TSTP Solution File: SEU496^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU496^1 : 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 : n004.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 03:49:09 EDT 2024
% Result : Theorem 0.23s 0.49s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU496^1 : TPTP v8.2.0. Released v3.6.0.
% 0.08/0.15 % 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
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 16:40:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH0_THM_EQU_NAR problem
% 0.15/0.37 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
% 0.23/0.39 % (32543)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)
% 0.23/0.40 % (32545)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)
% 0.23/0.40 % (32538)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.23/0.40 % (32540)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)
% 0.23/0.40 % (32541)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.23/0.40 % (32539)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)
% 0.23/0.40 % (32542)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)
% 0.23/0.40 % (32544)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.23/0.40 % (32545)Instruction limit reached!
% 0.23/0.40 % (32545)------------------------------
% 0.23/0.40 % (32545)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40 % (32545)Termination reason: Unknown
% 0.23/0.40 % (32545)Termination phase: shuffling
% 0.23/0.40
% 0.23/0.40 % (32545)Memory used [KB]: 1023
% 0.23/0.40 % (32545)Time elapsed: 0.004 s
% 0.23/0.40 % (32545)Instructions burned: 3 (million)
% 0.23/0.40 % (32545)------------------------------
% 0.23/0.40 % (32545)------------------------------
% 0.23/0.40 % (32541)Instruction limit reached!
% 0.23/0.40 % (32541)------------------------------
% 0.23/0.40 % (32541)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40 % (32541)Termination reason: Unknown
% 0.23/0.40 % (32542)Instruction limit reached!
% 0.23/0.40 % (32542)------------------------------
% 0.23/0.40 % (32542)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40 % (32541)Termination phase: shuffling
% 0.23/0.40
% 0.23/0.40 % (32541)Memory used [KB]: 1023
% 0.23/0.40 % (32541)Time elapsed: 0.004 s
% 0.23/0.40 % (32541)Instructions burned: 2 (million)
% 0.23/0.40 % (32541)------------------------------
% 0.23/0.40 % (32541)------------------------------
% 0.23/0.40 % (32542)Termination reason: Unknown
% 0.23/0.40 % (32542)Termination phase: shuffling
% 0.23/0.40
% 0.23/0.40 % (32542)Memory used [KB]: 1023
% 0.23/0.40 % (32542)Time elapsed: 0.004 s
% 0.23/0.40 % (32542)Instructions burned: 2 (million)
% 0.23/0.40 % (32542)------------------------------
% 0.23/0.40 % (32542)------------------------------
% 0.23/0.40 % (32539)Instruction limit reached!
% 0.23/0.40 % (32539)------------------------------
% 0.23/0.40 % (32539)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40 % (32539)Termination reason: Unknown
% 0.23/0.40 % (32539)Termination phase: shuffling
% 0.23/0.40
% 0.23/0.40 % (32539)Memory used [KB]: 1023
% 0.23/0.40 % (32539)Time elapsed: 0.006 s
% 0.23/0.40 % (32539)Instructions burned: 4 (million)
% 0.23/0.40 % (32539)------------------------------
% 0.23/0.40 % (32539)------------------------------
% 0.23/0.41 % (32544)Instruction limit reached!
% 0.23/0.41 % (32544)------------------------------
% 0.23/0.41 % (32544)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.41 % (32544)Termination reason: Unknown
% 0.23/0.41 % (32544)Termination phase: Saturation
% 0.23/0.41
% 0.23/0.41 % (32544)Memory used [KB]: 5628
% 0.23/0.41 % (32544)Time elapsed: 0.017 s
% 0.23/0.41 % (32544)Instructions burned: 18 (million)
% 0.23/0.41 % (32544)------------------------------
% 0.23/0.41 % (32544)------------------------------
% 0.23/0.42 % (32546)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)
% 0.23/0.42 % (32540)Instruction limit reached!
