TSTP Solution File: LCL601^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL601^1 : TPTP v8.2.0. Released v3.6.0.
% 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 : n026.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 00:16:09 EDT 2024
% Result : Theorem 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL601^1 : TPTP v8.2.0. Released v3.6.0.
% 0.03/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 20 02:56:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.38 % (28968)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.38 % (28972)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.21/0.38 % (28974)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.38 % (28973)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.38 % (28970)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.39 % (28968)Instruction limit reached!
% 0.21/0.39 % (28968)------------------------------
% 0.21/0.39 % (28968)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (28968)Termination reason: Unknown
% 0.21/0.39 % (28968)Termination phase: Property scanning
% 0.21/0.39
% 0.21/0.39 % (28968)Memory used [KB]: 1023
% 0.21/0.39 % (28968)Time elapsed: 0.005 s
% 0.21/0.39 % (28968)Instructions burned: 5 (million)
% 0.21/0.39 % (28968)------------------------------
% 0.21/0.39 % (28968)------------------------------
% 0.21/0.39 % (28974)Instruction limit reached!
% 0.21/0.39 % (28974)------------------------------
% 0.21/0.39 % (28974)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (28974)Termination reason: Unknown
% 0.21/0.39 % (28974)Termination phase: Property scanning
% 0.21/0.39
% 0.21/0.39 % (28974)Memory used [KB]: 1023
% 0.21/0.39 % (28970)Instruction limit reached!
% 0.21/0.39 % (28970)------------------------------
% 0.21/0.39 % (28970)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (28970)Termination reason: Unknown
% 0.21/0.39 % (28970)Termination phase: shuffling
% 0.21/0.39
% 0.21/0.39 % (28970)Memory used [KB]: 1023
% 0.21/0.39 % (28970)Time elapsed: 0.003 s
% 0.21/0.39 % (28970)Instructions burned: 3 (million)
% 0.21/0.39 % (28970)------------------------------
% 0.21/0.39 % (28970)------------------------------
% 0.21/0.39 % (28974)Time elapsed: 0.004 s
% 0.21/0.39 % (28974)Instructions burned: 4 (million)
% 0.21/0.39 % (28974)------------------------------
% 0.21/0.39 % (28974)------------------------------
% 0.21/0.39 % (28969)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.21/0.39 % (28967)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.39 % (28972)Refutation not found, incomplete strategy
% 0.21/0.39 % (28972)------------------------------
% 0.21/0.39 % (28972)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (28972)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.39
% 0.21/0.39
% 0.21/0.39 % (28972)Memory used [KB]: 5628
% 0.21/0.39 % (28972)Time elapsed: 0.010 s
% 0.21/0.39 % (28972)Instructions burned: 11 (million)
% 0.21/0.39 % (28972)------------------------------
% 0.21/0.39 % (28972)------------------------------
% 0.21/0.39 % (28971)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.39 % (28971)Instruction limit reached!
% 0.21/0.39 % (28971)------------------------------
% 0.21/0.39 % (28971)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (28971)Termination reason: Unknown
% 0.21/0.39 % (28971)Termination phase: shuffling
% 0.21/0.39
% 0.21/0.39 % (28971)Memory used [KB]: 1023
% 0.21/0.39 % (28971)Time elapsed: 0.003 s
% 0.21/0.39 % (28971)Instructions burned: 3 (million)
% 0.21/0.39 % (28971)------------------------------
% 0.21/0.39 % (28971)------------------------------
% 0.21/0.40 % (28973)Instruction limit reached!
% 0.21/0.40 % (28973)------------------------------
% 0.21/0.40 % (28973)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (28973)Termination reason: Unknown
% 0.21/0.40 % (28973)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (28973)Memory used [KB]: 5628
% 0.21/0.40 % (28973)Time elapsed: 0.013 s
% 0.21/0.40 % (28973)Instructions burned: 18 (million)
% 0.21/0.40 % (28973)------------------------------
% 0.21/0.40 % (28973)------------------------------
% 0.21/0.40 % (28975)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.40 % (28976)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.40 % (28977)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.40 % (28977)Instruction limit reached!
% 0.21/0.40 % (28977)------------------------------
% 0.21/0.40 % (28977)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (28977)Termination reason: Unknown
% 0.21/0.40 % (28977)Termination phase: shuffling
% 0.21/0.40
% 0.21/0.40 % (28977)Memory used [KB]: 1023
% 0.21/0.40 % (28977)Time elapsed: 0.003 s
% 0.21/0.40 % (28977)Instructions burned: 3 (million)
% 0.21/0.40 % (28977)------------------------------
% 0.21/0.40 % (28977)------------------------------
% 0.21/0.41 % (28969)Instruction limit reached!
% 0.21/0.41 % (28969)------------------------------
% 0.21/0.41 % (28969)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (28969)Termination reason: Unknown
% 0.21/0.41 % (28969)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (28969)Memory used [KB]: 5756
% 0.21/0.41 % (28969)Time elapsed: 0.018 s
% 0.21/0.41 % (28969)Instructions burned: 27 (million)
% 0.21/0.41 % (28969)------------------------------
% 0.21/0.41 % (28969)------------------------------
% 0.21/0.41 % (28979)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.41 % (28976)Instruction limit reached!
% 0.21/0.41 % (28976)------------------------------
% 0.21/0.41 % (28976)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (28976)Termination reason: Unknown
% 0.21/0.41 % (28976)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (28976)Memory used [KB]: 5628
% 0.21/0.41 % (28976)Time elapsed: 0.010 s
% 0.21/0.41 % (28976)Instructions burned: 15 (million)
% 0.21/0.41 % (28976)------------------------------
% 0.21/0.41 % (28976)------------------------------
% 0.21/0.41 % (28980)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.41 % (28978)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.21/0.41 % (28979)Instruction limit reached!
% 0.21/0.41 % (28979)------------------------------
% 0.21/0.41 % (28979)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (28979)Termination reason: Unknown
% 0.21/0.42 % (28979)Termination phase: Property scanning
% 0.21/0.42
% 0.21/0.42 % (28979)Memory used [KB]: 1023
% 0.21/0.42 % (28979)Time elapsed: 0.006 s
% 0.21/0.42 % (28979)Instructions burned: 8 (million)
% 0.21/0.42 % (28979)------------------------------
% 0.21/0.42 % (28979)------------------------------
% 0.21/0.42 % (28975)Instruction limit reached!
% 0.21/0.42 % (28975)------------------------------
% 0.21/0.42 % (28975)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (28975)Termination reason: Unknown
% 0.21/0.42 % (28975)Termination phase: Saturation
% 0.21/0.42
% 0.21/0.42 % (28975)Memory used [KB]: 6012
% 0.21/0.42 % (28975)Time elapsed: 0.022 s
% 0.21/0.42 % (28975)Instructions burned: 37 (million)
% 0.21/0.42 % (28975)------------------------------
% 0.21/0.42 % (28975)------------------------------
% 0.21/0.42 % (28980)Instruction limit reached!
