TSTP Solution File: SYO442^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO442^1 : 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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:04:27 EDT 2024
% Result : Theorem 0.17s 0.43s
% Output : Refutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SYO442^1 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.12 % 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
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon May 20 10:34:08 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 This is a TH0_THM_EQU_NAR problem
% 0.11/0.33 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
% 0.11/0.35 % (13998)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)
% 0.11/0.35 % (13997)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)
% 0.11/0.35 % (13995)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)
% 0.11/0.35 % (13993)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.35 % (13994)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)
% 0.11/0.35 % (13999)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.11/0.35 % (14000)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)
% 0.11/0.35 % (13997)Instruction limit reached!
% 0.11/0.35 % (13997)------------------------------
% 0.11/0.35 % (13997)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (13997)Termination reason: Unknown
% 0.11/0.35 % (13997)Termination phase: shuffling
% 0.11/0.35
% 0.11/0.35 % (13997)Memory used [KB]: 1023
% 0.11/0.35 % (13997)Time elapsed: 0.003 s
% 0.11/0.35 % (13997)Instructions burned: 3 (million)
% 0.11/0.35 % (13997)------------------------------
% 0.11/0.35 % (13997)------------------------------
% 0.11/0.35 % (13996)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.35 % (13996)Instruction limit reached!
% 0.11/0.35 % (13996)------------------------------
% 0.11/0.35 % (13996)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (13996)Termination reason: Unknown
% 0.11/0.35 % (13996)Termination phase: shuffling
% 0.11/0.35
% 0.11/0.35 % (13996)Memory used [KB]: 1023
% 0.11/0.35 % (13996)Time elapsed: 0.003 s
% 0.11/0.35 % (13996)Instructions burned: 2 (million)
% 0.11/0.35 % (13996)------------------------------
% 0.11/0.35 % (13996)------------------------------
% 0.11/0.35 % (14000)Instruction limit reached!
% 0.11/0.35 % (14000)------------------------------
% 0.11/0.35 % (14000)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (14000)Termination reason: Unknown
% 0.11/0.35 % (14000)Termination phase: shuffling
% 0.11/0.35
% 0.11/0.35 % (14000)Memory used [KB]: 1023
% 0.11/0.35 % (14000)Time elapsed: 0.003 s
% 0.11/0.35 % (14000)Instructions burned: 4 (million)
% 0.11/0.35 % (14000)------------------------------
% 0.11/0.35 % (14000)------------------------------
% 0.11/0.35 % (13994)Instruction limit reached!
% 0.11/0.35 % (13994)------------------------------
% 0.11/0.35 % (13994)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (13994)Termination reason: Unknown
% 0.11/0.35 % (13994)Termination phase: Property scanning
% 0.11/0.35
% 0.11/0.35 % (13994)Memory used [KB]: 1023
% 0.11/0.35 % (13994)Time elapsed: 0.004 s
% 0.11/0.35 % (13994)Instructions burned: 5 (million)
% 0.11/0.35 % (13994)------------------------------
% 0.11/0.35 % (13994)------------------------------
% 0.11/0.35 % (13998)Refutation not found, incomplete strategy
% 0.11/0.35 % (13998)------------------------------
% 0.11/0.35 % (13998)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (13998)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.35
% 0.11/0.35
% 0.11/0.35 % (13998)Memory used [KB]: 5628
% 0.11/0.35 % (13998)Time elapsed: 0.006 s
% 0.11/0.35 % (13998)Instructions burned: 9 (million)
% 0.11/0.35 % (13998)------------------------------
% 0.11/0.35 % (13998)------------------------------
% 0.11/0.36 % (13999)Instruction limit reached!
% 0.11/0.36 % (13999)------------------------------
% 0.11/0.36 % (13999)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.36 % (13999)Termination reason: Unknown
% 0.11/0.36 % (13999)Termination phase: Saturation
% 0.11/0.36
% 0.11/0.36 % (13999)Memory used [KB]: 5628
% 0.11/0.36 % (13999)Time elapsed: 0.010 s
% 0.11/0.36 % (13999)Instructions burned: 19 (million)
% 0.11/0.36 % (13999)------------------------------
% 0.11/0.36 % (13999)------------------------------
% 0.11/0.36 % (13995)Instruction limit reached!
% 0.11/0.36 % (13995)------------------------------
% 0.11/0.36 % (13995)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.36 % (13995)Termination reason: Unknown
% 0.11/0.36 % (13995)Termination phase: Saturation
% 0.11/0.36
% 0.11/0.36 % (13995)Memory used [KB]: 5628
% 0.11/0.36 % (13995)Time elapsed: 0.014 s
% 0.11/0.36 % (13995)Instructions burned: 28 (million)
% 0.11/0.36 % (13995)------------------------------
% 0.11/0.36 % (13995)------------------------------
% 0.11/0.36 % (14001)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)
% 0.11/0.37 % (14003)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)
% 0.11/0.37 % (14004)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)
% 0.11/0.37 % (14002)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)
% 0.11/0.37 % (14005)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.11/0.37 % (14003)Instruction limit reached!
% 0.11/0.37 % (14003)------------------------------
% 0.11/0.37 % (14003)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.37 % (14003)Termination reason: Unknown
% 0.11/0.37 % (14003)Termination phase: Property scanning
% 0.11/0.37
% 0.11/0.37 % (14003)Memory used [KB]: 1023
% 0.11/0.37 % (14003)Time elapsed: 0.004 s
% 0.11/0.37 % (14003)Instructions burned: 4 (million)
% 0.11/0.37 % (14003)------------------------------
% 0.11/0.37 % (14003)------------------------------
% 0.11/0.37 % (14005)Instruction limit reached!
% 0.11/0.37 % (14005)------------------------------
% 0.11/0.37 % (14005)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.37 % (14005)Termination reason: Unknown
% 0.11/0.37 % (14005)Termination phase: Function definition elimination
% 0.11/0.37
% 0.11/0.37 % (14005)Memory used [KB]: 1023
% 0.11/0.37 % (14005)Time elapsed: 0.005 s
% 0.11/0.37 % (14005)Instructions burned: 8 (million)
% 0.11/0.37 % (14005)------------------------------
% 0.11/0.37 % (14005)------------------------------
% 0.11/0.37 % (14006)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.11/0.37 % (14002)Instruction limit reached!
% 0.11/0.37 % (14002)------------------------------
% 0.11/0.37 % (14002)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.38 % (14002)Termination reason: Unknown
% 0.11/0.38 % (14002)Termination phase: Saturation
% 0.11/0.38
% 0.11/0.38 % (14002)Memory used [KB]: 5628
% 0.11/0.38 % (14002)Time elapsed: 0.010 s
% 0.11/0.38 % (14002)Instructions burned: 15 (million)
% 0.11/0.38 % (14002)------------------------------
% 0.11/0.38 % (14002)------------------------------
% 0.11/0.38 % (14007)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)
% 0.11/0.38 % (14007)Instruction limit reached!