% 0.23/0.42 % (32540)------------------------------
% 0.23/0.42 % (32540)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.42 % (32540)Termination reason: Unknown
% 0.23/0.42 % (32540)Termination phase: Saturation
% 0.23/0.42
% 0.23/0.42 % (32540)Memory used [KB]: 5628
% 0.23/0.42 % (32540)Time elapsed: 0.024 s
% 0.23/0.42 % (32540)Instructions burned: 27 (million)
% 0.23/0.42 % (32540)------------------------------
% 0.23/0.42 % (32540)------------------------------
% 0.23/0.42 % (32549)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)
% 0.23/0.43 % (32547)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)
% 0.23/0.43 % (32548)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)
% 0.23/0.43 % (32548)Instruction limit reached!
% 0.23/0.43 % (32548)------------------------------
% 0.23/0.43 % (32548)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.43 % (32548)Termination reason: Unknown
% 0.23/0.43 % (32548)Termination phase: shuffling
% 0.23/0.43
% 0.23/0.43 % (32548)Memory used [KB]: 1023
% 0.23/0.43 % (32548)Time elapsed: 0.005 s
% 0.23/0.43 % (32548)Instructions burned: 3 (million)
% 0.23/0.43 % (32548)------------------------------
% 0.23/0.43 % (32548)------------------------------
% 0.23/0.43 % (32546)Instruction limit reached!
% 0.23/0.43 % (32546)------------------------------
% 0.23/0.43 % (32546)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.43 % (32546)Termination reason: Unknown
% 0.23/0.43 % (32546)Termination phase: Saturation
% 0.23/0.43
% 0.23/0.43 % (32546)Memory used [KB]: 5628
% 0.23/0.43 % (32546)Time elapsed: 0.019 s
% 0.23/0.43 % (32546)Instructions burned: 37 (million)
% 0.23/0.43 % (32546)------------------------------
% 0.23/0.43 % (32546)------------------------------
% 0.23/0.44 % (32547)Instruction limit reached!
% 0.23/0.44 % (32547)------------------------------
% 0.23/0.44 % (32547)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.44 % (32547)Termination reason: Unknown
% 0.23/0.44 % (32547)Termination phase: Saturation
% 0.23/0.44
% 0.23/0.44 % (32547)Memory used [KB]: 5628
% 0.23/0.44 % (32547)Time elapsed: 0.014 s
% 0.23/0.44 % (32547)Instructions burned: 16 (million)
% 0.23/0.44 % (32547)------------------------------
% 0.23/0.44 % (32547)------------------------------
% 0.23/0.44 % (32550)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.23/0.44 % (32551)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.23/0.44 % (32550)Instruction limit reached!
% 0.23/0.44 % (32550)------------------------------
% 0.23/0.44 % (32550)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.44 % (32550)Termination reason: Unknown
% 0.23/0.44 % (32550)Termination phase: Property scanning
% 0.23/0.44
% 0.23/0.44 % (32550)Memory used [KB]: 1023
% 0.23/0.44 % (32550)Time elapsed: 0.007 s
% 0.23/0.44 % (32550)Instructions burned: 8 (million)
% 0.23/0.44 % (32550)------------------------------
% 0.23/0.44 % (32550)------------------------------
% 0.23/0.45 % (32553)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)
% 0.23/0.45 % (32552)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)
% 0.23/0.45 % (32553)Instruction limit reached!
% 0.23/0.45 % (32553)------------------------------
% 0.23/0.45 % (32553)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.45 % (32553)Termination reason: Unknown
% 0.23/0.45 % (32553)Termination phase: shuffling
% 0.23/0.45
% 0.23/0.45 % (32553)Memory used [KB]: 1023
% 0.23/0.45 % (32553)Time elapsed: 0.004 s
% 0.23/0.45 % (32553)Instructions burned: 4 (million)
% 0.23/0.45 % (32553)------------------------------
% 0.23/0.45 % (32553)------------------------------
% 0.23/0.45 % (32552)Instruction limit reached!
