TSTP Solution File: LCL864^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL864^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 00:23:32 EDT 2024
% Result : Theorem 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : LCL864^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.00/0.11 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.31 % Computer : n011.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon May 20 01:04:08 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.31 This is a TH0_THM_EQU_NAR problem
% 0.15/0.31 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.33 % (18982)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.33 % (18976)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.33 % (18981)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.15/0.33 % (18977)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.33 % (18978)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.15/0.33 % (18979)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.33 % (18983)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.33 % (18979)Instruction limit reached!
% 0.15/0.33 % (18979)------------------------------
% 0.15/0.33 % (18979)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (18979)Termination reason: Unknown
% 0.15/0.33 % (18979)Termination phase: shuffling
% 0.15/0.33
% 0.15/0.33 % (18979)Memory used [KB]: 1023
% 0.15/0.33 % (18979)Time elapsed: 0.003 s
% 0.15/0.33 % (18979)Instructions burned: 4 (million)
% 0.15/0.33 % (18979)------------------------------
% 0.15/0.33 % (18979)------------------------------
% 0.15/0.33 % (18983)Instruction limit reached!
% 0.15/0.33 % (18983)------------------------------
% 0.15/0.33 % (18983)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (18983)Termination reason: Unknown
% 0.15/0.33 % (18983)Termination phase: Property scanning
% 0.15/0.33
% 0.15/0.33 % (18983)Memory used [KB]: 1023
% 0.15/0.33 % (18983)Time elapsed: 0.003 s
% 0.15/0.33 % (18983)Instructions burned: 4 (million)
% 0.15/0.33 % (18983)------------------------------
% 0.15/0.33 % (18983)------------------------------
% 0.15/0.33 % (18977)Instruction limit reached!
% 0.15/0.33 % (18977)------------------------------
% 0.15/0.33 % (18977)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (18977)Termination reason: Unknown
% 0.15/0.33 % (18977)Termination phase: Preprocessing 3
% 0.15/0.33
% 0.15/0.33 % (18977)Memory used [KB]: 1023
% 0.15/0.33 % (18977)Time elapsed: 0.004 s
% 0.15/0.33 % (18977)Instructions burned: 5 (million)
% 0.15/0.33 % (18977)------------------------------
% 0.15/0.33 % (18977)------------------------------
% 0.15/0.33 % (18980)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.33 % (18980)Instruction limit reached!
% 0.15/0.33 % (18980)------------------------------
% 0.15/0.33 % (18980)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (18980)Termination reason: Unknown
% 0.15/0.33 % (18980)Termination phase: shuffling
% 0.15/0.33
% 0.15/0.33 % (18980)Memory used [KB]: 1023
% 0.15/0.33 % (18980)Time elapsed: 0.003 s
% 0.15/0.33 % (18980)Instructions burned: 3 (million)
% 0.15/0.33 % (18980)------------------------------
% 0.15/0.33 % (18980)------------------------------
% 0.15/0.34 % (18982)Instruction limit reached!
% 0.15/0.34 % (18982)------------------------------
% 0.15/0.34 % (18982)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34 % (18982)Termination reason: Unknown
% 0.15/0.34 % (18982)Termination phase: Saturation
% 0.15/0.34
% 0.15/0.34 % (18982)Memory used [KB]: 5628
% 0.15/0.34 % (18982)Time elapsed: 0.010 s
% 0.15/0.34 % (18982)Instructions burned: 18 (million)
% 0.15/0.34 % (18982)------------------------------
% 0.15/0.34 % (18982)------------------------------
% 0.15/0.34 % (18978)Instruction limit reached!
% 0.15/0.34 % (18978)------------------------------
% 0.15/0.34 % (18978)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34 % (18978)Termination reason: Unknown
% 0.15/0.34 % (18978)Termination phase: Saturation
% 0.15/0.34
% 0.15/0.34 % (18978)Memory used [KB]: 5756
% 0.15/0.34 % (18978)Time elapsed: 0.015 s
% 0.15/0.34 % (18978)Instructions burned: 28 (million)
% 0.15/0.34 % (18978)------------------------------
% 0.15/0.34 % (18978)------------------------------
% 0.15/0.34 % (18984)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.15/0.34 % (18985)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.15/0.34 % (18986)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.35 % (18986)Instruction limit reached!
% 0.15/0.35 % (18986)------------------------------
% 0.15/0.35 % (18986)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.35 % (18986)Termination reason: Unknown
% 0.15/0.35 % (18986)Termination phase: shuffling
% 0.15/0.35
% 0.15/0.35 % (18986)Memory used [KB]: 1023
% 0.15/0.35 % (18986)Time elapsed: 0.003 s
% 0.15/0.35 % (18986)Instructions burned: 4 (million)
% 0.15/0.35 % (18986)------------------------------
% 0.15/0.35 % (18986)------------------------------
% 0.15/0.35 % (18987)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.15/0.35 % (18985)Instruction limit reached!
% 0.15/0.35 % (18985)------------------------------
% 0.15/0.35 % (18985)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.35 % (18988)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.35 % (18985)Termination reason: Unknown
% 0.15/0.35 % (18985)Termination phase: Saturation
% 0.15/0.35
% 0.15/0.35 % (18985)Memory used [KB]: 5628
% 0.15/0.35 % (18985)Time elapsed: 0.008 s
% 0.15/0.35 % (18985)Instructions burned: 15 (million)
% 0.15/0.35 % (18985)------------------------------
% 0.15/0.35 % (18985)------------------------------
% 0.15/0.35 % (18988)Instruction limit reached!
% 0.15/0.35 % (18988)------------------------------
% 0.15/0.35 % (18988)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.35 % (18988)Termination reason: Unknown
% 0.15/0.35 % (18988)Termination phase: Property scanning
% 0.15/0.35
% 0.15/0.35 % (18988)Memory used [KB]: 1023
% 0.15/0.35 % (18988)Time elapsed: 0.005 s
% 0.15/0.35 % (18988)Instructions burned: 7 (million)
% 0.15/0.35 % (18988)------------------------------
% 0.15/0.35 % (18988)------------------------------
% 0.15/0.36 % (18989)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.15/0.36 % (18990)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)
% 0.15/0.36 % (18990)Instruction limit reached!
% 0.15/0.36 % (18990)------------------------------
% 0.15/0.36 % (18990)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.36 % (18990)Termination reason: Unknown
% 0.15/0.36 % (18990)Termination phase: shuffling
% 0.15/0.36
% 0.15/0.36 % (18990)Memory used [KB]: 1023
% 0.15/0.36 % (18990)Time elapsed: 0.003 s
% 0.15/0.36 % (18990)Instructions burned: 3 (million)
% 0.15/0.36 % (18990)------------------------------
% 0.15/0.36 % (18990)------------------------------
% 0.15/0.36 % (18984)Instruction limit reached!
% 0.15/0.36 % (18984)------------------------------
% 0.15/0.36 % (18984)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.36 % (18984)Termination reason: Unknown
% 0.15/0.36 % (18984)Termination phase: Saturation
% 0.15/0.36
% 0.15/0.36 % (18984)Memory used [KB]: 5628
% 0.15/0.36 % (18984)Time elapsed: 0.019 s
% 0.15/0.36 % (18984)Instructions burned: 37 (million)
% 0.15/0.36 % (18984)------------------------------
% 0.15/0.36 % (18984)------------------------------
% 0.15/0.36 % (18991)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)
% 0.15/0.36 % (18989)Instruction limit reached!