% 0.21/0.42 % (28980)------------------------------
% 0.21/0.42 % (28980)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (28980)Termination reason: Unknown
% 0.21/0.42 % (28982)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.42 % (28980)Termination phase: Saturation
% 0.21/0.42
% 0.21/0.42 % (28980)Memory used [KB]: 5884
% 0.21/0.42 % (28980)Time elapsed: 0.012 s
% 0.21/0.42 % (28980)Instructions burned: 16 (million)
% 0.21/0.42 % (28980)------------------------------
% 0.21/0.42 % (28980)------------------------------
% 0.21/0.42 % (28981)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.42 % (28981)Instruction limit reached!
% 0.21/0.42 % (28981)------------------------------
% 0.21/0.42 % (28981)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (28981)Termination reason: Unknown
% 0.21/0.42 % (28982)Instruction limit reached!
% 0.21/0.42 % (28982)------------------------------
% 0.21/0.42 % (28982)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (28981)Termination phase: shuffling
% 0.21/0.42
% 0.21/0.42 % (28981)Memory used [KB]: 1023
% 0.21/0.42 % (28981)Time elapsed: 0.003 s
% 0.21/0.42 % (28981)Instructions burned: 3 (million)
% 0.21/0.42 % (28981)------------------------------
% 0.21/0.42 % (28981)------------------------------
% 0.21/0.42 % (28982)Termination reason: Unknown
% 0.21/0.42 % (28982)Termination phase: shuffling
% 0.21/0.42
% 0.21/0.42 % (28982)Memory used [KB]: 1023
% 0.21/0.42 % (28982)Time elapsed: 0.004 s
% 0.21/0.42 % (28982)Instructions burned: 4 (million)
% 0.21/0.42 % (28982)------------------------------
% 0.21/0.42 % (28982)------------------------------
% 0.21/0.43 % (28983)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.43 % (28983)Instruction limit reached!
% 0.21/0.43 % (28983)------------------------------
% 0.21/0.43 % (28983)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (28983)Termination reason: Unknown
% 0.21/0.43 % (28983)Termination phase: Function definition elimination
% 0.21/0.43
% 0.21/0.43 % (28983)Memory used [KB]: 1151
% 0.21/0.43 % (28983)Time elapsed: 0.006 s
% 0.21/0.43 % (28983)Instructions burned: 8 (million)
% 0.21/0.43 % (28983)------------------------------
% 0.21/0.43 % (28983)------------------------------
% 0.21/0.43 % (28984)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.43 % (28984)Instruction limit reached!
% 0.21/0.43 % (28984)------------------------------
% 0.21/0.43 % (28984)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (28984)Termination reason: Unknown
% 0.21/0.43 % (28984)Termination phase: shuffling
% 0.21/0.43
% 0.21/0.43 % (28984)Memory used [KB]: 1023
% 0.21/0.43 % (28984)Time elapsed: 0.003 s
% 0.21/0.43 % (28984)Instructions burned: 3 (million)
% 0.21/0.43 % (28984)------------------------------
% 0.21/0.43 % (28984)------------------------------
% 0.21/0.44 % (28985)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.44 % (28985)Instruction limit reached!
% 0.21/0.44 % (28985)------------------------------
% 0.21/0.44 % (28985)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (28985)Termination reason: Unknown
% 0.21/0.44 % (28985)Termination phase: shuffling
% 0.21/0.44
% 0.21/0.44 % (28985)Memory used [KB]: 1023
% 0.21/0.44 % (28985)Time elapsed: 0.004 s
% 0.21/0.44 % (28985)Instructions burned: 4 (million)
% 0.21/0.44 % (28985)------------------------------
% 0.21/0.44 % (28985)------------------------------
% 0.21/0.44 % (28988)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.44 % (28987)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.44 % (28986)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.44 % (28988)Instruction limit reached!
% 0.21/0.44 % (28988)------------------------------
% 0.21/0.44 % (28988)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (28988)Termination reason: Unknown
% 0.21/0.44 % (28988)Termination phase: Property scanning
% 0.21/0.44
% 0.21/0.44 % (28988)Memory used [KB]: 1023
% 0.21/0.44 % (28988)Time elapsed: 0.005 s
% 0.21/0.44 % (28988)Instructions burned: 6 (million)
% 0.21/0.44 % (28988)------------------------------
% 0.21/0.44 % (28988)------------------------------
% 0.21/0.45 % (28989)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.21/0.45 % (28990)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.21/0.45 % (28991)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.21/0.45 % (28986)Instruction limit reached!
% 0.21/0.45 % (28986)------------------------------
% 0.21/0.45 % (28986)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (28986)Termination reason: Unknown
% 0.21/0.45 % (28986)Termination phase: Saturation
% 0.21/0.45
% 0.21/0.45 % (28986)Memory used [KB]: 5756
% 0.21/0.45 % (28986)Time elapsed: 0.034 s
% 0.21/0.45 % (28986)Instructions burned: 18 (million)
% 0.21/0.45 % (28986)------------------------------
% 0.21/0.45 % (28986)------------------------------
% 0.21/0.45 % (28991)Instruction limit reached!
% 0.21/0.45 % (28991)------------------------------
% 0.21/0.45 % (28991)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (28991)Termination reason: Unknown
% 0.21/0.45 % (28991)Termination phase: Property scanning
% 0.21/0.45
% 0.21/0.45 % (28991)Memory used [KB]: 1023
% 0.21/0.45 % (28991)Time elapsed: 0.005 s
% 0.21/0.45 % (28991)Instructions burned: 6 (million)
% 0.21/0.45 % (28991)------------------------------
% 0.21/0.45 % (28991)------------------------------
% 0.21/0.46 % (28992)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.46 % (28989)Refutation not found, incomplete strategy
% 0.21/0.46 % (28989)------------------------------
% 0.21/0.46 % (28989)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (28989)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.46
% 0.21/0.46
% 0.21/0.46 % (28989)Memory used [KB]: 5628
% 0.21/0.46 % (28989)Time elapsed: 0.030 s
% 0.21/0.46 % (28989)Instructions burned: 10 (million)
% 0.21/0.46 % (28989)------------------------------
% 0.21/0.46 % (28989)------------------------------
% 0.21/0.46 % (28978)First to succeed.
% 0.21/0.46 % (28992)Instruction limit reached!
% 0.21/0.46 % (28992)------------------------------
% 0.21/0.46 % (28992)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (28992)Termination reason: Unknown
% 0.21/0.46 % (28992)Termination phase: Saturation
% 0.21/0.46
% 0.21/0.46 % (28992)Memory used [KB]: 1023
% 0.21/0.46 % (28992)Time elapsed: 0.006 s
% 0.21/0.46 % (28992)Instructions burned: 7 (million)
% 0.21/0.46 % (28992)------------------------------
% 0.21/0.46 % (28992)------------------------------
% 0.21/0.46 % (28990)Instruction limit reached!