% 0.11/0.38 % (14007)------------------------------
% 0.11/0.38 % (14007)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.38 % (14007)Termination reason: Unknown
% 0.11/0.38 % (14007)Termination phase: shuffling
% 0.11/0.38
% 0.11/0.38 % (14007)Memory used [KB]: 1023
% 0.11/0.38 % (14007)Time elapsed: 0.003 s
% 0.11/0.38 % (14007)Instructions burned: 3 (million)
% 0.11/0.38 % (14007)------------------------------
% 0.11/0.38 % (14007)------------------------------
% 0.11/0.38 % (14001)Instruction limit reached!
% 0.11/0.38 % (14001)------------------------------
% 0.11/0.38 % (14001)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.38 % (14001)Termination reason: Unknown
% 0.11/0.38 % (14001)Termination phase: Saturation
% 0.11/0.38
% 0.11/0.38 % (14001)Memory used [KB]: 5756
% 0.11/0.38 % (14001)Time elapsed: 0.018 s
% 0.11/0.38 % (14001)Instructions burned: 38 (million)
% 0.11/0.38 % (14001)------------------------------
% 0.11/0.38 % (14001)------------------------------
% 0.11/0.38 % (14008)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)
% 0.11/0.38 % (14006)Instruction limit reached!
% 0.11/0.38 % (14006)------------------------------
% 0.11/0.38 % (14006)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.38 % (14006)Termination reason: Unknown
% 0.11/0.38 % (14006)Termination phase: Saturation
% 0.11/0.38
% 0.11/0.38 % (14006)Memory used [KB]: 5756
% 0.11/0.38 % (14006)Time elapsed: 0.011 s
% 0.11/0.38 % (14006)Instructions burned: 17 (million)
% 0.11/0.38 % (14006)------------------------------
% 0.11/0.38 % (14006)------------------------------
% 0.11/0.38 % (14008)Instruction limit reached!
% 0.11/0.38 % (14008)------------------------------
% 0.11/0.38 % (14008)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.38 % (14008)Termination reason: Unknown
% 0.11/0.38 % (14008)Termination phase: Property scanning
% 0.11/0.38
% 0.11/0.38 % (14008)Memory used [KB]: 1023
% 0.11/0.38 % (14008)Time elapsed: 0.004 s
% 0.11/0.38 % (14008)Instructions burned: 4 (million)
% 0.11/0.38 % (14008)------------------------------
% 0.11/0.38 % (14008)------------------------------
% 0.11/0.39 % (14009)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)
% 0.11/0.39 % (14009)Instruction limit reached!
% 0.11/0.39 % (14009)------------------------------
% 0.11/0.39 % (14009)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.39 % (14009)Termination reason: Unknown
% 0.11/0.39 % (14009)Termination phase: Function definition elimination
% 0.11/0.39
% 0.11/0.39 % (14009)Memory used [KB]: 1023
% 0.11/0.39 % (14009)Time elapsed: 0.005 s
% 0.11/0.39 % (14009)Instructions burned: 7 (million)
% 0.11/0.39 % (14009)------------------------------
% 0.11/0.39 % (14009)------------------------------
% 0.11/0.39 % (14010)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)
% 0.11/0.39 % (14011)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.11/0.39 % (14010)Instruction limit reached!
% 0.11/0.39 % (14010)------------------------------
% 0.11/0.39 % (14010)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.39 % (14010)Termination reason: Unknown
% 0.11/0.39 % (14010)Termination phase: shuffling
% 0.11/0.39
% 0.11/0.39 % (14010)Memory used [KB]: 1023
% 0.11/0.39 % (14010)Time elapsed: 0.003 s
% 0.11/0.39 % (14010)Instructions burned: 3 (million)
% 0.11/0.39 % (14010)------------------------------
% 0.11/0.39 % (14010)------------------------------
% 0.11/0.39 % (14011)Instruction limit reached!
% 0.11/0.39 % (14011)------------------------------
% 0.11/0.39 % (14011)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.39 % (14011)Termination reason: Unknown
% 0.11/0.39 % (14011)Termination phase: Property scanning
% 0.11/0.39
% 0.11/0.39 % (14011)Memory used [KB]: 1023
% 0.11/0.39 % (14011)Time elapsed: 0.004 s
% 0.11/0.39 % (14011)Instructions burned: 5 (million)
% 0.11/0.39 % (14011)------------------------------
% 0.11/0.39 % (14011)------------------------------
% 0.11/0.39 % (14012)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)
% 0.11/0.40 % (14014)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.11/0.40 % (14013)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.11/0.40 % (14014)Instruction limit reached!
% 0.11/0.40 % (14014)------------------------------
% 0.11/0.40 % (14014)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.40 % (14014)Termination reason: Unknown
% 0.11/0.40 % (14014)Termination phase: Function definition elimination
% 0.11/0.40
% 0.11/0.40 % (14014)Memory used [KB]: 1023
% 0.11/0.40 % (14014)Time elapsed: 0.005 s
% 0.11/0.40 % (14014)Instructions burned: 8 (million)
% 0.11/0.40 % (14014)------------------------------
% 0.11/0.40 % (14014)------------------------------
% 0.11/0.40 % (14015)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)
% 0.17/0.40 % (14013)Refutation not found, incomplete strategy
% 0.17/0.40 % (14013)------------------------------
% 0.17/0.40 % (14013)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.40 % (14013)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.40
% 0.17/0.40
% 0.17/0.40 % (14013)Memory used [KB]: 5628
% 0.17/0.40 % (14013)Time elapsed: 0.006 s
% 0.17/0.40 % (14013)Instructions burned: 9 (million)
% 0.17/0.40 % (14013)------------------------------
% 0.17/0.40 % (14013)------------------------------
% 0.17/0.40 % (14012)Instruction limit reached!
% 0.17/0.40 % (14012)------------------------------
% 0.17/0.40 % (14012)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.40 % (14012)Termination reason: Unknown
% 0.17/0.40 % (14012)Termination phase: Saturation
% 0.17/0.40
% 0.17/0.40 % (14012)Memory used [KB]: 5628
% 0.17/0.40 % (14012)Time elapsed: 0.011 s
% 0.17/0.40 % (14012)Instructions burned: 19 (million)
% 0.17/0.40 % (14012)------------------------------
% 0.17/0.40 % (14012)------------------------------
% 0.17/0.41 % (14017)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.17/0.41 % (14015)Refutation not found, incomplete strategy
% 0.17/0.41 % (14015)------------------------------
% 0.17/0.41 % (14015)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.41 % (14015)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.41
% 0.17/0.41
% 0.17/0.41 % (14015)Memory used [KB]: 5628
% 0.17/0.41 % (14015)Time elapsed: 0.006 s
% 0.17/0.41 % (14015)Instructions burned: 9 (million)
% 0.17/0.41 % (14015)------------------------------
% 0.17/0.41 % (14015)------------------------------
% 0.17/0.41 % (14016)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)
% 0.17/0.41 % (14017)Instruction limit reached!
% 0.17/0.41 % (14017)------------------------------
% 0.17/0.41 % (14017)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.41 % (14017)Termination reason: Unknown
% 0.17/0.41 % (14017)Termination phase: Property scanning
% 0.17/0.41
% 0.17/0.41 % (14017)Memory used [KB]: 1023
% 0.17/0.41 % (14017)Time elapsed: 0.004 s
% 0.17/0.41 % (14017)Instructions burned: 6 (million)
% 0.17/0.41 % (14017)------------------------------
% 0.17/0.41 % (14017)------------------------------
% 0.17/0.41 % (14018)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)
% 0.17/0.42 % (14020)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.17/0.42 % (14019)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.17/0.42 % (14018)Instruction limit reached!