% 0.15/0.36 % (18989)------------------------------
% 0.15/0.36 % (18989)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.36 % (18989)Termination reason: Unknown
% 0.15/0.36 % (18989)Termination phase: Saturation
% 0.15/0.36
% 0.15/0.36 % (18989)Memory used [KB]: 5884
% 0.15/0.36 % (18989)Time elapsed: 0.010 s
% 0.15/0.36 % (18989)Instructions burned: 16 (million)
% 0.15/0.36 % (18989)------------------------------
% 0.15/0.36 % (18989)------------------------------
% 0.15/0.36 % (18991)Instruction limit reached!
% 0.15/0.36 % (18991)------------------------------
% 0.15/0.36 % (18991)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.36 % (18991)Termination reason: Unknown
% 0.15/0.36 % (18991)Termination phase: Property scanning
% 0.15/0.36
% 0.15/0.36 % (18991)Memory used [KB]: 1023
% 0.15/0.36 % (18991)Time elapsed: 0.004 s
% 0.15/0.36 % (18991)Instructions burned: 5 (million)
% 0.15/0.36 % (18991)------------------------------
% 0.15/0.36 % (18991)------------------------------
% 0.15/0.37 % (18992)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)
% 0.15/0.37 % (18992)Instruction limit reached!
% 0.15/0.37 % (18992)------------------------------
% 0.15/0.37 % (18992)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (18992)Termination reason: Unknown
% 0.15/0.37 % (18992)Termination phase: Function definition elimination
% 0.15/0.37
% 0.15/0.37 % (18992)Memory used [KB]: 1023
% 0.15/0.37 % (18992)Time elapsed: 0.005 s
% 0.15/0.37 % (18992)Instructions burned: 7 (million)
% 0.15/0.37 % (18992)------------------------------
% 0.15/0.37 % (18992)------------------------------
% 0.15/0.37 % (18993)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)
% 0.15/0.37 % (18993)Instruction limit reached!
% 0.15/0.37 % (18993)------------------------------
% 0.15/0.37 % (18993)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (18993)Termination reason: Unknown
% 0.15/0.37 % (18993)Termination phase: shuffling
% 0.15/0.37
% 0.15/0.37 % (18993)Memory used [KB]: 1023
% 0.15/0.37 % (18993)Time elapsed: 0.003 s
% 0.15/0.37 % (18993)Instructions burned: 3 (million)
% 0.15/0.37 % (18993)------------------------------
% 0.15/0.37 % (18993)------------------------------
% 0.15/0.37 % (18994)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.38 % (18994)Instruction limit reached!
% 0.15/0.38 % (18994)------------------------------
% 0.15/0.38 % (18994)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (18994)Termination reason: Unknown
% 0.15/0.38 % (18994)Termination phase: Preprocessing 3
% 0.15/0.38
% 0.15/0.38 % (18994)Memory used [KB]: 1023
% 0.15/0.38 % (18994)Time elapsed: 0.004 s
% 0.15/0.38 % (18994)Instructions burned: 5 (million)
% 0.15/0.38 % (18994)------------------------------
% 0.15/0.38 % (18994)------------------------------
% 0.15/0.38 % (18995)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)
% 0.15/0.38 % (18996)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.15/0.38 % (18997)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.15/0.38 % (18997)Instruction limit reached!
% 0.15/0.38 % (18997)------------------------------
% 0.15/0.38 % (18997)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (18997)Termination reason: Unknown
% 0.15/0.38 % (18997)Termination phase: Function definition elimination
% 0.15/0.38
% 0.15/0.38 % (18997)Memory used [KB]: 1023
% 0.15/0.38 % (18997)Time elapsed: 0.005 s
% 0.15/0.38 % (18997)Instructions burned: 7 (million)
% 0.15/0.38 % (18997)------------------------------
% 0.15/0.38 % (18997)------------------------------
% 0.15/0.39 % (18998)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)
% 0.15/0.39 % (18995)Instruction limit reached!
% 0.15/0.39 % (18995)------------------------------
% 0.15/0.39 % (18995)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (18995)Termination reason: Unknown
% 0.15/0.39 % (18995)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (18995)Memory used [KB]: 5756
% 0.15/0.39 % (18995)Time elapsed: 0.011 s
% 0.15/0.39 % (18995)Instructions burned: 19 (million)
% 0.15/0.39 % (18995)------------------------------
% 0.15/0.39 % (18995)------------------------------
% 0.15/0.39 % (18999)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)
% 0.15/0.39 % (18998)Refutation not found, incomplete strategy
% 0.15/0.39 % (18998)------------------------------
% 0.15/0.39 % (18998)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (18998)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.39
% 0.15/0.39
% 0.15/0.39 % (18998)Memory used [KB]: 5628
% 0.15/0.39 % (18998)Time elapsed: 0.006 s
% 0.15/0.39 % (18998)Instructions burned: 9 (million)
% 0.15/0.39 % (18998)------------------------------
% 0.15/0.39 % (18998)------------------------------
% 0.15/0.39 % (18987)First to succeed.
% 0.15/0.40 % (19000)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.15/0.40 % (19001)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)
% 0.15/0.40 % (19000)Instruction limit reached!
% 0.15/0.40 % (19000)------------------------------
% 0.15/0.40 % (19000)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (19000)Termination reason: Unknown
% 0.15/0.40 % (19000)Termination phase: Clausification
% 0.15/0.40
% 0.15/0.40 % (19000)Memory used [KB]: 1023
% 0.15/0.40 % (19000)Time elapsed: 0.004 s
% 0.15/0.40 % (19000)Instructions burned: 5 (million)
% 0.15/0.40 % (19000)------------------------------
% 0.15/0.40 % (19000)------------------------------
% 0.15/0.40 % (18999)Instruction limit reached!
% 0.15/0.40 % (18999)------------------------------
% 0.15/0.40 % (18999)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (18999)Termination reason: Unknown
% 0.15/0.40 % (18999)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (18999)Memory used [KB]: 5756
% 0.15/0.40 % (18999)Time elapsed: 0.013 s
% 0.15/0.40 % (18999)Instructions burned: 22 (million)
% 0.15/0.40 % (18999)------------------------------
% 0.15/0.40 % (18999)------------------------------
% 0.15/0.40 % (19001)Instruction limit reached!
% 0.15/0.40 % (19001)------------------------------
% 0.15/0.40 % (19001)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (19001)Termination reason: Unknown
% 0.15/0.40 % (19001)Termination phase: SInE selection
% 0.15/0.40
% 0.15/0.40 % (19001)Memory used [KB]: 1023
% 0.15/0.40 % (19001)Time elapsed: 0.004 s
% 0.15/0.40 % (19001)Instructions burned: 6 (million)
% 0.15/0.40 % (19001)------------------------------
% 0.15/0.40 % (19001)------------------------------
% 0.15/0.40 % (18987)Refutation found. Thanks to Tanya!
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40 % SZS output start Proof for theBenchmark
% 0.15/0.40 thf(type_def_5, type, mu: $tType).