% 0.23/0.45 % (32552)------------------------------
% 0.23/0.45 % (32552)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.45 % (32552)Termination reason: Unknown
% 0.23/0.45 % (32552)Termination phase: Property scanning
% 0.23/0.45
% 0.23/0.45 % (32552)Memory used [KB]: 1023
% 0.23/0.45 % (32552)Time elapsed: 0.004 s
% 0.23/0.45 % (32552)Instructions burned: 4 (million)
% 0.23/0.45 % (32552)------------------------------
% 0.23/0.45 % (32552)------------------------------
% 0.23/0.45 % (32551)Instruction limit reached!
% 0.23/0.45 % (32551)------------------------------
% 0.23/0.45 % (32551)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.45 % (32551)Termination reason: Unknown
% 0.23/0.45 % (32551)Termination phase: Saturation
% 0.23/0.45
% 0.23/0.45 % (32551)Memory used [KB]: 5884
% 0.23/0.45 % (32551)Time elapsed: 0.011 s
% 0.23/0.45 % (32551)Instructions burned: 17 (million)
% 0.23/0.45 % (32551)------------------------------
% 0.23/0.45 % (32551)------------------------------
% 0.23/0.45 % (32554)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)
% 0.23/0.46 % (32554)Instruction limit reached!
% 0.23/0.46 % (32554)------------------------------
% 0.23/0.46 % (32554)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.46 % (32554)Termination reason: Unknown
% 0.23/0.46 % (32554)Termination phase: Function definition elimination
% 0.23/0.46
% 0.23/0.46 % (32554)Memory used [KB]: 1023
% 0.23/0.46 % (32554)Time elapsed: 0.005 s
% 0.23/0.46 % (32554)Instructions burned: 8 (million)
% 0.23/0.46 % (32554)------------------------------
% 0.23/0.46 % (32554)------------------------------
% 0.23/0.46 % (32555)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)
% 0.23/0.46 % (32555)Instruction limit reached!
% 0.23/0.46 % (32555)------------------------------
% 0.23/0.46 % (32555)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.46 % (32555)Termination reason: Unknown
% 0.23/0.46 % (32555)Termination phase: Property scanning
% 0.23/0.46
% 0.23/0.46 % (32555)Memory used [KB]: 1023
% 0.23/0.46 % (32555)Time elapsed: 0.004 s
% 0.23/0.46 % (32555)Instructions burned: 4 (million)
% 0.23/0.46 % (32555)------------------------------
% 0.23/0.46 % (32555)------------------------------
% 0.23/0.46 % (32556)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.23/0.47 % (32557)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)
% 0.23/0.47 % (32556)Instruction limit reached!
% 0.23/0.47 % (32556)------------------------------
% 0.23/0.47 % (32556)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.47 % (32556)Termination reason: Unknown
% 0.23/0.47 % (32556)Termination phase: shuffling
% 0.23/0.47
% 0.23/0.47 % (32556)Memory used [KB]: 1023
% 0.23/0.47 % (32556)Time elapsed: 0.004 s
% 0.23/0.47 % (32556)Instructions burned: 4 (million)
% 0.23/0.47 % (32556)------------------------------
% 0.23/0.47 % (32556)------------------------------
% 0.23/0.47 % (32558)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.23/0.47 % (32559)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.23/0.47 % (32558)Refutation not found, incomplete strategy
% 0.23/0.47 % (32558)------------------------------
% 0.23/0.47 % (32558)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.47 % (32558)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.47
% 0.23/0.47
% 0.23/0.47 % (32558)Memory used [KB]: 5628
% 0.23/0.47 % (32558)Time elapsed: 0.009 s
% 0.23/0.47 % (32558)Instructions burned: 12 (million)
% 0.23/0.47 % (32558)------------------------------
% 0.23/0.47 % (32558)------------------------------
% 0.23/0.48 % (32559)Instruction limit reached!