% 0.21/0.46 % (28990)------------------------------
% 0.21/0.46 % (28990)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (28990)Termination reason: Unknown
% 0.21/0.46 % (28990)Termination phase: Saturation
% 0.21/0.46
% 0.21/0.46 % (28990)Memory used [KB]: 5756
% 0.21/0.46 % (28990)Time elapsed: 0.015 s
% 0.21/0.46 % (28990)Instructions burned: 21 (million)
% 0.21/0.46 % (28990)------------------------------
% 0.21/0.46 % (28990)------------------------------
% 0.21/0.47 % (28978)Refutation found. Thanks to Tanya!
% 0.21/0.47 % SZS status Theorem for theBenchmark
% 0.21/0.47 % SZS output start Proof for theBenchmark
% 0.21/0.47 thf(type_def_6, type, individuals: $tType).
% 0.21/0.47 thf(func_def_1, type, prop_a: $i > $o).
% 0.21/0.47 thf(func_def_2, type, prop_b: $i > $o).
% 0.21/0.47 thf(func_def_3, type, prop_c: $i > $o).
% 0.21/0.47 thf(func_def_4, type, mfalse: $i > $o).
% 0.21/0.47 thf(func_def_5, type, mtrue: $i > $o).
% 0.21/0.47 thf(func_def_6, type, mnot: ($i > $o) > $i > $o).
% 0.21/0.47 thf(func_def_8, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.47 thf(func_def_9, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.47 thf(func_def_10, type, mimpl: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.47 thf(func_def_11, type, miff: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.47 thf(func_def_12, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.47 thf(func_def_13, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.47 thf(func_def_14, type, individuals: $tType).
% 0.21/0.47 thf(func_def_15, type, mall: (individuals > $i > $o) > $i > $o).
% 0.21/0.47 thf(func_def_16, type, mexists: (individuals > $i > $o) > $i > $o).
% 0.21/0.47 thf(func_def_17, type, mvalid: ($i > $o) > $o).
% 0.21/0.47 thf(func_def_18, type, msatisfiable: ($i > $o) > $o).
% 0.21/0.47 thf(func_def_19, type, mcountersatisfiable: ($i > $o) > $o).
% 0.21/0.47 thf(func_def_20, type, minvalid: ($i > $o) > $o).
% 0.21/0.47 thf(func_def_21, type, cartesian_product: ($i > $o) > ($i > $o) > $i > $i > $o).
% 0.21/0.47 thf(func_def_22, type, pair_rel: $i > $i > $i > $i > $o).
% 0.21/0.47 thf(func_def_23, type, id_rel: ($i > $o) > $i > $i > $o).
% 0.21/0.47 thf(func_def_24, type, sub_rel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.21/0.47 thf(func_def_25, type, is_rel_on: ($i > $i > $o) > ($i > $o) > ($i > $o) > $o).
% 0.21/0.47 thf(func_def_26, type, restrict_rel_domain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.21/0.47 thf(func_def_27, type, rel_diagonal: $i > $i > $o).
% 0.21/0.47 thf(func_def_28, type, rel_composition: ($i > $i > $o) > ($i > $i > $o) > $i > $i > $o).
% 0.21/0.47 thf(func_def_29, type, reflexive: ($i > $i > $o) > $o).
% 0.21/0.47 thf(func_def_30, type, irreflexive: ($i > $i > $o) > $o).
% 0.21/0.47 thf(func_def_31, type, symmetric: ($i > $i > $o) > $o).
% 0.21/0.47 thf(func_def_32, type, transitive: ($i > $i > $o) > $o).
% 0.21/0.47 thf(func_def_33, type, equiv_rel: ($i > $i > $o) > $o).
% 0.21/0.47 thf(func_def_34, type, rel_codomain: ($i > $i > $o) > $i > $o).
% 0.21/0.47 thf(func_def_35, type, rel_domain: ($i > $i > $o) > $i > $o).
% 0.21/0.47 thf(func_def_36, type, rel_inverse: ($i > $i > $o) > $i > $i > $o).
% 0.21/0.47 thf(func_def_37, type, equiv_classes: ($i > $i > $o) > ($i > $o) > $o).
% 0.21/0.47 thf(func_def_38, type, restrict_rel_codomain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.21/0.47 thf(func_def_39, type, rel_field: ($i > $i > $o) > $i > $o).
% 0.21/0.47 thf(func_def_40, type, well_founded: ($i > $i > $o) > $o).
% 0.21/0.47 thf(func_def_41, type, upwards_well_founded: ($i > $i > $o) > $o).
% 0.21/0.47 thf(func_def_61, type, ph1: !>[X0: $tType]:(X0)).
% 0.21/0.47 thf(func_def_62, type, sK2: $i > $i > $o).
% 0.21/0.47 thf(func_def_63, type, sK3: $i > $o).
% 0.21/0.47 thf(func_def_67, type, sK7: $i > $i > $o).
% 0.21/0.47 thf(func_def_71, type, sK11: ($i > $o) > $i).
% 0.21/0.47 thf(func_def_72, type, sK12: $i > ($i > $i > $o) > ($i > $o) > $i).
% 0.21/0.47 thf(f424,plain,(
% 0.21/0.47 $false),
% 0.21/0.47 inference(avatar_sat_refutation,[],[f165,f172,f263,f419,f422])).
% 0.21/0.47 thf(f422,plain,(
% 0.21/0.47 ~spl0_1 | ~spl0_4),
% 0.21/0.47 inference(avatar_contradiction_clause,[],[f421])).
% 0.21/0.47 thf(f421,plain,(
% 0.21/0.47 $false | (~spl0_1 | ~spl0_4)),
% 0.21/0.47 inference(trivial_inequality_removal,[],[f420])).
% 0.21/0.47 thf(f420,plain,(
% 0.21/0.47 ($true = $false) | (~spl0_1 | ~spl0_4)),
% 0.21/0.47 inference(backward_demodulation,[],[f171,f161])).
% 0.21/0.47 thf(f161,plain,(
% 0.21/0.47 ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => (Y1 @ Y4))))))))))))))) | ~spl0_1),
% 0.21/0.47 inference(avatar_component_clause,[],[f160])).
% 0.21/0.47 thf(f160,plain,(
% 0.21/0.47 spl0_1 <=> ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => (Y1 @ Y4)))))))))))))))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.21/0.47 thf(f171,plain,(
% 0.21/0.47 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => (Y1 @ Y4))))))))))))))) | ~spl0_4),
% 0.21/0.47 inference(avatar_component_clause,[],[f170])).
% 0.21/0.47 thf(f170,plain,(
% 0.21/0.47 spl0_4 <=> ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => (Y1 @ Y4)))))))))))))))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.21/0.47 thf(f419,plain,(
% 0.21/0.47 ~spl0_2),
% 0.21/0.47 inference(avatar_contradiction_clause,[],[f418])).
% 0.21/0.47 thf(f418,plain,(
% 0.21/0.47 $false | ~spl0_2),
% 0.21/0.47 inference(trivial_inequality_removal,[],[f417])).