% 0.15/0.40 thf(func_def_0, type, mu: $tType).
% 0.15/0.40 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.15/0.40 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_15, type, mtrue: $i > $o).
% 0.15/0.40 thf(func_def_16, type, mfalse: $i > $o).
% 0.15/0.40 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.40 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.15/0.40 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.15/0.40 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.15/0.40 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.15/0.40 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.15/0.40 thf(func_def_50, type, ph1: !>[X0: $tType]:(X0)).
% 0.15/0.40 thf(func_def_51, type, sK2: $i > $i > $o).
% 0.15/0.40 thf(func_def_60, type, sK11: $i > $i).
% 0.15/0.40 thf(f795,plain,(
% 0.15/0.40 $false),
% 0.15/0.40 inference(avatar_sat_refutation,[],[f153,f160,f201,f205,f214,f234,f239,f317,f508,f512,f522,f541,f554,f794])).
% 0.15/0.40 thf(f794,plain,(
% 0.15/0.40 ~spl0_1 | ~spl0_9),
% 0.15/0.40 inference(avatar_contradiction_clause,[],[f793])).
% 0.15/0.40 thf(f793,plain,(
% 0.15/0.40 $false | (~spl0_1 | ~spl0_9)),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f792])).
% 0.15/0.40 thf(f792,plain,(
% 0.15/0.40 ($true = $false) | (~spl0_1 | ~spl0_9)),
% 0.15/0.40 inference(boolean_simplification,[],[f791])).
% 0.15/0.40 thf(f791,plain,(
% 0.15/0.40 ($true = (~ $true)) | (~spl0_1 | ~spl0_9)),
% 0.15/0.40 inference(forward_demodulation,[],[f773,f613])).
% 0.15/0.40 thf(f613,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (((sK2 @ X1 @ (sK11 @ X1)) = $true)) ) | ~spl0_1),
% 0.15/0.40 inference(sigma_clausification,[],[f612])).
% 0.15/0.40 thf(f612,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (((?? @ $i @ (sK2 @ X1)) = $true)) ) | ~spl0_1),
% 0.15/0.40 inference(beta_eta_normalization,[],[f611])).
% 0.15/0.40 thf(f611,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))) @ X1))) ) | ~spl0_1),
% 0.15/0.40 inference(pi_clausification,[],[f610])).
% 0.15/0.40 thf(f610,plain,(
% 0.15/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) | ~spl0_1),
% 0.15/0.40 inference(boolean_simplification,[],[f609])).
% 0.15/0.40 thf(f609,plain,(
% 0.15/0.40 (($true & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) = $true) | ~spl0_1),
% 0.15/0.40 inference(backward_demodulation,[],[f559,f608])).
% 0.15/0.40 thf(f608,plain,(
% 0.15/0.40 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0)))))))) | ~spl0_1),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f559])).
% 0.15/0.40 thf(f559,plain,(
% 0.15/0.40 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) = $true) | ~spl0_1),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f533])).
% 0.15/0.40 thf(f533,plain,(
% 0.15/0.40 (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1))))))))) != $false) | ~spl0_1),
% 0.15/0.40 inference(backward_demodulation,[],[f144,f149])).
% 0.15/0.40 thf(f149,plain,(
% 0.15/0.40 (((!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1))))))))) = $false) | ~spl0_1),
% 0.15/0.40 inference(avatar_component_clause,[],[f148])).
% 0.15/0.40 thf(f148,plain,(
% 0.15/0.40 spl0_1 <=> (((!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1))))))))) = $false)),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.15/0.40 thf(f144,plain,(
% 0.15/0.40 (((!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1))))))))) != ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1))))))))))),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f143])).
% 0.15/0.40 thf(f143,plain,(
% 0.15/0.40 ((((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1))))))))) = ((!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))))) = $false)),
% 0.15/0.40 inference(beta_eta_normalization,[],[f142])).
% 0.15/0.40 thf(f142,plain,(
% 0.15/0.40 (((^[Y0 : $i > $i > $o]: (((((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (Y0 @ Y1))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) = ((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y1 @ Y2))))))))))) @ sK2) = $false)),
% 0.15/0.40 inference(sigma_clausification,[],[f139])).
% 0.15/0.40 thf(f139,plain,(
% 0.15/0.40 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (Y0 @ Y1))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) = ((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y1 @ Y2)))))))))))) = $false)),
% 0.15/0.40 inference(not_proxy_clausification,[],[f138])).
% 0.15/0.40 thf(f138,plain,(
% 0.15/0.40 ($true = (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (Y0 @ Y1))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) = ((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y1 @ Y2))))))))))))))),
% 0.15/0.40 inference(beta_eta_normalization,[],[f137])).
% 0.15/0.40 thf(f137,plain,(
% 0.15/0.40 ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((((((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y2 @ Y3))))))))) @ Y0) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2))))))) @ Y0)) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (Y1 @ Y2 @ Y3)))))) @ Y0)) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3))))))))) @ Y0)) = (((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2 @ Y2)))) @ Y0) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y2 @ Y3))))))))) @ Y0)))))) = $true)),
% 0.15/0.40 inference(definition_unfolding,[],[f111,f122,f103,f108,f123,f105,f122])).
% 0.15/0.40 thf(f105,plain,(
% 0.15/0.40 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.15/0.40 inference(cnf_transformation,[],[f56])).
% 0.15/0.40 thf(f56,plain,(
% 0.15/0.40 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.15/0.40 inference(fool_elimination,[],[f55])).
% 0.15/0.40 thf(f55,plain,(
% 0.15/0.40 ((^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))) = mreflexive)),
% 0.15/0.40 inference(rectify,[],[f18])).
% 0.15/0.40 thf(f18,axiom,(
% 0.15/0.40 ((^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))) = mreflexive)),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
% 0.15/0.40 thf(f123,plain,(
% 0.15/0.40 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f91])).
% 0.15/0.40 thf(f91,plain,(
% 0.15/0.40 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f90])).
% 0.15/0.40 thf(f90,plain,(
% 0.15/0.40 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X3 @ X1) & (X0 @ X1 @ X2)) => (X0 @ X3 @ X2)))) = mtransitive)),
% 0.15/0.40 inference(rectify,[],[f21])).
% 0.15/0.40 thf(f21,axiom,(
% 0.15/0.40 ((^[X6 : $i > $i > $o] : (! [X9,X10,X8] : (((X6 @ X8 @ X9) & (X6 @ X9 @ X10)) => (X6 @ X8 @ X10)))) = mtransitive)),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive)).
% 0.15/0.40 thf(f108,plain,(
% 0.15/0.40 (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f40])).
% 0.15/0.40 thf(f40,plain,(
% 0.15/0.40 (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.15/0.40 inference(fool_elimination,[],[f39])).
% 0.15/0.40 thf(f39,plain,(
% 0.15/0.40 (mserial = (^[X0 : $i > $i > $o] : (! [X1] : ? [X2] : (X0 @ X1 @ X2))))),
% 0.15/0.40 inference(rectify,[],[f20])).
% 0.15/0.40 thf(f20,axiom,(
% 0.15/0.40 (mserial = (^[X6 : $i > $i > $o] : (! [X8] : ? [X9] : (X6 @ X8 @ X9))))),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mserial)).