% 0.23/0.48 % (32559)------------------------------
% 0.23/0.48 % (32559)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.48 % (32559)Termination reason: Unknown
% 0.23/0.48 % (32559)Termination phase: Clausification
% 0.23/0.48
% 0.23/0.48 % (32559)Memory used [KB]: 1023
% 0.23/0.48 % (32559)Time elapsed: 0.005 s
% 0.23/0.48 % (32559)Instructions burned: 6 (million)
% 0.23/0.48 % (32559)------------------------------
% 0.23/0.48 % (32559)------------------------------
% 0.23/0.48 % (32557)Instruction limit reached!
% 0.23/0.48 % (32557)------------------------------
% 0.23/0.48 % (32557)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.48 % (32557)Termination reason: Unknown
% 0.23/0.48 % (32557)Termination phase: Saturation
% 0.23/0.48
% 0.23/0.48 % (32557)Memory used [KB]: 5628
% 0.23/0.48 % (32557)Time elapsed: 0.012 s
% 0.23/0.48 % (32557)Instructions burned: 18 (million)
% 0.23/0.48 % (32557)------------------------------
% 0.23/0.48 % (32557)------------------------------
% 0.23/0.48 % (32560)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)
% 0.23/0.48 % (32549)First to succeed.
% 0.23/0.48 % (32561)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)
% 0.23/0.48 % (32560)Refutation not found, incomplete strategy
% 0.23/0.48 % (32560)------------------------------
% 0.23/0.48 % (32560)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.48 % (32560)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.48
% 0.23/0.48
% 0.23/0.48 % (32560)Memory used [KB]: 5628
% 0.23/0.48 % (32560)Time elapsed: 0.007 s
% 0.23/0.48 % (32560)Instructions burned: 10 (million)
% 0.23/0.48 % (32560)------------------------------
% 0.23/0.48 % (32560)------------------------------
% 0.23/0.49 % (32549)Refutation found. Thanks to Tanya!
% 0.23/0.49 % SZS status Theorem for theBenchmark
% 0.23/0.49 % SZS output start Proof for theBenchmark
% 0.23/0.49 thf(func_def_0, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_2, type, inv: ($i > $i > $o) > $i > $i > $o).
% 0.23/0.49 thf(func_def_3, type, idem: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_4, type, infl: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_5, type, mono: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_6, type, refl: ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_7, type, irrefl: ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_8, type, rc: ($i > $i > $o) > $i > $i > $o).
% 0.23/0.49 thf(func_def_9, type, symm: ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_10, type, antisymm: ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_11, type, asymm: ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_12, type, sc: ($i > $i > $o) > $i > $i > $o).
% 0.23/0.49 thf(func_def_13, type, trans: ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_14, type, tc: ($i > $i > $o) > $i > $i > $o).
% 0.23/0.49 thf(func_def_15, type, trc: ($i > $i > $o) > $i > $i > $o).
% 0.23/0.49 thf(func_def_16, type, trsc: ($i > $i > $o) > $i > $i > $o).
% 0.23/0.49 thf(func_def_17, type, po: ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_18, type, so: ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_19, type, total: ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_20, type, term: ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_21, type, ind: ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_22, type, innf: ($i > $i > $o) > $i > $o).
% 0.23/0.49 thf(func_def_23, type, nfof: ($i > $i > $o) > $i > $i > $o).
% 0.23/0.49 thf(func_def_24, type, norm: ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_25, type, join: ($i > $i > $o) > $i > $i > $o).
% 0.23/0.49 thf(func_def_26, type, lconfl: ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_27, type, sconfl: ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_28, type, confl: ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_29, type, cr: ($i > $i > $o) > $o).
% 0.23/0.49 thf(func_def_49, type, ph1: !>[X0: $tType]:(X0)).
% 0.23/0.49 thf(func_def_50, type, sK2: $i > $i > $o).
% 0.23/0.49 thf(func_def_58, type, sK10: $i > $i > $o).
% 0.23/0.49 thf(f492,plain,(
% 0.23/0.49 $false),
% 0.23/0.49 inference(avatar_sat_refutation,[],[f167,f201,f225,f238,f243,f491])).
