% 0.21/0.49 inference(not_proxy_clausification,[],[f177])).
% 0.21/0.49 thf(f177,plain,(
% 0.21/0.49 ($false = (~ ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3))))))))))))))))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1))))))))))))))),
% 0.21/0.49 inference(beta_eta_normalization,[],[f176])).
% 0.21/0.49 thf(f176,plain,(
% 0.21/0.49 (((^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (p @ Y4))))))))))))))))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (p @ Y4)))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2)))))))))))))) @ sK2) = $false)),
% 0.21/0.49 inference(sigma_clausification,[],[f173])).
% 0.21/0.49 thf(f173,plain,(
% 0.21/0.49 ((!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (p @ Y4))))))))))))))))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (p @ Y4)))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2))))))))))))))) = $false)),
% 0.21/0.49 inference(not_proxy_clausification,[],[f161])).
% 0.21/0.49 thf(f161,plain,(
% 0.21/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (p @ Y4))))))))))))))))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (p @ Y4)))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2)))))))))))))))) = $true)),
% 0.21/0.49 inference(boolean_simplification,[],[f160])).
% 0.21/0.49 thf(f160,plain,(
% 0.21/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (p @ Y4))))))))))))))))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (p @ Y4)))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2)))))))))))))))) = $true)),
% 0.21/0.49 inference(boolean_simplification,[],[f159])).
% 0.21/0.49 thf(f159,plain,(
% 0.21/0.49 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (p @ Y4))))))))))))))))))) | (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2)))))))))))))))))),
% 0.21/0.49 inference(beta_eta_normalization,[],[f155])).
% 0.21/0.49 thf(f155,plain,(
% 0.21/0.49 ((~ ((^[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]: ((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_b @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p))))))) = $true)),
% 0.21/0.49 inference(definition_unfolding,[],[f129,f128,f147,f153,f115,f153,f115,f153,f115])).
% 0.21/0.49 thf(f115,plain,(
% 0.21/0.49 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f68])).
% 0.21/0.49 thf(f68,plain,(
% 0.21/0.49 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f67])).
% 0.21/0.49 thf(f67,plain,(
% 0.21/0.49 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_b @ X1 @ X2)))) = mbox_b)),
% 0.21/0.49 inference(rectify,[],[f32])).
% 0.21/0.49 thf(f32,axiom,(
% 0.21/0.49 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_b @ X2 @ X7)))) = mbox_b)),
% 0.21/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_b)).
% 0.21/0.49 thf(f153,plain,(
% 0.21/0.49 (mdia_b = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.21/0.49 inference(definition_unfolding,[],[f132,f134,f115,f134])).
% 0.21/0.49 thf(f134,plain,(
% 0.21/0.49 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f105])).
% 0.21/0.49 thf(f105,plain,(
% 0.21/0.49 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.49 inference(fool_elimination,[],[f104])).
% 0.21/0.49 thf(f104,plain,(
% 0.21/0.49 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.21/0.49 inference(rectify,[],[f3])).
% 0.21/0.49 thf(f3,axiom,(
% 0.21/0.49 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.21/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.21/0.49 thf(f132,plain,(
% 0.21/0.49 (mdia_b = (^[Y0 : $i > $o]: (mnot @ (mbox_b @ (mnot @ Y0)))))),
% 0.21/0.49 inference(cnf_transformation,[],[f44])).
% 0.21/0.49 thf(f44,plain,(
% 0.21/0.49 (mdia_b = (^[Y0 : $i > $o]: (mnot @ (mbox_b @ (mnot @ Y0)))))),
% 0.21/0.49 inference(fool_elimination,[],[f43])).
% 0.21/0.49 thf(f43,plain,(
% 0.21/0.49 ((^[X0 : $i > $o] : (mnot @ (mbox_b @ (mnot @ X0)))) = mdia_b)),
% 0.21/0.49 inference(rectify,[],[f33])).
% 0.21/0.49 thf(f33,axiom,(
% 0.21/0.49 ((^[X3 : $i > $o] : (mnot @ (mbox_b @ (mnot @ X3)))) = mdia_b)),
% 0.21/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_b)).
% 0.21/0.49 thf(f147,plain,(
% 0.21/0.49 (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]: ((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))))))),
% 0.21/0.49 inference(definition_unfolding,[],[f114,f144,f145,f145])).
% 0.21/0.49 thf(f145,plain,(
% 0.21/0.49 (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)))))),
% 0.21/0.49 inference(definition_unfolding,[],[f130,f119,f134])).
% 0.21/0.49 thf(f119,plain,(
% 0.21/0.49 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f99])).
% 0.21/0.49 thf(f99,plain,(
% 0.21/0.49 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f98])).