% 0.15/0.40 thf(f103,plain,(
% 0.15/0.40 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f79])).
% 0.15/0.40 thf(f79,plain,(
% 0.15/0.40 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f78])).
% 0.15/0.40 thf(f78,plain,(
% 0.15/0.40 (msymmetric = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))))),
% 0.15/0.40 inference(rectify,[],[f19])).
% 0.15/0.40 thf(f19,axiom,(
% 0.15/0.40 (msymmetric = (^[X6 : $i > $i > $o] : (! [X9,X8] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))))),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric)).
% 0.15/0.40 thf(f122,plain,(
% 0.15/0.40 (meuclidean = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f95])).
% 0.15/0.40 thf(f95,plain,(
% 0.15/0.40 (meuclidean = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f94])).
% 0.15/0.40 thf(f94,plain,(
% 0.15/0.40 (meuclidean = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X3 @ X2)))))),
% 0.15/0.40 inference(rectify,[],[f22])).
% 0.15/0.40 thf(f22,axiom,(
% 0.15/0.40 (meuclidean = (^[X6 : $i > $i > $o] : (! [X8,X10,X9] : (((X6 @ X8 @ X9) & (X6 @ X8 @ X10)) => (X6 @ X9 @ X10)))))),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meuclidean)).
% 0.15/0.40 thf(f111,plain,(
% 0.15/0.40 ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((((meuclidean @ Y0) & (msymmetric @ Y0)) & (mserial @ Y0)) & (mtransitive @ Y0)) = ((mreflexive @ Y0) & (meuclidean @ Y0)))))) = $true)),
% 0.15/0.40 inference(cnf_transformation,[],[f93])).
% 0.15/0.40 thf(f93,plain,(
% 0.15/0.40 ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((((meuclidean @ Y0) & (msymmetric @ Y0)) & (mserial @ Y0)) & (mtransitive @ Y0)) = ((mreflexive @ Y0) & (meuclidean @ Y0)))))) = $true)),
% 0.15/0.40 inference(fool_elimination,[],[f92])).
% 0.15/0.40 thf(f92,plain,(
% 0.15/0.40 ~! [X0 : $i > $i > $o] : (((mtransitive @ X0) & (mserial @ X0) & (msymmetric @ X0) & (meuclidean @ X0)) <=> ((meuclidean @ X0) & (mreflexive @ X0)))),
% 0.15/0.40 inference(rectify,[],[f33])).
% 0.15/0.40 thf(f33,negated_conjecture,(
% 0.15/0.40 ~! [X6 : $i > $i > $o] : (((mtransitive @ X6) & (mserial @ X6) & (msymmetric @ X6) & (meuclidean @ X6)) <=> ((meuclidean @ X6) & (mreflexive @ X6)))),
% 0.15/0.40 inference(negated_conjecture,[],[f32])).
% 0.15/0.40 thf(f32,conjecture,(
% 0.15/0.40 ! [X6 : $i > $i > $o] : (((mtransitive @ X6) & (mserial @ X6) & (msymmetric @ X6) & (meuclidean @ X6)) <=> ((meuclidean @ X6) & (mreflexive @ X6)))),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.15/0.40 thf(f773,plain,(
% 0.15/0.40 ($true = (~ (sK2 @ sK10 @ (sK11 @ sK10)))) | (~spl0_1 | ~spl0_9)),
% 0.15/0.40 inference(boolean_simplification,[],[f756])).
% 0.15/0.40 thf(f756,plain,(
% 0.15/0.40 ($true = ((sK2 @ sK10 @ (sK11 @ sK10)) => $false)) | (~spl0_1 | ~spl0_9)),
% 0.15/0.40 inference(superposition,[],[f733,f620])).
% 0.15/0.40 thf(f620,plain,(
% 0.15/0.40 ((sK2 @ (sK11 @ sK10) @ sK10) = $false) | (~spl0_1 | ~spl0_9)),
% 0.15/0.40 inference(boolean_simplification,[],[f614])).
% 0.15/0.40 thf(f614,plain,(
% 0.15/0.40 (((sK2 @ (sK11 @ sK10) @ sK10) & $true) = $false) | (~spl0_1 | ~spl0_9)),
% 0.15/0.40 inference(superposition,[],[f581,f613])).
% 0.15/0.40 thf(f581,plain,(
% 0.15/0.40 ( ! [X0 : $i] : ((((sK2 @ X0 @ sK10) & (sK2 @ sK10 @ X0)) = $false)) ) | (~spl0_1 | ~spl0_9)),
% 0.15/0.40 inference(not_proxy_clausification,[],[f578])).
% 0.15/0.40 thf(f578,plain,(
% 0.15/0.40 ( ! [X0 : $i] : (((~ ((sK2 @ X0 @ sK10) & (sK2 @ sK10 @ X0))) = $true)) ) | (~spl0_1 | ~spl0_9)),
% 0.15/0.40 inference(boolean_simplification,[],[f573])).
% 0.15/0.40 thf(f573,plain,(
% 0.15/0.40 ( ! [X0 : $i] : (($true = (((sK2 @ X0 @ sK10) & (sK2 @ sK10 @ X0)) => $false))) ) | (~spl0_1 | ~spl0_9)),
% 0.15/0.40 inference(superposition,[],[f571,f565])).
% 0.15/0.40 thf(f565,plain,(
% 0.15/0.40 ((sK2 @ sK10 @ sK10) = $false) | ~spl0_9),
% 0.15/0.40 inference(beta_eta_normalization,[],[f564])).
% 0.15/0.40 thf(f564,plain,(
% 0.15/0.40 (((^[Y0 : $i]: (sK2 @ Y0 @ Y0)) @ sK10) = $false) | ~spl0_9),
% 0.15/0.40 inference(sigma_clausification,[],[f537])).
% 0.15/0.40 thf(f537,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0))) = $false) | ~spl0_9),
% 0.15/0.40 inference(avatar_component_clause,[],[f536])).
% 0.15/0.40 thf(f536,plain,(
% 0.15/0.40 spl0_9 <=> ((!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0))) = $false)),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])).
% 0.15/0.40 thf(f571,plain,(
% 0.15/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((sK2 @ X3 @ X2) & (sK2 @ X1 @ X3)) => (sK2 @ X1 @ X2)))) ) | ~spl0_1),
% 0.15/0.40 inference(beta_eta_normalization,[],[f570])).
% 0.15/0.40 thf(f570,plain,(
% 0.15/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((sK2 @ Y0 @ X2) & (sK2 @ X1 @ Y0)) => (sK2 @ X1 @ X2))) @ X3))) ) | ~spl0_1),
% 0.15/0.40 inference(pi_clausification,[],[f569])).
% 0.15/0.40 thf(f569,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ Y0 @ X2) & (sK2 @ X1 @ Y0)) => (sK2 @ X1 @ X2)))))) ) | ~spl0_1),
% 0.15/0.40 inference(beta_eta_normalization,[],[f568])).
% 0.15/0.40 thf(f568,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ X1 @ Y1)) => (sK2 @ X1 @ Y0))))) @ X2))) ) | ~spl0_1),
% 0.15/0.40 inference(pi_clausification,[],[f567])).