% 0.17/0.42 % (14018)------------------------------
% 0.17/0.42 % (14018)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.42 % (14018)Termination reason: Unknown
% 0.17/0.42 % (14018)Termination phase: Property scanning
% 0.17/0.42 % (14016)Instruction limit reached!
% 0.17/0.42 % (14016)------------------------------
% 0.17/0.42 % (14016)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.42
% 0.17/0.42 % (14018)Memory used [KB]: 1023
% 0.17/0.42 % (14018)Time elapsed: 0.005 s
% 0.17/0.42 % (14018)Instructions burned: 7 (million)
% 0.17/0.42 % (14018)------------------------------
% 0.17/0.42 % (14018)------------------------------
% 0.17/0.42 % (14016)Termination reason: Unknown
% 0.17/0.42 % (14016)Termination phase: Saturation
% 0.17/0.42
% 0.17/0.42 % (14016)Memory used [KB]: 5628
% 0.17/0.42 % (14016)Time elapsed: 0.012 s
% 0.17/0.42 % (14016)Instructions burned: 21 (million)
% 0.17/0.42 % (14016)------------------------------
% 0.17/0.42 % (14016)------------------------------
% 0.17/0.42 % (14021)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2999ds/19Mi)
% 0.17/0.42 % (14022)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2999ds/879Mi)
% 0.17/0.42 % (14004)First to succeed.
% 0.17/0.42 % (14021)Refutation not found, incomplete strategy
% 0.17/0.42 % (14021)------------------------------
% 0.17/0.42 % (14021)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.42 % (14021)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.42
% 0.17/0.42
% 0.17/0.42 % (14021)Memory used [KB]: 5628
% 0.17/0.42 % (14021)Time elapsed: 0.005 s
% 0.17/0.42 % (14021)Instructions burned: 8 (million)
% 0.17/0.42 % (14021)------------------------------
% 0.17/0.42 % (14021)------------------------------
% 0.17/0.43 % (14023)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.17/0.43 % (14024)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.17/0.43 % (14004)Refutation found. Thanks to Tanya!
% 0.17/0.43 % SZS status Theorem for theBenchmark
% 0.17/0.43 % SZS output start Proof for theBenchmark
% 0.17/0.43 thf(type_def_5, type, mu: $tType).
% 0.17/0.43 thf(func_def_0, type, mu: $tType).
% 0.17/0.43 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.17/0.43 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.17/0.43 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.17/0.43 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.17/0.43 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.17/0.43 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.17/0.43 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.17/0.43 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.17/0.43 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.17/0.43 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.17/0.43 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.17/0.43 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.17/0.43 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.17/0.43 thf(func_def_15, type, mtrue: $i > $o).
% 0.17/0.43 thf(func_def_16, type, mfalse: $i > $o).
% 0.17/0.43 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.17/0.43 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.17/0.43 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.17/0.43 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.17/0.43 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.17/0.43 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.17/0.43 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.17/0.43 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.17/0.43 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.17/0.43 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.17/0.43 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.17/0.43 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.17/0.43 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.17/0.43 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.17/0.43 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.17/0.43 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.17/0.43 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.17/0.43 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.17/0.43 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.17/0.43 thf(func_def_36, type, p: $i > $o).
% 0.17/0.43 thf(func_def_53, type, ph1: !>[X0: $tType]:(X0)).
% 0.17/0.43 thf(f822,plain,(
% 0.17/0.43 $false),
% 0.17/0.43 inference(avatar_sat_refutation,[],[f208,f627,f821])).
% 0.17/0.43 thf(f821,plain,(
% 0.17/0.43 ~spl0_1),
% 0.17/0.43 inference(avatar_contradiction_clause,[],[f820])).
% 0.17/0.43 thf(f820,plain,(
% 0.17/0.43 $false | ~spl0_1),
% 0.17/0.43 inference(trivial_inequality_removal,[],[f819])).
% 0.17/0.43 thf(f819,plain,(
% 0.17/0.43 ($false = $true) | ~spl0_1),
% 0.17/0.43 inference(boolean_simplification,[],[f818])).
% 0.17/0.43 thf(f818,plain,(
% 0.17/0.43 ((~ $true) = $true) | ~spl0_1),
% 0.17/0.43 inference(forward_demodulation,[],[f803,f662])).
% 0.17/0.43 thf(f662,plain,(
% 0.17/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))) | ~spl0_1),
% 0.17/0.43 inference(boolean_simplification,[],[f661])).
% 0.17/0.43 thf(f661,plain,(
% 0.17/0.43 (($false | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))) = $true) | ~spl0_1),
% 0.17/0.43 inference(boolean_simplification,[],[f659])).
% 0.17/0.43 thf(f659,plain,(
% 0.17/0.43 (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))) = $true) | ~spl0_1),
% 0.17/0.43 inference(superposition,[],[f657,f168])).
% 0.17/0.43 thf(f168,plain,(
% 0.17/0.43 ( ! [X1 : $i] : (((rel_s5 @ X1 @ X1) = $true)) )),
% 0.17/0.43 inference(beta_eta_normalization,[],[f167])).
% 0.17/0.43 thf(f167,plain,(
% 0.17/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: (rel_s5 @ Y0 @ Y0)) @ X1) = $true)) )),
% 0.17/0.43 inference(pi_clausification,[],[f166])).
% 0.17/0.43 thf(f166,plain,(
% 0.17/0.43 ((!! @ $i @ (^[Y0 : $i]: (rel_s5 @ Y0 @ Y0))) = $true)),
% 0.17/0.43 inference(beta_eta_normalization,[],[f161])).
% 0.17/0.43 thf(f161,plain,(
% 0.17/0.43 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s5) = $true)),
% 0.17/0.43 inference(definition_unfolding,[],[f134,f122])).
% 0.17/0.43 thf(f122,plain,(
% 0.17/0.43 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.17/0.43 inference(cnf_transformation,[],[f73])).
% 0.17/0.43 thf(f73,plain,(
% 0.17/0.43 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.17/0.43 inference(fool_elimination,[],[f72])).
% 0.17/0.43 thf(f72,plain,(
% 0.17/0.43 ((^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))) = mreflexive)),
% 0.17/0.43 inference(rectify,[],[f18])).
% 0.17/0.43 thf(f18,axiom,(
% 0.17/0.43 ((^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))) = mreflexive)),
% 0.17/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive)).
% 0.17/0.43 thf(f134,plain,(
% 0.17/0.43 ((mreflexive @ rel_s5) = $true)),
% 0.17/0.43 inference(cnf_transformation,[],[f51])).
% 0.17/0.43 thf(f51,plain,(
% 0.17/0.43 ((mreflexive @ rel_s5) = $true)),
% 0.17/0.43 inference(fool_elimination,[],[f50])).
% 0.17/0.43 thf(f50,plain,(
% 0.17/0.43 (mreflexive @ rel_s5)),
% 0.17/0.43 inference(rectify,[],[f34])).
% 0.17/0.43 thf(f34,axiom,(
% 0.17/0.43 (mreflexive @ rel_s5)),
% 0.17/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1)).