% 0.21/0.49 thf(f98,plain,(
% 0.21/0.49 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.21/0.49 inference(rectify,[],[f4])).
% 0.21/0.49 thf(f4,axiom,(
% 0.21/0.49 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.21/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.21/0.49 thf(f130,plain,(
% 0.21/0.49 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.49 inference(cnf_transformation,[],[f90])).
% 0.21/0.49 thf(f90,plain,(
% 0.21/0.49 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.49 inference(fool_elimination,[],[f89])).
% 0.21/0.49 thf(f89,plain,(
% 0.21/0.49 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.21/0.49 inference(rectify,[],[f6])).
% 0.21/0.49 thf(f6,axiom,(
% 0.21/0.49 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.21/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.21/0.49 thf(f144,plain,(
% 0.21/0.49 (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)))))))),
% 0.21/0.49 inference(definition_unfolding,[],[f126,f134,f119,f134,f134])).
% 0.21/0.49 thf(f126,plain,(
% 0.21/0.49 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f70])).
% 0.21/0.49 thf(f70,plain,(
% 0.21/0.49 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.21/0.49 inference(fool_elimination,[],[f69])).
% 0.21/0.49 thf(f69,plain,(
% 0.21/0.49 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.21/0.49 inference(rectify,[],[f5])).
% 0.21/0.49 thf(f5,axiom,(
% 0.21/0.49 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.21/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.21/0.49 thf(f114,plain,(
% 0.21/0.49 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f74])).
% 0.21/0.49 thf(f74,plain,(
% 0.21/0.49 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.21/0.49 inference(fool_elimination,[],[f73])).
% 0.21/0.49 thf(f73,plain,(
% 0.21/0.49 ((^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))) = mequiv)),
% 0.21/0.49 inference(rectify,[],[f8])).
% 0.21/0.49 thf(f8,axiom,(
% 0.21/0.49 ((^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))) = mequiv)),
% 0.21/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv)).
% 0.21/0.49 thf(f128,plain,(
% 0.21/0.49 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.49 inference(cnf_transformation,[],[f50])).
% 0.21/0.49 thf(f50,plain,(
% 0.21/0.49 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.49 inference(fool_elimination,[],[f49])).
% 0.21/0.49 thf(f49,plain,(
% 0.21/0.49 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.21/0.49 inference(rectify,[],[f28])).
% 0.21/0.49 thf(f28,axiom,(
% 0.21/0.49 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.21/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.21/0.49 thf(f129,plain,(
% 0.21/0.49 ($true = (~ (mvalid @ (mequiv @ (mdia_b @ (mbox_b @ p)) @ (mdia_b @ (mbox_b @ (mdia_b @ (mbox_b @ p))))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f88])).
% 0.21/0.49 thf(f88,plain,(
% 0.21/0.49 ($true = (~ (mvalid @ (mequiv @ (mdia_b @ (mbox_b @ p)) @ (mdia_b @ (mbox_b @ (mdia_b @ (mbox_b @ p))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f87])).
% 0.21/0.49 thf(f87,plain,(
% 0.21/0.49 ~(mvalid @ (mequiv @ (mdia_b @ (mbox_b @ p)) @ (mdia_b @ (mbox_b @ (mdia_b @ (mbox_b @ p))))))),
% 0.21/0.49 inference(rectify,[],[f37])).
% 0.21/0.49 thf(f37,negated_conjecture,(
% 0.21/0.49 ~(mvalid @ (mequiv @ (mdia_b @ (mbox_b @ p)) @ (mdia_b @ (mbox_b @ (mdia_b @ (mbox_b @ p))))))),
% 0.21/0.49 inference(negated_conjecture,[],[f36])).
% 0.21/0.49 thf(f36,conjecture,(
% 0.21/0.49 (mvalid @ (mequiv @ (mdia_b @ (mbox_b @ p)) @ (mdia_b @ (mbox_b @ (mdia_b @ (mbox_b @ p))))))),
% 0.21/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.21/0.49 % SZS output end Proof for theBenchmark
% 0.21/0.49 % (23645)------------------------------
% 0.21/0.49 % (23645)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49 % (23645)Termination reason: Refutation
% 0.21/0.49
% 0.21/0.49 % (23645)Memory used [KB]: 5884
% 0.21/0.49 % (23645)Time elapsed: 0.063 s
% 0.21/0.49 % (23645)Instructions burned: 67 (million)
% 0.21/0.49 % (23645)------------------------------
% 0.21/0.49 % (23645)------------------------------
% 0.21/0.49 % (23633)Success in time 0.106 s
% 0.21/0.49 % Vampire---4.8 exiting
%------------------------------------------------------------------------------