% 0.15/0.40 thf(f567,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ X1 @ Y1)) => (sK2 @ X1 @ Y0)))))))) ) | ~spl0_1),
% 0.15/0.40 inference(beta_eta_normalization,[],[f566])).
% 0.15/0.40 thf(f566,plain,(
% 0.15/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1))))))) @ X1) = $true)) ) | ~spl0_1),
% 0.15/0.40 inference(pi_clausification,[],[f563])).
% 0.15/0.40 thf(f563,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1)))))))) != $false) | ~spl0_1),
% 0.15/0.40 inference(boolean_simplification,[],[f561])).
% 0.15/0.40 thf(f561,plain,(
% 0.15/0.40 (($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1))))))))) != $false) | ~spl0_1),
% 0.15/0.40 inference(backward_demodulation,[],[f533,f559])).
% 0.15/0.40 thf(f733,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : ((((sK2 @ X1 @ X2) => (sK2 @ X2 @ X1)) = $true)) ) | ~spl0_1),
% 0.15/0.40 inference(beta_eta_normalization,[],[f732])).
% 0.15/0.40 thf(f732,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((sK2 @ X1 @ Y0) => (sK2 @ Y0 @ X1))) @ X2) = $true)) ) | ~spl0_1),
% 0.15/0.40 inference(pi_clausification,[],[f709])).
% 0.15/0.40 thf(f709,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ X1 @ Y0) => (sK2 @ Y0 @ X1)))) = $true)) ) | ~spl0_1),
% 0.15/0.40 inference(beta_eta_normalization,[],[f708])).
% 0.15/0.40 thf(f708,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))) @ X1))) ) | ~spl0_1),
% 0.15/0.40 inference(pi_clausification,[],[f687])).
% 0.15/0.40 thf(f687,plain,(
% 0.15/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) | ~spl0_1),
% 0.15/0.40 inference(boolean_simplification,[],[f686])).
% 0.15/0.40 thf(f686,plain,(
% 0.15/0.40 (($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) = $true) | ~spl0_1),
% 0.15/0.40 inference(backward_demodulation,[],[f608,f685])).
% 0.15/0.40 thf(f685,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) = $true) | ~spl0_1),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f608])).
% 0.15/0.40 thf(f554,plain,(
% 0.15/0.40 ~spl0_4 | ~spl0_10),
% 0.15/0.40 inference(avatar_contradiction_clause,[],[f553])).
% 0.15/0.40 thf(f553,plain,(
% 0.15/0.40 $false | (~spl0_4 | ~spl0_10)),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f552])).
% 0.15/0.40 thf(f552,plain,(
% 0.15/0.40 ($true = $false) | (~spl0_4 | ~spl0_10)),
% 0.15/0.40 inference(boolean_simplification,[],[f551])).
% 0.15/0.40 thf(f551,plain,(
% 0.15/0.40 ($true = ($false & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1)))))))))) | (~spl0_4 | ~spl0_10)),
% 0.15/0.40 inference(boolean_simplification,[],[f550])).
% 0.15/0.40 thf(f550,plain,(
% 0.15/0.40 ((($false & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1))))))))) = $true) | (~spl0_4 | ~spl0_10)),
% 0.15/0.40 inference(boolean_simplification,[],[f542])).
% 0.15/0.40 thf(f542,plain,(
% 0.15/0.40 ($true = ((($false & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1)))))))))) | (~spl0_4 | ~spl0_10)),
% 0.15/0.40 inference(backward_demodulation,[],[f159,f540])).
% 0.15/0.40 thf(f540,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) = $false) | ~spl0_10),
% 0.15/0.40 inference(avatar_component_clause,[],[f539])).
% 0.15/0.40 thf(f539,plain,(
% 0.15/0.40 spl0_10 <=> ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) = $false)),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_10])])).
% 0.15/0.40 thf(f159,plain,(
% 0.15/0.40 ($true = ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1)))))))))) | ~spl0_4),
% 0.15/0.40 inference(avatar_component_clause,[],[f158])).
% 0.15/0.40 thf(f158,plain,(
% 0.15/0.40 spl0_4 <=> ($true = ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1))))))))))),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.15/0.40 thf(f541,plain,(
% 0.15/0.40 spl0_9 | spl0_10 | ~spl0_1),
% 0.15/0.40 inference(avatar_split_clause,[],[f534,f148,f539,f536])).
% 0.15/0.40 thf(f534,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0))) = $false) | ~spl0_1),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f149])).
% 0.15/0.40 thf(f522,plain,(
% 0.15/0.40 ~spl0_4 | ~spl0_8),
% 0.15/0.40 inference(avatar_contradiction_clause,[],[f521])).
% 0.15/0.40 thf(f521,plain,(
% 0.15/0.40 $false | (~spl0_4 | ~spl0_8)),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f520])).
% 0.15/0.40 thf(f520,plain,(
% 0.15/0.40 ($true = $false) | (~spl0_4 | ~spl0_8)),
% 0.15/0.40 inference(boolean_simplification,[],[f519])).
% 0.15/0.40 thf(f519,plain,(
% 0.15/0.40 ($true = ($false & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1)))))))))) | (~spl0_4 | ~spl0_8)),
% 0.15/0.40 inference(boolean_simplification,[],[f518])).
% 0.15/0.40 thf(f518,plain,(
% 0.15/0.40 ((($false & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1))))))))) = $true) | (~spl0_4 | ~spl0_8)),
% 0.15/0.40 inference(boolean_simplification,[],[f517])).
% 0.15/0.40 thf(f517,plain,(
% 0.15/0.40 (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) & $false) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1))))))))) = $true) | (~spl0_4 | ~spl0_8)),
% 0.15/0.40 inference(backward_demodulation,[],[f159,f213])).
% 0.15/0.40 thf(f213,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0)))))) = $false) | ~spl0_8),
% 0.15/0.40 inference(avatar_component_clause,[],[f212])).
% 0.15/0.40 thf(f212,plain,(
% 0.15/0.40 spl0_8 <=> ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0)))))) = $false)),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])).
% 0.15/0.40 thf(f512,plain,(
% 0.15/0.40 ~spl0_4 | ~spl0_6),
% 0.15/0.40 inference(avatar_contradiction_clause,[],[f511])).
% 0.15/0.40 thf(f511,plain,(
% 0.15/0.40 $false | (~spl0_4 | ~spl0_6)),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f510])).
% 0.15/0.40 thf(f510,plain,(
% 0.15/0.40 ($true = $false) | (~spl0_4 | ~spl0_6)),
% 0.15/0.40 inference(boolean_simplification,[],[f509])).
% 0.15/0.40 thf(f509,plain,(
% 0.15/0.40 ($true = ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) & $false)) | (~spl0_4 | ~spl0_6)),
% 0.15/0.40 inference(forward_demodulation,[],[f159,f200])).
% 0.15/0.40 thf(f200,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1)))))))) = $false) | ~spl0_6),
% 0.15/0.40 inference(avatar_component_clause,[],[f199])).
% 0.15/0.40 thf(f199,plain,(
% 0.15/0.40 spl0_6 <=> ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1)))))))) = $false)),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.15/0.40 thf(f508,plain,(
% 0.15/0.40 ~spl0_3 | ~spl0_6),
% 0.15/0.40 inference(avatar_contradiction_clause,[],[f507])).