% 0.21/0.47 thf(f417,plain,(
% 0.21/0.47 ($true = $false) | ~spl0_2),
% 0.21/0.47 inference(forward_demodulation,[],[f407,f287])).
% 0.21/0.47 thf(f287,plain,(
% 0.21/0.47 ($false = (sK7 @ sK10 @ sK9)) | ~spl0_2),
% 0.21/0.47 inference(boolean_simplification,[],[f286])).
% 0.21/0.47 thf(f286,plain,(
% 0.21/0.47 ($false = ($true => (sK7 @ sK10 @ sK9))) | ~spl0_2),
% 0.21/0.47 inference(backward_demodulation,[],[f282,f285])).
% 0.21/0.47 thf(f285,plain,(
% 0.21/0.47 ($true = ((sK7 @ sK8 @ sK9) & (sK7 @ sK10 @ sK8))) | ~spl0_2),
% 0.21/0.47 inference(binary_proxy_clausification,[],[f282])).
% 0.21/0.47 thf(f282,plain,(
% 0.21/0.47 ((((sK7 @ sK8 @ sK9) & (sK7 @ sK10 @ sK8)) => (sK7 @ sK10 @ sK9)) = $false) | ~spl0_2),
% 0.21/0.47 inference(beta_eta_normalization,[],[f281])).
% 0.21/0.47 thf(f281,plain,(
% 0.21/0.47 ($false = ((^[Y0 : $i]: (((sK7 @ sK8 @ sK9) & (sK7 @ Y0 @ sK8)) => (sK7 @ Y0 @ sK9))) @ sK10)) | ~spl0_2),
% 0.21/0.47 inference(sigma_clausification,[],[f278])).
% 0.21/0.47 thf(f278,plain,(
% 0.21/0.47 ($false = (!! @ $i @ (^[Y0 : $i]: (((sK7 @ sK8 @ sK9) & (sK7 @ Y0 @ sK8)) => (sK7 @ Y0 @ sK9))))) | ~spl0_2),
% 0.21/0.47 inference(beta_eta_normalization,[],[f277])).
% 0.21/0.47 thf(f277,plain,(
% 0.21/0.47 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK7 @ sK8 @ Y0) & (sK7 @ Y1 @ sK8)) => (sK7 @ Y1 @ Y0))))) @ sK9)) | ~spl0_2),
% 0.21/0.47 inference(sigma_clausification,[],[f274])).
% 0.21/0.47 thf(f274,plain,(
% 0.21/0.47 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK7 @ sK8 @ Y0) & (sK7 @ Y1 @ sK8)) => (sK7 @ Y1 @ Y0))))))) | ~spl0_2),
% 0.21/0.47 inference(beta_eta_normalization,[],[f273])).
% 0.21/0.47 thf(f273,plain,(
% 0.21/0.47 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK7 @ Y0 @ Y1) & (sK7 @ Y2 @ Y0)) => (sK7 @ Y2 @ Y1))))))) @ sK8)) | ~spl0_2),
% 0.21/0.47 inference(sigma_clausification,[],[f270])).
% 0.21/0.47 thf(f270,plain,(
% 0.21/0.47 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK7 @ Y0 @ Y1) & (sK7 @ Y2 @ Y0)) => (sK7 @ Y2 @ Y1)))))))) = $false) | ~spl0_2),
% 0.21/0.47 inference(beta_eta_normalization,[],[f269])).
% 0.21/0.47 thf(f269,plain,(
% 0.21/0.47 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) @ sK7) = $false) | ~spl0_2),
% 0.21/0.47 inference(sigma_clausification,[],[f164])).
% 0.21/0.47 thf(f164,plain,(
% 0.21/0.47 ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))))) | ~spl0_2),
% 0.21/0.47 inference(avatar_component_clause,[],[f163])).
% 0.21/0.47 thf(f163,plain,(
% 0.21/0.47 spl0_2 <=> ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2)))))))))))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.21/0.47 thf(f407,plain,(
% 0.21/0.47 ($true = (sK7 @ sK10 @ sK9)) | ~spl0_2),
% 0.21/0.47 inference(boolean_simplification,[],[f404])).
% 0.21/0.47 thf(f404,plain,(
% 0.21/0.47 ($true = ($true => (sK7 @ sK10 @ sK9))) | ~spl0_2),
% 0.21/0.47 inference(superposition,[],[f399,f289])).
% 0.21/0.47 thf(f289,plain,(
% 0.21/0.47 ($true = (sK7 @ sK8 @ sK9)) | ~spl0_2),
% 0.21/0.47 inference(binary_proxy_clausification,[],[f285])).
% 0.21/0.47 thf(f399,plain,(
% 0.21/0.47 ( ! [X0 : $i] : ((((sK7 @ sK8 @ X0) => (sK7 @ sK10 @ X0)) = $true)) ) | ~spl0_2),
% 0.21/0.47 inference(trivial_inequality_removal,[],[f398])).
% 0.21/0.47 thf(f398,plain,(
% 0.21/0.47 ( ! [X0 : $i] : (($true = $false) | (((sK7 @ sK8 @ X0) => (sK7 @ sK10 @ X0)) = $true)) ) | ~spl0_2),
% 0.21/0.47 inference(boolean_simplification,[],[f393])).
% 0.21/0.47 thf(f393,plain,(
% 0.21/0.47 ( ! [X0 : $i] : ((((sK7 @ sK8 @ X0) => (sK7 @ sK10 @ X0)) = $true) | ($false = ($false => $false))) ) | ~spl0_2),
% 0.21/0.47 inference(superposition,[],[f343,f390])).
% 0.21/0.47 thf(f390,plain,(
% 0.21/0.47 ((sK7 @ sK10 @ (sK11 @ (sK7 @ sK10))) = $false) | ~spl0_2),
% 0.21/0.47 inference(trivial_inequality_removal,[],[f389])).
% 0.21/0.47 thf(f389,plain,(
% 0.21/0.47 ($true = $false) | ((sK7 @ sK10 @ (sK11 @ (sK7 @ sK10))) = $false) | ~spl0_2),
% 0.21/0.47 inference(boolean_simplification,[],[f388])).
% 0.21/0.47 thf(f388,plain,(
% 0.21/0.47 ((~ $true) = $true) | ((sK7 @ sK10 @ (sK11 @ (sK7 @ sK10))) = $false) | ~spl0_2),
% 0.21/0.47 inference(forward_demodulation,[],[f384,f289])).
% 0.21/0.47 thf(f384,plain,(
% 0.21/0.47 ((sK7 @ sK10 @ (sK11 @ (sK7 @ sK10))) = $false) | ((~ (sK7 @ sK8 @ sK9)) = $true) | ~spl0_2),
% 0.21/0.47 inference(boolean_simplification,[],[f376])).
% 0.21/0.47 thf(f376,plain,(
% 0.21/0.47 ($true = ((sK7 @ sK8 @ sK9) => $false)) | ((sK7 @ sK10 @ (sK11 @ (sK7 @ sK10))) = $false) | ~spl0_2),
% 0.21/0.47 inference(superposition,[],[f370,f287])).