% 0.17/0.43 thf(f657,plain,(
% 0.17/0.43 ( ! [X1 : $i] : ((((~ (rel_s5 @ sK2 @ X1)) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (p @ Y0))))) = $true)) ) | ~spl0_1),
% 0.17/0.43 inference(beta_eta_normalization,[],[f656])).
% 0.17/0.43 thf(f656,plain,(
% 0.17/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))) @ X1) = $true)) ) | ~spl0_1),
% 0.17/0.43 inference(pi_clausification,[],[f653])).
% 0.17/0.43 thf(f653,plain,(
% 0.17/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))) = $true) | ~spl0_1),
% 0.17/0.43 inference(not_proxy_clausification,[],[f636])).
% 0.17/0.43 thf(f636,plain,(
% 0.17/0.43 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))))) | ~spl0_1),
% 0.17/0.43 inference(boolean_simplification,[],[f635])).
% 0.17/0.43 thf(f635,plain,(
% 0.17/0.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))) | $false)) | ~spl0_1),
% 0.17/0.43 inference(backward_demodulation,[],[f630,f633])).
% 0.17/0.43 thf(f633,plain,(
% 0.17/0.43 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | ~spl0_1),
% 0.17/0.43 inference(binary_proxy_clausification,[],[f630])).
% 0.17/0.43 thf(f630,plain,(
% 0.17/0.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3))))))))))))))))) | ~spl0_1),
% 0.17/0.43 inference(not_proxy_clausification,[],[f204])).
% 0.17/0.43 thf(f204,plain,(
% 0.17/0.43 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3))))))))))))))))) = $true) | ~spl0_1),
% 0.17/0.43 inference(avatar_component_clause,[],[f203])).
% 0.17/0.43 thf(f203,plain,(
% 0.17/0.43 spl0_1 <=> ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3))))))))))))))))) = $true)),
% 0.17/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.17/0.43 thf(f803,plain,(
% 0.17/0.43 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))) = $true) | ~spl0_1),
% 0.17/0.43 inference(boolean_simplification,[],[f802])).
% 0.17/0.43 thf(f802,plain,(
% 0.17/0.43 (($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0)))))) = $true) | ~spl0_1),
% 0.17/0.43 inference(boolean_simplification,[],[f801])).
% 0.17/0.43 thf(f801,plain,(
% 0.17/0.43 (((~ $true) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0)))))) = $true) | ~spl0_1),
% 0.17/0.43 inference(superposition,[],[f783,f685])).
% 0.17/0.43 thf(f685,plain,(
% 0.17/0.43 ((rel_s5 @ sK7 @ sK2) = $true) | ~spl0_1),
% 0.17/0.43 inference(trivial_inequality_removal,[],[f684])).
% 0.17/0.43 thf(f684,plain,(
% 0.17/0.43 ((rel_s5 @ sK7 @ sK2) = $true) | ($false = $true) | ~spl0_1),
% 0.17/0.43 inference(boolean_simplification,[],[f683])).
% 0.17/0.43 thf(f683,plain,(
% 0.17/0.43 (($true | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK7 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))))) = $false) | ((rel_s5 @ sK7 @ sK2) = $true) | ~spl0_1),
% 0.17/0.43 inference(boolean_simplification,[],[f682])).
% 0.17/0.43 thf(f682,plain,(
% 0.17/0.43 ((rel_s5 @ sK7 @ sK2) = $true) | (((~ $false) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK7 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))))) = $false) | ~spl0_1),
% 0.17/0.43 inference(superposition,[],[f677,f173])).
% 0.17/0.43 thf(f173,plain,(
% 0.17/0.43 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s5 @ X2 @ X1)) | ((rel_s5 @ X1 @ X2) = $true)) )),
% 0.17/0.43 inference(binary_proxy_clausification,[],[f172])).
% 0.17/0.43 thf(f172,plain,(
% 0.17/0.43 ( ! [X2 : $i,X1 : $i] : ((((rel_s5 @ X2 @ X1) => (rel_s5 @ X1 @ X2)) = $true)) )),
% 0.17/0.43 inference(beta_eta_normalization,[],[f171])).
% 0.17/0.43 thf(f171,plain,(
% 0.17/0.43 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((rel_s5 @ Y0 @ X1) => (rel_s5 @ X1 @ Y0))) @ X2))) )),
% 0.17/0.43 inference(pi_clausification,[],[f170])).
% 0.17/0.43 thf(f170,plain,(
% 0.17/0.43 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((rel_s5 @ Y0 @ X1) => (rel_s5 @ X1 @ Y0)))) = $true)) )),
% 0.17/0.43 inference(beta_eta_normalization,[],[f169])).
% 0.17/0.43 thf(f169,plain,(
% 0.17/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y1 @ Y0) => (rel_s5 @ Y0 @ Y1))))) @ X1) = $true)) )),
% 0.17/0.43 inference(pi_clausification,[],[f162])).
% 0.17/0.43 thf(f162,plain,(
% 0.17/0.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y1 @ Y0) => (rel_s5 @ Y0 @ Y1)))))) = $true)),
% 0.17/0.43 inference(beta_eta_normalization,[],[f159])).
% 0.17/0.43 thf(f159,plain,(
% 0.17/0.43 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))) @ rel_s5))),
% 0.17/0.43 inference(definition_unfolding,[],[f118,f125])).
% 0.17/0.43 thf(f125,plain,(
% 0.17/0.43 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.17/0.43 inference(cnf_transformation,[],[f71])).
% 0.17/0.43 thf(f71,plain,(
% 0.17/0.43 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.17/0.43 inference(fool_elimination,[],[f70])).
% 0.17/0.43 thf(f70,plain,(
% 0.17/0.43 ((^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)))) = msymmetric)),
% 0.17/0.43 inference(rectify,[],[f19])).
% 0.17/0.43 thf(f19,axiom,(
% 0.17/0.43 ((^[X6 : $i > $i > $o] : (! [X8,X9] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))) = msymmetric)),
% 0.17/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)).
% 0.17/0.43 thf(f118,plain,(
% 0.17/0.43 ((msymmetric @ rel_s5) = $true)),
% 0.17/0.43 inference(cnf_transformation,[],[f53])).
% 0.17/0.43 thf(f53,plain,(
% 0.17/0.43 ((msymmetric @ rel_s5) = $true)),
% 0.17/0.43 inference(fool_elimination,[],[f52])).
% 0.17/0.43 thf(f52,plain,(
% 0.17/0.43 (msymmetric @ rel_s5)),
% 0.17/0.43 inference(rectify,[],[f36])).
% 0.17/0.43 thf(f36,axiom,(
% 0.17/0.43 (msymmetric @ rel_s5)),
% 0.17/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3)).
% 0.17/0.43 thf(f677,plain,(
% 0.17/0.43 ($false = ((~ (rel_s5 @ sK2 @ sK7)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK7 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))))))))) | ~spl0_1),
% 0.17/0.43 inference(beta_eta_normalization,[],[f676])).
% 0.17/0.43 thf(f676,plain,(
% 0.17/0.43 (((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))) @ sK7) = $false) | ~spl0_1),
% 0.17/0.43 inference(sigma_clausification,[],[f633])).