% 0.15/0.40 thf(f507,plain,(
% 0.15/0.40 $false | (~spl0_3 | ~spl0_6)),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f506])).
% 0.15/0.40 thf(f506,plain,(
% 0.15/0.40 ($true = $false) | (~spl0_3 | ~spl0_6)),
% 0.15/0.40 inference(boolean_simplification,[],[f505])).
% 0.15/0.40 thf(f505,plain,(
% 0.15/0.40 ($true = (~ $true)) | (~spl0_3 | ~spl0_6)),
% 0.15/0.40 inference(forward_demodulation,[],[f499,f378])).
% 0.15/0.40 thf(f378,plain,(
% 0.15/0.40 ($true = (sK2 @ sK9 @ sK6)) | (~spl0_3 | ~spl0_6)),
% 0.15/0.40 inference(boolean_simplification,[],[f369])).
% 0.15/0.40 thf(f369,plain,(
% 0.15/0.40 (($true => (sK2 @ sK9 @ sK6)) = $true) | (~spl0_3 | ~spl0_6)),
% 0.15/0.40 inference(superposition,[],[f295,f368])).
% 0.15/0.40 thf(f368,plain,(
% 0.15/0.40 ((sK2 @ sK6 @ sK9) = $true) | ~spl0_6),
% 0.15/0.40 inference(boolean_simplification,[],[f367])).
% 0.15/0.40 thf(f367,plain,(
% 0.15/0.40 (($true & (sK2 @ sK6 @ sK9)) = $true) | ~spl0_6),
% 0.15/0.40 inference(backward_demodulation,[],[f359,f366])).
% 0.15/0.40 thf(f366,plain,(
% 0.15/0.40 ((sK2 @ sK9 @ sK7) = $true) | ~spl0_6),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f359])).
% 0.15/0.40 thf(f359,plain,(
% 0.15/0.40 ($true = ((sK2 @ sK9 @ sK7) & (sK2 @ sK6 @ sK9))) | ~spl0_6),
% 0.15/0.40 inference(not_proxy_clausification,[],[f346])).
% 0.15/0.40 thf(f346,plain,(
% 0.15/0.40 ((~ ((sK2 @ sK9 @ sK7) & (sK2 @ sK6 @ sK9))) = $false) | ~spl0_6),
% 0.15/0.40 inference(beta_eta_normalization,[],[f345])).
% 0.15/0.40 thf(f345,plain,(
% 0.15/0.40 (((^[Y0 : $i]: (~ ((sK2 @ Y0 @ sK7) & (sK2 @ sK6 @ Y0)))) @ sK9) = $false) | ~spl0_6),
% 0.15/0.40 inference(sigma_clausification,[],[f341])).
% 0.15/0.40 thf(f341,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (~ ((sK2 @ Y0 @ sK7) & (sK2 @ sK6 @ Y0))))) = $false) | ~spl0_6),
% 0.15/0.40 inference(boolean_simplification,[],[f340])).
% 0.15/0.40 thf(f340,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (((sK2 @ Y0 @ sK7) & (sK2 @ sK6 @ Y0)) => $false))) = $false) | ~spl0_6),
% 0.15/0.40 inference(backward_demodulation,[],[f334,f337])).
% 0.15/0.40 thf(f337,plain,(
% 0.15/0.40 ((sK2 @ sK6 @ sK7) = $false) | ~spl0_6),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f336])).
% 0.15/0.40 thf(f336,plain,(
% 0.15/0.40 ((((sK2 @ sK8 @ sK7) & (sK2 @ sK6 @ sK8)) => (sK2 @ sK6 @ sK7)) = $false) | ~spl0_6),
% 0.15/0.40 inference(beta_eta_normalization,[],[f335])).
% 0.15/0.40 thf(f335,plain,(
% 0.15/0.40 (((^[Y0 : $i]: (((sK2 @ Y0 @ sK7) & (sK2 @ sK6 @ Y0)) => (sK2 @ sK6 @ sK7))) @ sK8) = $false) | ~spl0_6),
% 0.15/0.40 inference(sigma_clausification,[],[f334])).
% 0.15/0.40 thf(f334,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (((sK2 @ Y0 @ sK7) & (sK2 @ sK6 @ Y0)) => (sK2 @ sK6 @ sK7)))) = $false) | ~spl0_6),
% 0.15/0.40 inference(beta_eta_normalization,[],[f333])).
% 0.15/0.40 thf(f333,plain,(
% 0.15/0.40 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ sK6 @ Y1)) => (sK2 @ sK6 @ Y0))))) @ sK7) = $false) | ~spl0_6),
% 0.15/0.40 inference(sigma_clausification,[],[f332])).
% 0.15/0.40 thf(f332,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ sK6 @ Y1)) => (sK2 @ sK6 @ Y0)))))) = $false) | ~spl0_6),
% 0.15/0.40 inference(beta_eta_normalization,[],[f331])).
% 0.15/0.40 thf(f331,plain,(
% 0.15/0.40 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1))))))) @ sK6) = $false) | ~spl0_6),
% 0.15/0.40 inference(sigma_clausification,[],[f200])).
% 0.15/0.40 thf(f295,plain,(
% 0.15/0.40 ( ! [X0 : $i,X1 : $i] : (($true = ((sK2 @ X0 @ X1) => (sK2 @ X1 @ X0)))) ) | ~spl0_3),
% 0.15/0.40 inference(boolean_simplification,[],[f283])).
% 0.15/0.40 thf(f283,plain,(
% 0.15/0.40 ( ! [X0 : $i,X1 : $i] : (((($true & (sK2 @ X0 @ X1)) => (sK2 @ X1 @ X0)) = $true)) ) | ~spl0_3),
% 0.15/0.40 inference(superposition,[],[f273,f269])).
% 0.15/0.40 thf(f269,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($true = (sK2 @ X1 @ X1))) ) | ~spl0_3),
% 0.15/0.40 inference(beta_eta_normalization,[],[f268])).
% 0.15/0.40 thf(f268,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (sK2 @ Y0 @ Y0)) @ X1))) ) | ~spl0_3),
% 0.15/0.40 inference(pi_clausification,[],[f263])).
% 0.15/0.40 thf(f263,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0))) = $true) | ~spl0_3),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f156])).
% 0.15/0.40 thf(f156,plain,(
% 0.15/0.40 ($true = ((!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))))) | ~spl0_3),
% 0.15/0.40 inference(avatar_component_clause,[],[f155])).
% 0.15/0.40 thf(f155,plain,(
% 0.15/0.40 spl0_3 <=> ($true = ((!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1))))))))))),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.15/0.40 thf(f273,plain,(
% 0.15/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((sK2 @ X3 @ X2) & (sK2 @ X3 @ X1)) => (sK2 @ X1 @ X2)))) ) | ~spl0_3),
% 0.15/0.40 inference(beta_eta_normalization,[],[f272])).
% 0.15/0.40 thf(f272,plain,(
% 0.15/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((sK2 @ Y0 @ X2) & (sK2 @ Y0 @ X1)) => (sK2 @ X1 @ X2))) @ X3))) ) | ~spl0_3),
% 0.15/0.40 inference(pi_clausification,[],[f271])).