% 0.23/0.49 thf(f491,plain,(
% 0.23/0.49 ~spl0_1),
% 0.23/0.49 inference(avatar_contradiction_clause,[],[f490])).
% 0.23/0.49 thf(f490,plain,(
% 0.23/0.49 $false | ~spl0_1),
% 0.23/0.49 inference(trivial_inequality_removal,[],[f489])).
% 0.23/0.49 thf(f489,plain,(
% 0.23/0.49 ($false = $true) | ~spl0_1),
% 0.23/0.49 inference(forward_demodulation,[],[f488,f422])).
% 0.23/0.49 thf(f422,plain,(
% 0.23/0.49 ($false = (sK10 @ sK8 @ sK7)) | ~spl0_1),
% 0.23/0.49 inference(boolean_simplification,[],[f416])).
% 0.23/0.49 thf(f416,plain,(
% 0.23/0.49 (((sK10 @ sK8 @ sK7) & $true) = $false) | ~spl0_1),
% 0.23/0.49 inference(superposition,[],[f388,f375])).
% 0.23/0.49 thf(f375,plain,(
% 0.23/0.49 ((sK10 @ sK9 @ sK8) = $true) | ~spl0_1),
% 0.23/0.49 inference(boolean_simplification,[],[f374])).
% 0.23/0.49 thf(f374,plain,(
% 0.23/0.49 ($true = ($true => (sK10 @ sK9 @ sK8))) | ~spl0_1),
% 0.23/0.49 inference(forward_demodulation,[],[f373,f302])).
% 0.23/0.49 thf(f302,plain,(
% 0.23/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK10 @ Y1 @ Y0)))))) = $true) | ~spl0_1),
% 0.23/0.49 inference(binary_proxy_clausification,[],[f298])).
% 0.23/0.49 thf(f298,plain,(
% 0.23/0.49 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK10 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK10 @ Y1 @ Y0) & (sK10 @ Y2 @ Y1)) => (sK10 @ Y2 @ Y0)))))))))) | ~spl0_1),
% 0.23/0.49 inference(binary_proxy_clausification,[],[f291])).
% 0.23/0.49 thf(f291,plain,(
% 0.23/0.49 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK10 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK10 @ Y1 @ Y0) & (sK10 @ Y2 @ Y1)) => (sK10 @ Y2 @ Y0))))))))) => (sK10 @ sK9 @ sK7))) | ~spl0_1),
% 0.23/0.49 inference(beta_eta_normalization,[],[f290])).
% 0.23/0.49 thf(f290,plain,(
% 0.23/0.49 (((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK9 @ sK7))) @ sK10) = $false) | ~spl0_1),
% 0.23/0.49 inference(sigma_clausification,[],[f284])).
% 0.23/0.49 thf(f284,plain,(
% 0.23/0.49 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK9 @ sK7)))) = $false) | ~spl0_1),
% 0.23/0.49 inference(boolean_simplification,[],[f283])).
% 0.23/0.49 thf(f283,plain,(
% 0.23/0.49 ($false = ($true => (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK9 @ sK7)))))) | ~spl0_1),
% 0.23/0.49 inference(backward_demodulation,[],[f267,f282])).
% 0.23/0.49 thf(f282,plain,(
% 0.23/0.49 (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK8 @ sK7)))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK9 @ sK8))))) = $true) | ~spl0_1),
% 0.23/0.49 inference(binary_proxy_clausification,[],[f267])).
% 0.23/0.49 thf(f267,plain,(
% 0.23/0.49 ((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK8 @ sK7)))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK9 @ sK8))))) => (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK9 @ sK7))))) = $false) | ~spl0_1),
% 0.23/0.49 inference(beta_eta_normalization,[],[f266])).
% 0.23/0.49 thf(f266,plain,(
% 0.23/0.49 (((^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ sK8 @ sK7)))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ Y0 @ sK8))))) => (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ Y0 @ sK7)))))) @ sK9) = $false) | ~spl0_1),
% 0.23/0.49 inference(sigma_clausification,[],[f260])).