% 0.21/0.47 thf(f370,plain,(
% 0.21/0.47 ( ! [X0 : $i > $o,X1 : $i] : (($true = ((sK7 @ sK8 @ X1) => (X0 @ X1))) | ($false = (X0 @ (sK11 @ X0)))) ) | ~spl0_2),
% 0.21/0.47 inference(binary_proxy_clausification,[],[f343])).
% 0.21/0.47 thf(f343,plain,(
% 0.21/0.47 ( ! [X0 : $i > $o,X1 : $i] : (($false = ((sK7 @ sK10 @ (sK11 @ X0)) => (X0 @ (sK11 @ X0)))) | ($true = ((sK7 @ sK8 @ X1) => (X0 @ X1)))) ) | ~spl0_2),
% 0.21/0.47 inference(beta_eta_normalization,[],[f336])).
% 0.21/0.47 thf(f336,plain,(
% 0.21/0.47 ( ! [X0 : $i > $o,X1 : $i] : (($true = ((sK7 @ sK8 @ X1) => (X0 @ X1))) | (((^[Y0 : $i]: ((sK7 @ sK10 @ Y0) => (X0 @ Y0))) @ (sK11 @ X0)) = $false)) ) | ~spl0_2),
% 0.21/0.47 inference(sigma_clausification,[],[f316])).
% 0.21/0.47 thf(f316,plain,(
% 0.21/0.47 ( ! [X0 : $i > $o,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((sK7 @ sK10 @ Y0) => (X0 @ Y0))))) | ($true = ((sK7 @ sK8 @ X1) => (X0 @ X1)))) ) | ~spl0_2),
% 0.21/0.47 inference(beta_eta_normalization,[],[f312])).
% 0.21/0.47 thf(f312,plain,(
% 0.21/0.47 ( ! [X0 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i]: ((sK7 @ sK8 @ Y0) => (X0 @ Y0))) @ X1)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK7 @ sK10 @ Y0) => (X0 @ Y0)))))) ) | ~spl0_2),
% 0.21/0.47 inference(pi_clausification,[],[f306])).
% 0.21/0.47 thf(f306,plain,(
% 0.21/0.47 ( ! [X0 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK7 @ sK8 @ Y0) => (X0 @ Y0))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK7 @ sK10 @ Y0) => (X0 @ Y0)))))) ) | ~spl0_2),
% 0.21/0.47 inference(not_proxy_clausification,[],[f303])).
% 0.21/0.47 thf(f303,plain,(
% 0.21/0.47 ( ! [X0 : $i > $o] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((sK7 @ sK10 @ Y0) => (X0 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK7 @ sK8 @ Y0) => (X0 @ Y0)))))) ) | ~spl0_2),
% 0.21/0.47 inference(boolean_simplification,[],[f302])).
% 0.21/0.47 thf(f302,plain,(
% 0.21/0.47 ( ! [X0 : $i > $o] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((sK7 @ sK10 @ Y0) => (X0 @ Y0)))))) | ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((sK7 @ sK8 @ Y0) => (X0 @ Y0))))))) ) | ~spl0_2),
% 0.21/0.47 inference(superposition,[],[f297,f291])).
% 0.21/0.47 thf(f291,plain,(
% 0.21/0.47 ($true = (sK7 @ sK10 @ sK8)) | ~spl0_2),
% 0.21/0.47 inference(boolean_simplification,[],[f290])).
% 0.21/0.47 thf(f290,plain,(
% 0.21/0.47 (($true & (sK7 @ sK10 @ sK8)) = $true) | ~spl0_2),
% 0.21/0.47 inference(backward_demodulation,[],[f285,f289])).
% 0.21/0.47 thf(f297,plain,(
% 0.21/0.47 ( ! [X2 : $i > $o,X3 : $i,X1 : $i > $i > $o,X4 : $i] : (($true = ((X1 @ X3 @ X4) => (!! @ $i @ (^[Y0 : $i]: ((X1 @ X4 @ Y0) => (X2 @ Y0)))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ X3 @ Y0) => (X2 @ Y0))))))) ) | ~spl0_2),
% 0.21/0.47 inference(beta_eta_normalization,[],[f295])).
% 0.21/0.47 thf(f295,plain,(
% 0.21/0.47 ( ! [X2 : $i > $o,X3 : $i,X1 : $i > $i > $o,X4 : $i] : (($true = ((^[Y0 : $i]: ((X1 @ X3 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) => (X2 @ Y1)))))) @ X4)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ X3 @ Y0) => (X2 @ Y0))))))) ) | ~spl0_2),
% 0.21/0.47 inference(pi_clausification,[],[f283])).
% 0.21/0.47 thf(f283,plain,(
% 0.21/0.47 ( ! [X2 : $i > $o,X3 : $i,X1 : $i > $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((X1 @ X3 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) => (X2 @ Y1)))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ X3 @ Y0) => (X2 @ Y0))))))) ) | ~spl0_2),
% 0.21/0.47 inference(binary_proxy_clausification,[],[f280])).
% 0.21/0.47 thf(f280,plain,(
% 0.21/0.47 ( ! [X2 : $i > $o,X3 : $i,X1 : $i > $i > $o] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((X1 @ X3 @ Y0) => (X2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((X1 @ X3 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) => (X2 @ Y1)))))))))) ) | ~spl0_2),
% 0.21/0.47 inference(beta_eta_normalization,[],[f279])).
% 0.21/0.47 thf(f279,plain,(
% 0.21/0.47 ( ! [X2 : $i > $o,X3 : $i,X1 : $i > $i > $o] : (($true = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) => (X2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((X1 @ Y1 @ Y2) => (X2 @ Y2))))))))) @ X3))) ) | ~spl0_2),
% 0.21/0.47 inference(pi_clausification,[],[f276])).
% 0.21/0.47 thf(f276,plain,(
% 0.21/0.47 ( ! [X2 : $i > $o,X1 : $i > $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) => (X2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((X1 @ Y1 @ Y2) => (X2 @ Y2)))))))))))) ) | ~spl0_2),
% 0.21/0.47 inference(beta_eta_normalization,[],[f275])).
% 0.21/0.47 thf(f275,plain,(
% 0.21/0.47 ( ! [X2 : $i > $o,X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((X1 @ Y1 @ Y2) => (Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((X1 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((X1 @ Y2 @ Y3) => (Y0 @ Y3))))))))))) @ X2))) ) | ~spl0_2),
% 0.21/0.47 inference(pi_clausification,[],[f272])).
% 0.21/0.47 thf(f272,plain,(
% 0.21/0.47 ( ! [X1 : $i > $i > $o] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((X1 @ Y1 @ Y2) => (Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((X1 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((X1 @ Y2 @ Y3) => (Y0 @ Y3)))))))))))))) ) | ~spl0_2),
% 0.21/0.47 inference(beta_eta_normalization,[],[f271])).