% 0.17/0.43 thf(f783,plain,(
% 0.17/0.43 ( ! [X1 : $i] : ((((~ (rel_s5 @ sK7 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (p @ Y0)))))) = $true)) ) | ~spl0_1),
% 0.17/0.43 inference(beta_eta_normalization,[],[f780])).
% 0.17/0.43 thf(f780,plain,(
% 0.17/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s5 @ sK7 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))) @ X1) = $true)) ) | ~spl0_1),
% 0.17/0.43 inference(pi_clausification,[],[f736])).
% 0.17/0.43 thf(f736,plain,(
% 0.17/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK7 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))) = $true) | ~spl0_1),
% 0.17/0.43 inference(boolean_simplification,[],[f735])).
% 0.17/0.43 thf(f735,plain,(
% 0.17/0.43 (($false | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK7 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))))) = $true) | ~spl0_1),
% 0.17/0.43 inference(boolean_simplification,[],[f732])).
% 0.17/0.43 thf(f732,plain,(
% 0.17/0.43 ($true = ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK7 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))))) | ~spl0_1),
% 0.17/0.43 inference(superposition,[],[f728,f168])).
% 0.17/0.43 thf(f728,plain,(
% 0.17/0.43 ( ! [X1 : $i] : ((((~ (rel_s5 @ sK7 @ X1)) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))))) = $true)) ) | ~spl0_1),
% 0.17/0.43 inference(beta_eta_normalization,[],[f727])).
% 0.17/0.43 thf(f727,plain,(
% 0.17/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s5 @ sK7 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))))) @ X1) = $true)) ) | ~spl0_1),
% 0.17/0.43 inference(pi_clausification,[],[f704])).
% 0.17/0.43 thf(f704,plain,(
% 0.17/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK7 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))) = $true) | ~spl0_1),
% 0.17/0.43 inference(not_proxy_clausification,[],[f680])).
% 0.17/0.43 thf(f680,plain,(
% 0.17/0.43 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK7 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))))) | ~spl0_1),
% 0.17/0.43 inference(binary_proxy_clausification,[],[f677])).
% 0.17/0.43 thf(f627,plain,(
% 0.17/0.43 ~spl0_2),
% 0.17/0.43 inference(avatar_contradiction_clause,[],[f626])).
% 0.17/0.43 thf(f626,plain,(
% 0.17/0.43 $false | ~spl0_2),
% 0.17/0.43 inference(trivial_inequality_removal,[],[f625])).
% 0.17/0.43 thf(f625,plain,(
% 0.17/0.43 ($false = $true) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f624])).
% 0.17/0.43 thf(f624,plain,(
% 0.17/0.43 ((~ $true) = $true) | ~spl0_2),
% 0.17/0.43 inference(forward_demodulation,[],[f622,f524])).
% 0.17/0.43 thf(f524,plain,(
% 0.17/0.43 ((rel_s5 @ sK4 @ sK5) = $true) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f517])).
% 0.17/0.43 thf(f517,plain,(
% 0.17/0.43 (($true => (rel_s5 @ sK4 @ sK5)) = $true) | ~spl0_2),
% 0.17/0.43 inference(superposition,[],[f322,f448])).
% 0.17/0.43 thf(f448,plain,(
% 0.17/0.43 ((rel_s5 @ sK4 @ sK2) = $true) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f445])).
% 0.17/0.43 thf(f445,plain,(
% 0.17/0.43 (($true => (rel_s5 @ sK4 @ sK2)) = $true) | ~spl0_2),
% 0.17/0.43 inference(superposition,[],[f172,f422])).
% 0.17/0.43 thf(f422,plain,(
% 0.17/0.43 ((rel_s5 @ sK2 @ sK4) = $true) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f420])).
% 0.17/0.43 thf(f420,plain,(
% 0.17/0.43 (($true => (rel_s5 @ sK2 @ sK4)) = $true) | ~spl0_2),
% 0.17/0.43 inference(superposition,[],[f242,f270])).
% 0.17/0.43 thf(f270,plain,(
% 0.17/0.43 ((rel_s5 @ sK3 @ sK4) = $true) | ~spl0_2),
% 0.17/0.43 inference(not_proxy_clausification,[],[f262])).
% 0.17/0.43 thf(f262,plain,(
% 0.17/0.43 ($false = (~ (rel_s5 @ sK3 @ sK4))) | ~spl0_2),
% 0.17/0.43 inference(binary_proxy_clausification,[],[f250])).
% 0.17/0.43 thf(f250,plain,(
% 0.17/0.43 (((~ (rel_s5 @ sK3 @ sK4)) | (p @ sK4)) = $false) | ~spl0_2),
% 0.17/0.43 inference(beta_eta_normalization,[],[f249])).
% 0.17/0.43 thf(f249,plain,(
% 0.17/0.43 ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (p @ Y0))) @ sK4)) | ~spl0_2),
% 0.17/0.43 inference(sigma_clausification,[],[f226])).
% 0.17/0.43 thf(f226,plain,(
% 0.17/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (p @ Y0)))) = $false) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f225])).
% 0.17/0.43 thf(f225,plain,(
% 0.17/0.43 (($false | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (p @ Y0))))) = $false) | ~spl0_2),
% 0.17/0.43 inference(backward_demodulation,[],[f219,f224])).
% 0.17/0.43 thf(f224,plain,(
% 0.17/0.43 ($false = (~ (rel_s5 @ sK2 @ sK3))) | ~spl0_2),
% 0.17/0.43 inference(binary_proxy_clausification,[],[f219])).
% 0.17/0.43 thf(f219,plain,(
% 0.17/0.43 ($false = ((~ (rel_s5 @ sK2 @ sK3)) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (p @ Y0)))))) | ~spl0_2),
% 0.17/0.43 inference(beta_eta_normalization,[],[f218])).
% 0.17/0.43 thf(f218,plain,(
% 0.17/0.43 (((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))) @ sK3) = $false) | ~spl0_2),
% 0.17/0.43 inference(sigma_clausification,[],[f214])).
% 0.17/0.43 thf(f214,plain,(
% 0.17/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))) = $false) | ~spl0_2),
% 0.17/0.43 inference(binary_proxy_clausification,[],[f211])).
% 0.17/0.43 thf(f211,plain,(
% 0.17/0.43 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))) = $false) | ~spl0_2),
% 0.17/0.43 inference(not_proxy_clausification,[],[f207])).
% 0.17/0.43 thf(f207,plain,(
% 0.17/0.43 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))))) = $true) | ~spl0_2),
% 0.17/0.43 inference(avatar_component_clause,[],[f206])).
% 0.17/0.43 thf(f206,plain,(
% 0.17/0.43 spl0_2 <=> ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))))) = $true)),
% 0.17/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.17/0.43 thf(f242,plain,(
% 0.17/0.43 ( ! [X0 : $i] : (($true = ((rel_s5 @ sK3 @ X0) => (rel_s5 @ sK2 @ X0)))) ) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f237])).
% 0.17/0.43 thf(f237,plain,(
% 0.17/0.43 ( ! [X0 : $i] : (($true = (($true & (rel_s5 @ sK3 @ X0)) => (rel_s5 @ sK2 @ X0)))) ) | ~spl0_2),
% 0.17/0.43 inference(superposition,[],[f183,f229])).