% 0.15/0.40 thf(f271,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((sK2 @ Y0 @ X2) & (sK2 @ Y0 @ X1)) => (sK2 @ X1 @ X2)))) = $true)) ) | ~spl0_3),
% 0.15/0.40 inference(beta_eta_normalization,[],[f270])).
% 0.15/0.40 thf(f270,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y1 @ X1)) => (sK2 @ X1 @ Y0))))) @ X2))) ) | ~spl0_3),
% 0.15/0.40 inference(pi_clausification,[],[f267])).
% 0.15/0.40 thf(f267,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y1 @ X1)) => (sK2 @ X1 @ Y0)))))) = $true)) ) | ~spl0_3),
% 0.15/0.40 inference(beta_eta_normalization,[],[f266])).
% 0.15/0.40 thf(f266,plain,(
% 0.15/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1))))))) @ X1) = $true)) ) | ~spl0_3),
% 0.15/0.40 inference(pi_clausification,[],[f265])).
% 0.15/0.40 thf(f265,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) = $true) | ~spl0_3),
% 0.15/0.40 inference(boolean_simplification,[],[f264])).
% 0.15/0.40 thf(f264,plain,(
% 0.15/0.40 ($true = ($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))))) | ~spl0_3),
% 0.15/0.40 inference(backward_demodulation,[],[f156,f263])).
% 0.15/0.40 thf(f499,plain,(
% 0.15/0.40 ($true = (~ (sK2 @ sK9 @ sK6))) | (~spl0_3 | ~spl0_6)),
% 0.15/0.40 inference(boolean_simplification,[],[f491])).
% 0.15/0.40 thf(f491,plain,(
% 0.15/0.40 (((sK2 @ sK9 @ sK6) => $false) = $true) | (~spl0_3 | ~spl0_6)),
% 0.15/0.40 inference(superposition,[],[f386,f362])).
% 0.15/0.40 thf(f362,plain,(
% 0.15/0.40 ((sK2 @ sK7 @ sK6) = $false) | (~spl0_3 | ~spl0_6)),
% 0.15/0.40 inference(not_proxy_clausification,[],[f354])).
% 0.15/0.40 thf(f354,plain,(
% 0.15/0.40 ($true = (~ (sK2 @ sK7 @ sK6))) | (~spl0_3 | ~spl0_6)),
% 0.15/0.40 inference(boolean_simplification,[],[f348])).
% 0.15/0.40 thf(f348,plain,(
% 0.15/0.40 (((sK2 @ sK7 @ sK6) => $false) = $true) | (~spl0_3 | ~spl0_6)),
% 0.15/0.40 inference(superposition,[],[f295,f337])).
% 0.15/0.40 thf(f386,plain,(
% 0.15/0.40 ( ! [X0 : $i] : ((((sK2 @ sK9 @ X0) => (sK2 @ sK7 @ X0)) = $true)) ) | (~spl0_3 | ~spl0_6)),
% 0.15/0.40 inference(boolean_simplification,[],[f382])).
% 0.15/0.40 thf(f382,plain,(
% 0.15/0.40 ( ! [X0 : $i] : (($true = (((sK2 @ sK9 @ X0) & $true) => (sK2 @ sK7 @ X0)))) ) | (~spl0_3 | ~spl0_6)),
% 0.15/0.40 inference(superposition,[],[f273,f366])).
% 0.15/0.40 thf(f317,plain,(
% 0.15/0.40 ~spl0_3 | ~spl0_8),
% 0.15/0.40 inference(avatar_contradiction_clause,[],[f316])).
% 0.15/0.40 thf(f316,plain,(
% 0.15/0.40 $false | (~spl0_3 | ~spl0_8)),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f315])).
% 0.15/0.40 thf(f315,plain,(
% 0.15/0.40 ($true = $false) | (~spl0_3 | ~spl0_8)),
% 0.15/0.40 inference(boolean_simplification,[],[f314])).
% 0.15/0.40 thf(f314,plain,(
% 0.15/0.40 ($true = (~ $true)) | (~spl0_3 | ~spl0_8)),
% 0.15/0.40 inference(forward_demodulation,[],[f301,f259])).
% 0.15/0.40 thf(f259,plain,(
% 0.15/0.40 ((sK2 @ sK4 @ sK5) = $true) | ~spl0_8),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f257])).
% 0.15/0.40 thf(f257,plain,(
% 0.15/0.40 (((sK2 @ sK4 @ sK5) => (sK2 @ sK5 @ sK4)) = $false) | ~spl0_8),
% 0.15/0.40 inference(beta_eta_normalization,[],[f256])).
% 0.15/0.40 thf(f256,plain,(
% 0.15/0.40 (((^[Y0 : $i]: ((sK2 @ sK4 @ Y0) => (sK2 @ Y0 @ sK4))) @ sK5) = $false) | ~spl0_8),
% 0.15/0.40 inference(sigma_clausification,[],[f255])).
% 0.15/0.40 thf(f255,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) => (sK2 @ Y0 @ sK4)))) = $false) | ~spl0_8),
% 0.15/0.40 inference(beta_eta_normalization,[],[f254])).
% 0.15/0.40 thf(f254,plain,(
% 0.15/0.40 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))) @ sK4) = $false) | ~spl0_8),
% 0.15/0.40 inference(sigma_clausification,[],[f213])).
% 0.15/0.40 thf(f301,plain,(
% 0.15/0.40 ($true = (~ (sK2 @ sK4 @ sK5))) | (~spl0_3 | ~spl0_8)),
% 0.15/0.40 inference(boolean_simplification,[],[f300])).
% 0.15/0.40 thf(f300,plain,(
% 0.15/0.40 ($true = (~ ($true & (sK2 @ sK4 @ sK5)))) | (~spl0_3 | ~spl0_8)),
% 0.15/0.40 inference(superposition,[],[f292,f269])).
% 0.15/0.40 thf(f292,plain,(
% 0.15/0.40 ( ! [X0 : $i] : (($true = (~ ((sK2 @ X0 @ sK4) & (sK2 @ X0 @ sK5))))) ) | (~spl0_3 | ~spl0_8)),
% 0.15/0.40 inference(boolean_simplification,[],[f275])).
% 0.15/0.40 thf(f275,plain,(
% 0.15/0.40 ( ! [X0 : $i] : (((((sK2 @ X0 @ sK4) & (sK2 @ X0 @ sK5)) => $false) = $true)) ) | (~spl0_3 | ~spl0_8)),
% 0.15/0.40 inference(superposition,[],[f273,f261])).
% 0.15/0.40 thf(f261,plain,(
% 0.15/0.40 ((sK2 @ sK5 @ sK4) = $false) | ~spl0_8),
% 0.15/0.40 inference(boolean_simplification,[],[f260])).
% 0.15/0.40 thf(f260,plain,(
% 0.15/0.40 (($true => (sK2 @ sK5 @ sK4)) = $false) | ~spl0_8),
% 0.15/0.40 inference(backward_demodulation,[],[f257,f259])).
% 0.15/0.40 thf(f239,plain,(
% 0.15/0.40 ~spl0_4 | ~spl0_7),
% 0.15/0.40 inference(avatar_contradiction_clause,[],[f238])).