% 0.21/0.47 thf(f271,plain,(
% 0.21/0.47 ( ! [X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => (Y1 @ Y4))))))))))))) @ X1))) ) | ~spl0_2),
% 0.21/0.47 inference(pi_clausification,[],[f268])).
% 0.21/0.47 thf(f268,plain,(
% 0.21/0.47 ($false != (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => (Y1 @ Y4))))))))))))))) | ~spl0_2),
% 0.21/0.47 inference(forward_demodulation,[],[f156,f164])).
% 0.21/0.47 thf(f156,plain,(
% 0.21/0.47 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => (Y1 @ Y4)))))))))))))) != (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2)))))))))))),
% 0.21/0.47 inference(binary_proxy_clausification,[],[f155])).
% 0.21/0.47 thf(f155,plain,(
% 0.21/0.47 ($false = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => (Y1 @ Y4)))))))))))))) = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))))))),
% 0.21/0.47 inference(not_proxy_clausification,[],[f154])).
% 0.21/0.47 thf(f154,plain,(
% 0.21/0.47 ($true = (~ ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => (Y1 @ Y4)))))))))))))) = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2)))))))))))))),
% 0.21/0.47 inference(beta_eta_normalization,[],[f153])).
% 0.21/0.47 thf(f153,plain,(
% 0.21/0.47 ($true = (~ ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (Y2 @ 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)))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y4 @ Y5) => (Y3 @ Y5))))))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y4 @ Y5) => (Y3 @ Y5))))))))) @ Y0 @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y4 @ Y5) => (Y3 @ Y5))))))))) @ Y0 @ Y1)))))))) = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y4 @ Y3))))))))) @ Y0))))))),
% 0.21/0.47 inference(definition_unfolding,[],[f112,f130,f149,f141,f141,f141,f125])).
% 0.21/0.47 thf(f125,plain,(
% 0.21/0.47 (transitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))))),
% 0.21/0.47 inference(cnf_transformation,[],[f85])).
% 0.21/0.47 thf(f85,plain,(
% 0.21/0.47 (transitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))))),
% 0.21/0.47 inference(fool_elimination,[],[f84])).
% 0.21/0.47 thf(f84,plain,(
% 0.21/0.47 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X3) & (X0 @ X3 @ X2)) => (X0 @ X1 @ X2)))) = transitive)),
% 0.21/0.47 inference(rectify,[],[f27])).
% 0.21/0.47 thf(f27,axiom,(
% 0.21/0.47 ((^[X4 : $i > $i > $o] : (! [X0,X12,X2] : (((X4 @ X0 @ X2) & (X4 @ X2 @ X12)) => (X4 @ X0 @ X12)))) = transitive)),
% 0.21/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive)).
% 0.21/0.47 thf(f141,plain,(
% 0.21/0.47 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 0.21/0.47 inference(cnf_transformation,[],[f91])).
% 0.21/0.47 thf(f91,plain,(
% 0.21/0.47 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 0.21/0.47 inference(fool_elimination,[],[f90])).
% 0.21/0.47 thf(f90,plain,(
% 0.21/0.47 (mbox = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X0 @ X2 @ X3) => (X1 @ X3)))))),
% 0.21/0.47 inference(rectify,[],[f8])).
% 0.21/0.47 thf(f8,axiom,(
% 0.21/0.47 (mbox = (^[X4 : $i > $i > $o, X5 : $i > $o, X0 : $i] : (! [X2] : ((X4 @ X0 @ X2) => (X5 @ X2)))))),
% 0.21/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox)).
% 0.21/0.47 thf(f149,plain,(
% 0.21/0.47 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.21/0.47 inference(definition_unfolding,[],[f118,f126,f114])).
% 0.21/0.47 thf(f114,plain,(
% 0.21/0.47 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.47 inference(cnf_transformation,[],[f58])).
% 0.21/0.47 thf(f58,plain,(
% 0.21/0.47 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.47 inference(fool_elimination,[],[f57])).
% 0.21/0.47 thf(f57,plain,(
% 0.21/0.47 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.21/0.47 inference(rectify,[],[f3])).
% 0.21/0.47 thf(f3,axiom,(
% 0.21/0.47 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.21/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.21/0.47 thf(f126,plain,(
% 0.21/0.47 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.47 inference(cnf_transformation,[],[f48])).
% 0.21/0.47 thf(f48,plain,(
% 0.21/0.47 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.47 inference(fool_elimination,[],[f47])).
% 0.21/0.47 thf(f47,plain,(
% 0.21/0.47 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.21/0.47 inference(rectify,[],[f4])).
% 0.21/0.47 thf(f4,axiom,(
% 0.21/0.47 (mor = (^[X0 : $i > $o, X2 : $i > $o, X1 : $i] : ((X2 @ X1) | (X0 @ X1))))),
% 0.21/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.21/0.47 thf(f118,plain,(
% 0.21/0.47 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.47 inference(cnf_transformation,[],[f72])).
% 0.21/0.47 thf(f72,plain,(
% 0.21/0.47 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.47 inference(fool_elimination,[],[f71])).
% 0.21/0.47 thf(f71,plain,(
% 0.21/0.47 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimpl)),
% 0.21/0.47 inference(rectify,[],[f6])).
% 0.21/0.47 thf(f6,axiom,(
% 0.21/0.47 ((^[X1 : $i > $o, X3 : $i > $o] : (mor @ (mnot @ X1) @ X3)) = mimpl)),
% 0.21/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimpl)).
% 0.21/0.47 thf(f130,plain,(
% 0.21/0.47 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.47 inference(cnf_transformation,[],[f77])).
% 0.21/0.47 thf(f77,plain,(
% 0.21/0.47 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.47 inference(fool_elimination,[],[f76])).
% 0.21/0.47 thf(f76,plain,(
% 0.21/0.47 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.21/0.47 inference(rectify,[],[f12])).
% 0.21/0.47 thf(f12,axiom,(
% 0.21/0.47 (mvalid = (^[X5 : $i > $o] : (! [X6] : (X5 @ X6))))),
% 0.21/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.21/0.47 thf(f112,plain,(
% 0.21/0.47 ($true = (~ ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (mvalid @ (mimpl @ (mbox @ Y0 @ Y1) @ (mbox @ Y0 @ (mbox @ Y0 @ Y1)))))))) = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (transitive @ Y0))))))),
% 0.21/0.47 inference(cnf_transformation,[],[f111])).
% 0.21/0.47 thf(f111,plain,(
% 0.21/0.47 ($true = (~ ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (mvalid @ (mimpl @ (mbox @ Y0 @ Y1) @ (mbox @ Y0 @ (mbox @ Y0 @ Y1)))))))) = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (transitive @ Y0))))))),
% 0.21/0.47 inference(fool_elimination,[],[f110])).
% 0.21/0.47 thf(f110,plain,(
% 0.21/0.47 ~(! [X0 : $i > $o,X1 : $i > $i > $o] : (mvalid @ (mimpl @ (mbox @ X1 @ X0) @ (mbox @ X1 @ (mbox @ X1 @ X0)))) <=> ! [X2 : $i > $i > $o] : (transitive @ X2))),
% 0.21/0.47 inference(rectify,[],[f38])).