% 0.17/0.43 thf(f229,plain,(
% 0.17/0.43 ($true = (rel_s5 @ sK2 @ sK3)) | ~spl0_2),
% 0.17/0.43 inference(not_proxy_clausification,[],[f224])).
% 0.17/0.43 thf(f183,plain,(
% 0.17/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((rel_s5 @ X1 @ X3) & (rel_s5 @ X3 @ X2)) => (rel_s5 @ X1 @ X2)) = $true)) )),
% 0.17/0.43 inference(beta_eta_normalization,[],[f182])).
% 0.17/0.43 thf(f182,plain,(
% 0.17/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((rel_s5 @ X1 @ Y0) & (rel_s5 @ Y0 @ X2)) => (rel_s5 @ X1 @ X2))) @ X3))) )),
% 0.17/0.43 inference(pi_clausification,[],[f181])).
% 0.17/0.43 thf(f181,plain,(
% 0.17/0.43 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s5 @ X1 @ Y0) & (rel_s5 @ Y0 @ X2)) => (rel_s5 @ X1 @ X2)))))) )),
% 0.17/0.43 inference(beta_eta_normalization,[],[f180])).
% 0.17/0.43 thf(f180,plain,(
% 0.17/0.43 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ X1 @ Y1) & (rel_s5 @ Y1 @ Y0)) => (rel_s5 @ X1 @ Y0))))) @ X2) = $true)) )),
% 0.17/0.43 inference(pi_clausification,[],[f179])).
% 0.17/0.43 thf(f179,plain,(
% 0.17/0.43 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ X1 @ Y1) & (rel_s5 @ Y1 @ Y0)) => (rel_s5 @ X1 @ Y0)))))) = $true)) )),
% 0.17/0.43 inference(beta_eta_normalization,[],[f178])).
% 0.17/0.43 thf(f178,plain,(
% 0.17/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y0 @ Y2) & (rel_s5 @ Y2 @ Y1)) => (rel_s5 @ Y0 @ Y1))))))) @ X1))) )),
% 0.17/0.43 inference(pi_clausification,[],[f165])).
% 0.17/0.43 thf(f165,plain,(
% 0.17/0.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y0 @ Y2) & (rel_s5 @ Y2 @ Y1)) => (rel_s5 @ Y0 @ Y1)))))))) = $true)),
% 0.17/0.43 inference(beta_eta_normalization,[],[f160])).
% 0.17/0.43 thf(f160,plain,(
% 0.17/0.43 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) @ rel_s5) = $true)),
% 0.17/0.43 inference(definition_unfolding,[],[f130,f128])).
% 0.17/0.43 thf(f128,plain,(
% 0.17/0.43 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.17/0.43 inference(cnf_transformation,[],[f47])).
% 0.17/0.43 thf(f47,plain,(
% 0.17/0.43 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.17/0.43 inference(fool_elimination,[],[f46])).
% 0.17/0.43 thf(f46,plain,(
% 0.17/0.43 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X2) & (X0 @ X3 @ X1)) => (X0 @ X3 @ X2)))) = mtransitive)),
% 0.17/0.43 inference(rectify,[],[f21])).
% 0.17/0.43 thf(f21,axiom,(
% 0.17/0.43 ((^[X6 : $i > $i > $o] : (! [X9,X10,X8] : (((X6 @ X9 @ X10) & (X6 @ X8 @ X9)) => (X6 @ X8 @ X10)))) = mtransitive)),
% 0.17/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)).
% 0.17/0.43 thf(f130,plain,(
% 0.17/0.43 ((mtransitive @ rel_s5) = $true)),
% 0.17/0.43 inference(cnf_transformation,[],[f106])).
% 0.17/0.43 thf(f106,plain,(
% 0.17/0.43 ((mtransitive @ rel_s5) = $true)),
% 0.17/0.43 inference(fool_elimination,[],[f105])).
% 0.17/0.43 thf(f105,plain,(
% 0.17/0.43 (mtransitive @ rel_s5)),
% 0.17/0.43 inference(rectify,[],[f35])).
% 0.17/0.43 thf(f35,axiom,(
% 0.17/0.43 (mtransitive @ rel_s5)),
% 0.17/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 0.17/0.43 thf(f322,plain,(
% 0.17/0.43 ( ! [X0 : $i] : ((((rel_s5 @ X0 @ sK2) => (rel_s5 @ X0 @ sK5)) = $true)) ) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f315])).
% 0.17/0.43 thf(f315,plain,(
% 0.17/0.43 ( ! [X0 : $i] : (((((rel_s5 @ X0 @ sK2) & $true) => (rel_s5 @ X0 @ sK5)) = $true)) ) | ~spl0_2),
% 0.17/0.43 inference(superposition,[],[f183,f304])).
% 0.17/0.43 thf(f304,plain,(
% 0.17/0.43 ((rel_s5 @ sK2 @ sK5) = $true) | ~spl0_2),
% 0.17/0.43 inference(not_proxy_clausification,[],[f289])).
% 0.17/0.43 thf(f289,plain,(
% 0.17/0.43 ($false = (~ (rel_s5 @ sK2 @ sK5))) | ~spl0_2),
% 0.17/0.43 inference(binary_proxy_clausification,[],[f277])).
% 0.17/0.43 thf(f277,plain,(
% 0.17/0.43 ($false = ((~ (rel_s5 @ sK2 @ sK5)) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))))) | ~spl0_2),
% 0.17/0.43 inference(beta_eta_normalization,[],[f273])).
% 0.17/0.43 thf(f273,plain,(
% 0.17/0.43 ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))))) @ sK5)) | ~spl0_2),
% 0.17/0.43 inference(sigma_clausification,[],[f265])).
% 0.17/0.43 thf(f265,plain,(
% 0.17/0.43 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))))))) | ~spl0_2),
% 0.17/0.43 inference(not_proxy_clausification,[],[f235])).
% 0.17/0.43 thf(f235,plain,(
% 0.17/0.43 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))))))) = $true) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f234])).
% 0.17/0.43 thf(f234,plain,(
% 0.17/0.43 (($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))))) = $true) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f233])).
% 0.17/0.43 thf(f233,plain,(
% 0.17/0.43 (((~ $true) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))))) = $true) | ~spl0_2),
% 0.17/0.43 inference(superposition,[],[f228,f168])).
% 0.17/0.43 thf(f228,plain,(
% 0.17/0.43 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK2 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))))))) ) | ~spl0_2),
% 0.17/0.43 inference(beta_eta_normalization,[],[f227])).
% 0.17/0.43 thf(f227,plain,(
% 0.17/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))) @ X1))) ) | ~spl0_2),
% 0.17/0.43 inference(pi_clausification,[],[f220])).
% 0.17/0.43 thf(f220,plain,(
% 0.17/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3))))))))))))))) = $true) | ~spl0_2),
% 0.17/0.43 inference(not_proxy_clausification,[],[f217])).
% 0.17/0.43 thf(f217,plain,(
% 0.17/0.43 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) = $false) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f216])).
% 0.17/0.43 thf(f216,plain,(
% 0.17/0.43 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | $false)) | ~spl0_2),
% 0.17/0.43 inference(backward_demodulation,[],[f211,f214])).
% 0.17/0.43 thf(f622,plain,(
% 0.17/0.43 ((~ (rel_s5 @ sK4 @ sK5)) = $true) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f609])).