% 0.15/0.40 thf(f238,plain,(
% 0.15/0.40 $false | (~spl0_4 | ~spl0_7)),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f237])).
% 0.15/0.40 thf(f237,plain,(
% 0.15/0.40 ($true = $false) | (~spl0_4 | ~spl0_7)),
% 0.15/0.40 inference(boolean_simplification,[],[f236])).
% 0.15/0.40 thf(f236,plain,(
% 0.15/0.40 ($true = ($false & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1)))))))))) | (~spl0_4 | ~spl0_7)),
% 0.15/0.40 inference(boolean_simplification,[],[f235])).
% 0.15/0.40 thf(f235,plain,(
% 0.15/0.40 ($true = ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & $false) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1)))))))))) | (~spl0_4 | ~spl0_7)),
% 0.15/0.40 inference(forward_demodulation,[],[f159,f210])).
% 0.15/0.40 thf(f210,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0)))) = $false) | ~spl0_7),
% 0.15/0.40 inference(avatar_component_clause,[],[f209])).
% 0.15/0.40 thf(f209,plain,(
% 0.15/0.40 spl0_7 <=> ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0)))) = $false)),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])).
% 0.15/0.40 thf(f234,plain,(
% 0.15/0.40 ~spl0_3 | ~spl0_7),
% 0.15/0.40 inference(avatar_contradiction_clause,[],[f233])).
% 0.15/0.40 thf(f233,plain,(
% 0.15/0.40 $false | (~spl0_3 | ~spl0_7)),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f229])).
% 0.15/0.40 thf(f229,plain,(
% 0.15/0.40 ($true = $false) | (~spl0_3 | ~spl0_7)),
% 0.15/0.40 inference(superposition,[],[f228,f222])).
% 0.15/0.40 thf(f222,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (((sK2 @ sK3 @ X1) = $false)) ) | ~spl0_7),
% 0.15/0.40 inference(pi_clausification,[],[f221])).
% 0.15/0.40 thf(f221,plain,(
% 0.15/0.40 ((?? @ $i @ (sK2 @ sK3)) = $false) | ~spl0_7),
% 0.15/0.40 inference(beta_eta_normalization,[],[f220])).
% 0.15/0.40 thf(f220,plain,(
% 0.15/0.40 (((^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))) @ sK3) = $false) | ~spl0_7),
% 0.15/0.40 inference(sigma_clausification,[],[f210])).
% 0.15/0.40 thf(f228,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($true = (sK2 @ X1 @ X1))) ) | ~spl0_3),
% 0.15/0.40 inference(beta_eta_normalization,[],[f227])).
% 0.15/0.40 thf(f227,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (sK2 @ Y0 @ Y0)) @ X1))) ) | ~spl0_3),
% 0.15/0.40 inference(pi_clausification,[],[f226])).
% 0.15/0.40 thf(f226,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0))) = $true) | ~spl0_3),
% 0.15/0.40 inference(boolean_simplification,[],[f225])).
% 0.15/0.40 thf(f225,plain,(
% 0.15/0.40 (((!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0))) & $true) = $true) | ~spl0_3),
% 0.15/0.40 inference(backward_demodulation,[],[f156,f223])).
% 0.15/0.40 thf(f223,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) = $true) | ~spl0_3),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f156])).
% 0.15/0.40 thf(f214,plain,(
% 0.15/0.40 spl0_7 | spl0_8 | ~spl0_5),
% 0.15/0.40 inference(avatar_split_clause,[],[f207,f196,f212,f209])).
% 0.15/0.40 thf(f196,plain,(
% 0.15/0.40 spl0_5 <=> (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) = $false)),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.15/0.40 thf(f207,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0)))))) = $false) | ~spl0_5),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f197])).
% 0.15/0.40 thf(f197,plain,(
% 0.15/0.40 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) = $false) | ~spl0_5),
% 0.15/0.40 inference(avatar_component_clause,[],[f196])).
% 0.15/0.40 thf(f205,plain,(
% 0.15/0.40 ~spl0_1 | ~spl0_3),
% 0.15/0.40 inference(avatar_contradiction_clause,[],[f204])).
% 0.15/0.40 thf(f204,plain,(
% 0.15/0.40 $false | (~spl0_1 | ~spl0_3)),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f203])).
% 0.15/0.40 thf(f203,plain,(
% 0.15/0.40 ($true = $false) | (~spl0_1 | ~spl0_3)),
% 0.15/0.40 inference(backward_demodulation,[],[f156,f149])).
% 0.15/0.40 thf(f201,plain,(
% 0.15/0.40 spl0_5 | spl0_6 | ~spl0_2),
% 0.15/0.40 inference(avatar_split_clause,[],[f194,f151,f199,f196])).
% 0.15/0.40 thf(f151,plain,(
% 0.15/0.40 spl0_2 <=> (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1))))))))) = $false)),
% 0.15/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.15/0.40 thf(f194,plain,(
% 0.15/0.40 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1)))))))) = $false) | ~spl0_2),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f168])).
% 0.15/0.40 thf(f168,plain,(
% 0.15/0.40 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1))))))))) = $false) | ~spl0_2),
% 0.15/0.40 inference(boolean_simplification,[],[f166])).
% 0.15/0.40 thf(f166,plain,(
% 0.15/0.40 (((($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1))))))))) = $false) | ~spl0_2),
% 0.15/0.40 inference(backward_demodulation,[],[f152,f162])).
% 0.15/0.40 thf(f162,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) = $true) | ~spl0_2),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f161])).
% 0.15/0.40 thf(f161,plain,(
% 0.15/0.40 (((!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1))))))))) != $false) | ~spl0_2),
% 0.15/0.40 inference(backward_demodulation,[],[f144,f152])).
% 0.15/0.40 thf(f152,plain,(
% 0.15/0.40 (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1))))))))) = $false) | ~spl0_2),
% 0.15/0.40 inference(avatar_component_clause,[],[f151])).
% 0.15/0.40 thf(f160,plain,(
% 0.15/0.40 spl0_3 | spl0_4),
% 0.15/0.40 inference(avatar_split_clause,[],[f145,f158,f155])).
% 0.15/0.40 thf(f145,plain,(
% 0.15/0.40 ($true = ((!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))))) | ($true = ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1))))))))))),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f144])).
% 0.15/0.40 thf(f153,plain,(
% 0.15/0.40 spl0_1 | spl0_2),
% 0.15/0.40 inference(avatar_split_clause,[],[f146,f151,f148])).
% 0.15/0.40 thf(f146,plain,(
% 0.15/0.40 (((!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1))))))))) = $false) | (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y0 @ Y1)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK2 @ Y1 @ Y0))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y0 @ Y2)) => (sK2 @ Y0 @ Y1))))))))) = $false)),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f144])).
% 0.15/0.40 % SZS output end Proof for theBenchmark
% 0.15/0.40 % (18987)------------------------------
% 0.15/0.40 % (18987)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (18987)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (18987)Memory used [KB]: 6140
% 0.15/0.40 % (18987)Time elapsed: 0.055 s
% 0.15/0.40 % (18987)Instructions burned: 94 (million)
% 0.15/0.40 % (18987)------------------------------
% 0.15/0.40 % (18987)------------------------------
% 0.15/0.40 % (18975)Success in time 0.072 s
% 0.15/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------