% 0.21/0.47 thf(f38,negated_conjecture,(
% 0.21/0.47 ~(! [X10 : $i > $o,X4 : $i > $i > $o] : (mvalid @ (mimpl @ (mbox @ X4 @ X10) @ (mbox @ X4 @ (mbox @ X4 @ X10)))) <=> ! [X4 : $i > $i > $o] : (transitive @ X4))),
% 0.21/0.47 inference(negated_conjecture,[],[f37])).
% 0.21/0.47 thf(f37,conjecture,(
% 0.21/0.47 ! [X10 : $i > $o,X4 : $i > $i > $o] : (mvalid @ (mimpl @ (mbox @ X4 @ X10) @ (mbox @ X4 @ (mbox @ X4 @ X10)))) <=> ! [X4 : $i > $i > $o] : (transitive @ X4)),
% 0.21/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm)).
% 0.21/0.47 thf(f263,plain,(
% 0.21/0.47 ~spl0_1 | ~spl0_3),
% 0.21/0.47 inference(avatar_contradiction_clause,[],[f262])).
% 0.21/0.47 thf(f262,plain,(
% 0.21/0.47 $false | (~spl0_1 | ~spl0_3)),
% 0.21/0.47 inference(trivial_inequality_removal,[],[f261])).
% 0.21/0.47 thf(f261,plain,(
% 0.21/0.47 ($true = $false) | (~spl0_1 | ~spl0_3)),
% 0.21/0.47 inference(boolean_simplification,[],[f260])).
% 0.21/0.47 thf(f260,plain,(
% 0.21/0.47 ((~ $true) = $true) | (~spl0_1 | ~spl0_3)),
% 0.21/0.47 inference(forward_demodulation,[],[f254,f224])).
% 0.21/0.47 thf(f224,plain,(
% 0.21/0.47 ($true = (sK2 @ sK5 @ sK6)) | ~spl0_1),
% 0.21/0.47 inference(binary_proxy_clausification,[],[f214])).
% 0.21/0.47 thf(f214,plain,(
% 0.21/0.47 ($false = ((sK2 @ sK5 @ sK6) => (sK3 @ sK6))) | ~spl0_1),
% 0.21/0.47 inference(beta_eta_normalization,[],[f213])).
% 0.21/0.47 thf(f213,plain,(
% 0.21/0.47 ($false = ((^[Y0 : $i]: ((sK2 @ sK5 @ Y0) => (sK3 @ Y0))) @ sK6)) | ~spl0_1),
% 0.21/0.47 inference(sigma_clausification,[],[f212])).
% 0.21/0.47 thf(f212,plain,(
% 0.21/0.47 ($false = (!! @ $i @ (^[Y0 : $i]: ((sK2 @ sK5 @ Y0) => (sK3 @ Y0))))) | ~spl0_1),
% 0.21/0.47 inference(boolean_simplification,[],[f211])).
% 0.21/0.47 thf(f211,plain,(
% 0.21/0.47 (($true => (!! @ $i @ (^[Y0 : $i]: ((sK2 @ sK5 @ Y0) => (sK3 @ Y0))))) = $false) | ~spl0_1),
% 0.21/0.47 inference(backward_demodulation,[],[f208,f210])).
% 0.21/0.47 thf(f210,plain,(
% 0.21/0.47 ($true = (sK2 @ sK4 @ sK5)) | ~spl0_1),
% 0.21/0.47 inference(binary_proxy_clausification,[],[f208])).
% 0.21/0.47 thf(f208,plain,(
% 0.21/0.47 (((sK2 @ sK4 @ sK5) => (!! @ $i @ (^[Y0 : $i]: ((sK2 @ sK5 @ Y0) => (sK3 @ Y0))))) = $false) | ~spl0_1),
% 0.21/0.47 inference(beta_eta_normalization,[],[f207])).
% 0.21/0.47 thf(f207,plain,(
% 0.21/0.47 ($false = ((^[Y0 : $i]: ((sK2 @ sK4 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK3 @ Y1)))))) @ sK5)) | ~spl0_1),
% 0.21/0.47 inference(sigma_clausification,[],[f197])).
% 0.21/0.47 thf(f197,plain,(
% 0.21/0.47 ($false = (!! @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK3 @ Y1)))))))) | ~spl0_1),
% 0.21/0.47 inference(binary_proxy_clausification,[],[f196])).
% 0.21/0.47 thf(f196,plain,(
% 0.21/0.47 (((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) => (sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK3 @ Y1)))))))) = $false) | ~spl0_1),
% 0.21/0.47 inference(beta_eta_normalization,[],[f195])).
% 0.21/0.47 thf(f195,plain,(
% 0.21/0.47 ($false = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (sK3 @ Y2))))))))) @ sK4)) | ~spl0_1),
% 0.21/0.47 inference(sigma_clausification,[],[f194])).
% 0.21/0.47 thf(f194,plain,(
% 0.21/0.47 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK3 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (sK3 @ Y2)))))))))) = $false) | ~spl0_1),
% 0.21/0.47 inference(beta_eta_normalization,[],[f193])).
% 0.21/0.47 thf(f193,plain,(
% 0.21/0.47 ($false = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y0 @ Y3))))))))))) @ sK3)) | ~spl0_1),
% 0.21/0.47 inference(sigma_clausification,[],[f192])).
% 0.21/0.47 thf(f192,plain,(
% 0.21/0.47 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y2 @ Y3) => (Y0 @ Y3))))))))))))) | ~spl0_1),
% 0.21/0.47 inference(beta_eta_normalization,[],[f191])).
% 0.21/0.47 thf(f191,plain,(
% 0.21/0.47 (((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => (Y1 @ Y4))))))))))))) @ sK2) = $false) | ~spl0_1),
% 0.21/0.47 inference(sigma_clausification,[],[f161])).
% 0.21/0.47 thf(f254,plain,(
% 0.21/0.47 ($true = (~ (sK2 @ sK5 @ sK6))) | (~spl0_1 | ~spl0_3)),
% 0.21/0.47 inference(boolean_simplification,[],[f252])).
% 0.21/0.47 thf(f252,plain,(
% 0.21/0.47 ($true = ((sK2 @ sK5 @ sK6) => $false)) | (~spl0_1 | ~spl0_3)),
% 0.21/0.47 inference(superposition,[],[f220,f237])).
% 0.21/0.47 thf(f237,plain,(
% 0.21/0.47 ($false = (sK2 @ sK4 @ sK6)) | ~spl0_1),
% 0.21/0.47 inference(not_proxy_clausification,[],[f228])).
% 0.21/0.47 thf(f228,plain,(
% 0.21/0.47 ($true = (~ (sK2 @ sK4 @ sK6))) | ~spl0_1),
% 0.21/0.47 inference(boolean_simplification,[],[f227])).
% 0.21/0.47 thf(f227,plain,(
% 0.21/0.47 (((sK2 @ sK4 @ sK6) => $false) = $true) | ~spl0_1),
% 0.21/0.47 inference(superposition,[],[f205,f226])).