% 0.17/0.43 thf(f609,plain,(
% 0.17/0.43 (((rel_s5 @ sK4 @ sK5) => $false) = $true) | ~spl0_2),
% 0.17/0.43 inference(superposition,[],[f361,f397])).
% 0.17/0.43 thf(f397,plain,(
% 0.17/0.43 ($false = (rel_s5 @ sK4 @ sK6)) | ~spl0_2),
% 0.17/0.43 inference(not_proxy_clausification,[],[f390])).
% 0.17/0.43 thf(f390,plain,(
% 0.17/0.43 ((~ (rel_s5 @ sK4 @ sK6)) = $true) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f387])).
% 0.17/0.43 thf(f387,plain,(
% 0.17/0.43 ($true = ((rel_s5 @ sK4 @ sK6) => $false)) | ~spl0_2),
% 0.17/0.43 inference(superposition,[],[f172,f375])).
% 0.17/0.43 thf(f375,plain,(
% 0.17/0.43 ($false = (rel_s5 @ sK6 @ sK4)) | ~spl0_2),
% 0.17/0.43 inference(not_proxy_clausification,[],[f347])).
% 0.17/0.43 thf(f347,plain,(
% 0.17/0.43 ($true = (~ (rel_s5 @ sK6 @ sK4))) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f345])).
% 0.17/0.43 thf(f345,plain,(
% 0.17/0.43 (((~ (rel_s5 @ sK6 @ sK4)) | $false) = $true) | ~spl0_2),
% 0.17/0.43 inference(superposition,[],[f340,f264])).
% 0.17/0.43 thf(f264,plain,(
% 0.17/0.43 ((p @ sK4) = $false) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f263])).
% 0.17/0.43 thf(f263,plain,(
% 0.17/0.43 ($false = ($false | (p @ sK4))) | ~spl0_2),
% 0.17/0.43 inference(backward_demodulation,[],[f250,f262])).
% 0.17/0.43 thf(f340,plain,(
% 0.17/0.43 ( ! [X1 : $i] : ((((~ (rel_s5 @ sK6 @ X1)) | (p @ X1)) = $true)) ) | ~spl0_2),
% 0.17/0.43 inference(beta_eta_normalization,[],[f339])).
% 0.17/0.43 thf(f339,plain,(
% 0.17/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s5 @ sK6 @ Y0)) | (p @ Y0))) @ X1) = $true)) ) | ~spl0_2),
% 0.17/0.43 inference(pi_clausification,[],[f326])).
% 0.17/0.43 thf(f326,plain,(
% 0.17/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK6 @ Y0)) | (p @ Y0)))) = $true) | ~spl0_2),
% 0.17/0.43 inference(not_proxy_clausification,[],[f312])).
% 0.17/0.43 thf(f312,plain,(
% 0.17/0.43 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK6 @ Y0)) | (p @ Y0))))) = $false) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f311])).
% 0.17/0.43 thf(f311,plain,(
% 0.17/0.43 (($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK6 @ Y0)) | (p @ Y0)))))) = $false) | ~spl0_2),
% 0.17/0.43 inference(backward_demodulation,[],[f303,f310])).
% 0.17/0.43 thf(f310,plain,(
% 0.17/0.43 ($false = (~ (rel_s5 @ sK5 @ sK6))) | ~spl0_2),
% 0.17/0.43 inference(binary_proxy_clausification,[],[f303])).
% 0.17/0.43 thf(f303,plain,(
% 0.17/0.43 (((~ (rel_s5 @ sK5 @ sK6)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK6 @ Y0)) | (p @ Y0)))))) = $false) | ~spl0_2),
% 0.17/0.43 inference(beta_eta_normalization,[],[f302])).
% 0.17/0.43 thf(f302,plain,(
% 0.17/0.43 ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))) @ sK6)) | ~spl0_2),
% 0.17/0.43 inference(sigma_clausification,[],[f291])).
% 0.17/0.43 thf(f291,plain,(
% 0.17/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))) = $false) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f290])).
% 0.17/0.43 thf(f290,plain,(
% 0.17/0.43 ($false = ($false | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))))) | ~spl0_2),
% 0.17/0.43 inference(backward_demodulation,[],[f277,f289])).
% 0.17/0.43 thf(f361,plain,(
% 0.17/0.43 ( ! [X0 : $i] : ((((rel_s5 @ X0 @ sK5) => (rel_s5 @ X0 @ sK6)) = $true)) ) | ~spl0_2),
% 0.17/0.43 inference(boolean_simplification,[],[f353])).
% 0.17/0.43 thf(f353,plain,(
% 0.17/0.43 ( ! [X0 : $i] : (((((rel_s5 @ X0 @ sK5) & $true) => (rel_s5 @ X0 @ sK6)) = $true)) ) | ~spl0_2),
% 0.17/0.43 inference(superposition,[],[f183,f341])).
% 0.17/0.43 thf(f341,plain,(
% 0.17/0.43 ((rel_s5 @ sK5 @ sK6) = $true) | ~spl0_2),
% 0.17/0.43 inference(not_proxy_clausification,[],[f310])).
% 0.17/0.43 thf(f208,plain,(
% 0.17/0.43 spl0_1 | spl0_2),
% 0.17/0.43 inference(avatar_split_clause,[],[f201,f206,f203])).
% 0.17/0.43 thf(f201,plain,(
% 0.17/0.43 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3))))))))))))))))) = $true) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))))) = $true)),
% 0.17/0.43 inference(binary_proxy_clausification,[],[f198])).
% 0.17/0.43 thf(f198,plain,(
% 0.17/0.43 (((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))))) = $true)),
% 0.17/0.43 inference(not_proxy_clausification,[],[f197])).
% 0.17/0.43 thf(f197,plain,(
% 0.17/0.43 ($false = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3))))))))))))))))))))),
% 0.17/0.43 inference(beta_eta_normalization,[],[f196])).
% 0.17/0.43 thf(f196,plain,(
% 0.17/0.43 ($false = ((^[Y0 : $i]: (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))))) @ sK2))),
% 0.17/0.43 inference(sigma_clausification,[],[f193])).
% 0.17/0.43 thf(f193,plain,(
% 0.17/0.43 ((!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4))))))))))))))))))))) = $false)),
% 0.17/0.43 inference(not_proxy_clausification,[],[f164])).
% 0.17/0.43 thf(f164,plain,(
% 0.17/0.43 ((~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))))))) = $true)),
% 0.17/0.43 inference(boolean_simplification,[],[f163])).
% 0.17/0.43 thf(f163,plain,(
% 0.17/0.43 ((~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s5 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))))))))) = $true)),
% 0.17/0.43 inference(beta_eta_normalization,[],[f158])).
% 0.17/0.43 thf(f158,plain,(
% 0.17/0.43 ((~ ((^[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]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p))))) = $true)),
% 0.17/0.43 inference(definition_unfolding,[],[f111,f143,f151,f129,f157,f157,f129,f129,f129])).
% 0.17/0.43 thf(f157,plain,(
% 0.17/0.43 (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)))))),
% 0.17/0.43 inference(definition_unfolding,[],[f138,f142,f129,f142])).
% 0.17/0.43 thf(f142,plain,(
% 0.17/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.17/0.43 inference(cnf_transformation,[],[f61])).