% 0.21/0.47 thf(f226,plain,(
% 0.21/0.47 ($false = (sK3 @ sK6)) | ~spl0_1),
% 0.21/0.47 inference(boolean_simplification,[],[f225])).
% 0.21/0.47 thf(f225,plain,(
% 0.21/0.47 ($false = ($true => (sK3 @ sK6))) | ~spl0_1),
% 0.21/0.47 inference(backward_demodulation,[],[f214,f224])).
% 0.21/0.47 thf(f205,plain,(
% 0.21/0.47 ( ! [X1 : $i] : (($true = ((sK2 @ sK4 @ X1) => (sK3 @ X1)))) ) | ~spl0_1),
% 0.21/0.47 inference(beta_eta_normalization,[],[f204])).
% 0.21/0.47 thf(f204,plain,(
% 0.21/0.47 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK2 @ sK4 @ Y0) => (sK3 @ Y0))) @ X1))) ) | ~spl0_1),
% 0.21/0.47 inference(pi_clausification,[],[f201])).
% 0.21/0.47 thf(f201,plain,(
% 0.21/0.47 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) => (sK3 @ Y0))))) | ~spl0_1),
% 0.21/0.47 inference(not_proxy_clausification,[],[f200])).
% 0.21/0.47 thf(f200,plain,(
% 0.21/0.47 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) => (sK3 @ Y0)))))) | ~spl0_1),
% 0.21/0.47 inference(boolean_simplification,[],[f199])).
% 0.21/0.47 thf(f199,plain,(
% 0.21/0.47 (((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) => (sK3 @ Y0))))) | $false) = $false) | ~spl0_1),
% 0.21/0.47 inference(backward_demodulation,[],[f196,f197])).
% 0.21/0.47 thf(f220,plain,(
% 0.21/0.47 ( ! [X0 : $i] : (($true = ((sK2 @ sK5 @ X0) => (sK2 @ sK4 @ X0)))) ) | (~spl0_1 | ~spl0_3)),
% 0.21/0.47 inference(boolean_simplification,[],[f217])).
% 0.21/0.47 thf(f217,plain,(
% 0.21/0.47 ( ! [X0 : $i] : (((((sK2 @ sK5 @ X0) & $true) => (sK2 @ sK4 @ X0)) = $true)) ) | (~spl0_1 | ~spl0_3)),
% 0.21/0.47 inference(superposition,[],[f189,f210])).
% 0.21/0.47 thf(f189,plain,(
% 0.21/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i] : (((((X1 @ X2 @ X3) & (X1 @ X4 @ X2)) => (X1 @ X4 @ X3)) = $true)) ) | ~spl0_3),
% 0.21/0.47 inference(beta_eta_normalization,[],[f188])).
% 0.21/0.47 thf(f188,plain,(
% 0.21/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i] : (($true = ((^[Y0 : $i]: (((X1 @ X2 @ X3) & (X1 @ Y0 @ X2)) => (X1 @ Y0 @ X3))) @ X4))) ) | ~spl0_3),
% 0.21/0.47 inference(pi_clausification,[],[f187])).
% 0.21/0.47 thf(f187,plain,(
% 0.21/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: (((X1 @ X2 @ X3) & (X1 @ Y0 @ X2)) => (X1 @ Y0 @ X3)))))) ) | ~spl0_3),
% 0.21/0.47 inference(beta_eta_normalization,[],[f186])).
% 0.21/0.47 thf(f186,plain,(
% 0.21/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X1 @ X2 @ Y0) & (X1 @ Y1 @ X2)) => (X1 @ Y1 @ Y0))))) @ X3))) ) | ~spl0_3),
% 0.21/0.47 inference(pi_clausification,[],[f185])).
% 0.21/0.47 thf(f185,plain,(
% 0.21/0.47 ( ! [X2 : $i,X1 : $i > $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((X1 @ X2 @ Y0) & (X1 @ Y1 @ X2)) => (X1 @ Y1 @ Y0)))))))) ) | ~spl0_3),
% 0.21/0.47 inference(beta_eta_normalization,[],[f184])).
% 0.21/0.47 thf(f184,plain,(
% 0.21/0.47 ( ! [X2 : $i,X1 : $i > $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X1 @ Y0 @ Y1) & (X1 @ Y2 @ Y0)) => (X1 @ Y2 @ Y1))))))) @ X2) = $true)) ) | ~spl0_3),
% 0.21/0.47 inference(pi_clausification,[],[f183])).
% 0.21/0.47 thf(f183,plain,(
% 0.21/0.47 ( ! [X1 : $i > $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X1 @ Y0 @ Y1) & (X1 @ Y2 @ Y0)) => (X1 @ Y2 @ Y1)))))))))) ) | ~spl0_3),
% 0.21/0.47 inference(beta_eta_normalization,[],[f182])).
% 0.21/0.47 thf(f182,plain,(
% 0.21/0.47 ( ! [X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) @ X1))) ) | ~spl0_3),
% 0.21/0.47 inference(pi_clausification,[],[f168])).
% 0.21/0.47 thf(f168,plain,(
% 0.21/0.47 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))))) | ~spl0_3),
% 0.21/0.47 inference(avatar_component_clause,[],[f167])).
% 0.21/0.47 thf(f167,plain,(
% 0.21/0.47 spl0_3 <=> ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2)))))))))))),
% 0.21/0.47 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.21/0.47 thf(f172,plain,(
% 0.21/0.47 spl0_3 | spl0_4),
% 0.21/0.47 inference(avatar_split_clause,[],[f157,f170,f167])).
% 0.21/0.47 thf(f157,plain,(
% 0.21/0.47 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))))) | ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => (Y1 @ Y4)))))))))))))))),
% 0.21/0.47 inference(binary_proxy_clausification,[],[f156])).
% 0.21/0.47 thf(f165,plain,(
% 0.21/0.47 spl0_1 | spl0_2),
% 0.21/0.47 inference(avatar_split_clause,[],[f158,f163,f160])).
% 0.21/0.47 thf(f158,plain,(
% 0.21/0.47 ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))))) | ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => (Y1 @ Y4)))))))))))))))),
% 0.21/0.47 inference(binary_proxy_clausification,[],[f156])).
% 0.21/0.47 % SZS output end Proof for theBenchmark
% 0.21/0.47 % (28978)------------------------------
% 0.21/0.47 % (28978)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (28978)Termination reason: Refutation
% 0.21/0.47
% 0.21/0.47 % (28978)Memory used [KB]: 6012
% 0.21/0.47 % (28978)Time elapsed: 0.051 s
% 0.21/0.47 % (28978)Instructions burned: 68 (million)
% 0.21/0.47 % (28978)------------------------------
% 0.21/0.47 % (28978)------------------------------
% 0.21/0.47 % (28966)Success in time 0.105 s
% 0.21/0.47 % Vampire---4.8 exiting
%------------------------------------------------------------------------------