% 0.17/0.43 thf(f61,plain,(
% 0.17/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.17/0.43 inference(fool_elimination,[],[f60])).
% 0.17/0.43 thf(f60,plain,(
% 0.17/0.43 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.17/0.43 inference(rectify,[],[f3])).
% 0.17/0.43 thf(f3,axiom,(
% 0.17/0.43 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.17/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.17/0.43 thf(f138,plain,(
% 0.17/0.43 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.17/0.43 inference(cnf_transformation,[],[f94])).
% 0.17/0.43 thf(f94,plain,(
% 0.17/0.43 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.17/0.43 inference(fool_elimination,[],[f93])).
% 0.17/0.43 thf(f93,plain,(
% 0.17/0.43 ((^[X0 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X0)))) = mdia_s5)),
% 0.17/0.43 inference(rectify,[],[f33])).
% 0.17/0.43 thf(f33,axiom,(
% 0.17/0.43 ((^[X3 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X3)))) = mdia_s5)),
% 0.17/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s5)).
% 0.17/0.43 thf(f129,plain,(
% 0.17/0.43 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.17/0.43 inference(cnf_transformation,[],[f84])).
% 0.17/0.43 thf(f84,plain,(
% 0.17/0.43 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.17/0.43 inference(fool_elimination,[],[f83])).
% 0.17/0.43 thf(f83,plain,(
% 0.17/0.43 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s5 @ X1 @ X2)))) = mbox_s5)),
% 0.17/0.43 inference(rectify,[],[f32])).
% 0.17/0.43 thf(f32,axiom,(
% 0.17/0.43 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_s5 @ X2 @ X7)))) = mbox_s5)),
% 0.17/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s5)).
% 0.17/0.43 thf(f151,plain,(
% 0.17/0.43 (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))))))),
% 0.17/0.43 inference(definition_unfolding,[],[f121,f148,f149,f149])).
% 0.17/0.43 thf(f149,plain,(
% 0.17/0.43 (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)))))),
% 0.17/0.43 inference(definition_unfolding,[],[f132,f137,f142])).
% 0.17/0.43 thf(f137,plain,(
% 0.17/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.17/0.43 inference(cnf_transformation,[],[f90])).
% 0.17/0.43 thf(f90,plain,(
% 0.17/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.17/0.43 inference(fool_elimination,[],[f89])).
% 0.17/0.43 thf(f89,plain,(
% 0.17/0.43 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.17/0.43 inference(rectify,[],[f4])).
% 0.17/0.43 thf(f4,axiom,(
% 0.17/0.43 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.17/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.17/0.43 thf(f132,plain,(
% 0.17/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.17/0.43 inference(cnf_transformation,[],[f103])).
% 0.17/0.43 thf(f103,plain,(
% 0.17/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.17/0.43 inference(fool_elimination,[],[f102])).
% 0.17/0.43 thf(f102,plain,(
% 0.17/0.43 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.17/0.43 inference(rectify,[],[f6])).
% 0.17/0.43 thf(f6,axiom,(
% 0.17/0.43 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.17/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.17/0.43 thf(f148,plain,(
% 0.17/0.43 (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)))))))),
% 0.17/0.43 inference(definition_unfolding,[],[f145,f142,f137,f142,f142])).
% 0.17/0.43 thf(f145,plain,(
% 0.17/0.43 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.17/0.43 inference(cnf_transformation,[],[f92])).
% 0.17/0.43 thf(f92,plain,(
% 0.17/0.43 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.17/0.43 inference(fool_elimination,[],[f91])).
% 0.17/0.43 thf(f91,plain,(
% 0.17/0.43 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.17/0.43 inference(rectify,[],[f5])).
% 0.17/0.43 thf(f5,axiom,(
% 0.17/0.43 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.17/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.17/0.43 thf(f121,plain,(
% 0.17/0.43 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.17/0.43 inference(cnf_transformation,[],[f59])).
% 0.17/0.43 thf(f59,plain,(
% 0.17/0.43 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.17/0.43 inference(fool_elimination,[],[f58])).
% 0.17/0.43 thf(f58,plain,(
% 0.17/0.43 ((^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))) = mequiv)),
% 0.17/0.43 inference(rectify,[],[f8])).
% 0.17/0.43 thf(f8,axiom,(
% 0.17/0.43 ((^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))) = mequiv)),
% 0.17/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv)).
% 0.17/0.43 thf(f143,plain,(
% 0.17/0.43 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.17/0.43 inference(cnf_transformation,[],[f88])).
% 0.17/0.43 thf(f88,plain,(
% 0.17/0.43 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.17/0.43 inference(fool_elimination,[],[f87])).
% 0.17/0.43 thf(f87,plain,(
% 0.17/0.43 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.17/0.43 inference(rectify,[],[f28])).
% 0.17/0.43 thf(f28,axiom,(
% 0.17/0.43 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.17/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.17/0.43 thf(f111,plain,(
% 0.17/0.43 ($true = (~ (mvalid @ (mequiv @ (mbox_s5 @ (mdia_s5 @ (mdia_s5 @ (mbox_s5 @ p)))) @ (mbox_s5 @ (mbox_s5 @ p))))))),
% 0.17/0.43 inference(cnf_transformation,[],[f77])).
% 0.17/0.43 thf(f77,plain,(
% 0.17/0.43 ($true = (~ (mvalid @ (mequiv @ (mbox_s5 @ (mdia_s5 @ (mdia_s5 @ (mbox_s5 @ p)))) @ (mbox_s5 @ (mbox_s5 @ p))))))),
% 0.17/0.43 inference(fool_elimination,[],[f76])).
% 0.17/0.43 thf(f76,plain,(
% 0.17/0.43 ~(mvalid @ (mequiv @ (mbox_s5 @ (mdia_s5 @ (mdia_s5 @ (mbox_s5 @ p)))) @ (mbox_s5 @ (mbox_s5 @ p))))),
% 0.17/0.43 inference(rectify,[],[f38])).
% 0.17/0.43 thf(f38,negated_conjecture,(
% 0.17/0.43 ~(mvalid @ (mequiv @ (mbox_s5 @ (mdia_s5 @ (mdia_s5 @ (mbox_s5 @ p)))) @ (mbox_s5 @ (mbox_s5 @ p))))),
% 0.17/0.43 inference(negated_conjecture,[],[f37])).
% 0.17/0.43 thf(f37,conjecture,(
% 0.17/0.43 (mvalid @ (mequiv @ (mbox_s5 @ (mdia_s5 @ (mdia_s5 @ (mbox_s5 @ p)))) @ (mbox_s5 @ (mbox_s5 @ p))))),
% 0.17/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.17/0.43 % SZS output end Proof for theBenchmark
% 0.17/0.43 % (14004)------------------------------
% 0.17/0.43 % (14004)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.43 % (14004)Termination reason: Refutation
% 0.17/0.43
% 0.17/0.43 % (14004)Memory used [KB]: 6140
% 0.17/0.43 % (14004)Time elapsed: 0.065 s
% 0.17/0.43 % (14004)Instructions burned: 99 (million)
% 0.17/0.43 % (14004)------------------------------
% 0.17/0.43 % (14004)------------------------------
% 0.17/0.43 % (13992)Success in time 0.104 s
% 0.17/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------