% 0.23/0.49 thf(f260,plain,(
% 0.23/0.49 ((!! @ $i @ (^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ sK8 @ sK7)))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ Y0 @ sK8))))) => (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ Y0 @ sK7))))))) = $false) | ~spl0_1),
% 0.23/0.49 inference(beta_eta_normalization,[],[f259])).
% 0.23/0.49 thf(f259,plain,(
% 0.23/0.49 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y0 @ sK7)))) & (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ sK7)))))))) @ sK8)) | ~spl0_1),
% 0.23/0.49 inference(sigma_clausification,[],[f247])).
% 0.23/0.49 thf(f247,plain,(
% 0.23/0.49 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y0 @ sK7)))) & (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ sK7)))))))))) | ~spl0_1),
% 0.23/0.49 inference(beta_eta_normalization,[],[f246])).
% 0.23/0.49 thf(f246,plain,(
% 0.23/0.49 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0)))) & (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y1))))) => (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y0)))))))))) @ sK7) = $false) | ~spl0_1),
% 0.23/0.49 inference(sigma_clausification,[],[f163])).
% 0.23/0.49 thf(f163,plain,(
% 0.23/0.49 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0)))) & (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y1))))) => (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y0)))))))))))) | ~spl0_1),
% 0.23/0.49 inference(avatar_component_clause,[],[f162])).
% 0.23/0.49 thf(f162,plain,(
% 0.23/0.49 spl0_1 <=> ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0)))) & (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y1))))) => (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y0))))))))))))),
% 0.23/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.23/0.49 thf(f373,plain,(
% 0.23/0.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK10 @ Y1 @ Y0)))))) => (sK10 @ sK9 @ sK8)) = $true) | ~spl0_1),
% 0.23/0.49 inference(boolean_simplification,[],[f368])).
% 0.23/0.49 thf(f368,plain,(
% 0.23/0.49 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK10 @ Y1 @ Y0)))))) & $true) => (sK10 @ sK9 @ sK8)) = $true) | ~spl0_1),
% 0.23/0.49 inference(superposition,[],[f360,f304])).
% 0.23/0.49 thf(f304,plain,(
% 0.23/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK10 @ Y1 @ Y0) & (sK10 @ Y2 @ Y1)) => (sK10 @ Y2 @ Y0)))))))) = $true) | ~spl0_1),
% 0.23/0.49 inference(boolean_simplification,[],[f303])).
% 0.23/0.49 thf(f303,plain,(
% 0.23/0.49 (($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK10 @ Y1 @ Y0) & (sK10 @ Y2 @ Y1)) => (sK10 @ Y2 @ Y0))))))))) = $true) | ~spl0_1),
% 0.23/0.49 inference(backward_demodulation,[],[f298,f302])).
% 0.23/0.49 thf(f360,plain,(
% 0.23/0.49 ( ! [X1 : $i > $i > $o] : (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (X1 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X1 @ Y1 @ Y0) & (X1 @ Y2 @ Y1)) => (X1 @ Y2 @ Y0))))))))) => (X1 @ sK9 @ sK8)) = $true)) ) | ~spl0_1),
% 0.23/0.49 inference(beta_eta_normalization,[],[f359])).
% 0.23/0.49 thf(f359,plain,(
% 0.23/0.49 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK9 @ sK8))) @ X1) = $true)) ) | ~spl0_1),
% 0.23/0.49 inference(pi_clausification,[],[f350])).
% 0.23/0.49 thf(f350,plain,(
% 0.23/0.49 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK9 @ sK8))))) | ~spl0_1),
% 0.23/0.49 inference(boolean_simplification,[],[f349])).
% 0.23/0.49 thf(f349,plain,(
% 0.23/0.49 (($true & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK9 @ sK8))))) = $true) | ~spl0_1),
% 0.23/0.49 inference(backward_demodulation,[],[f282,f348])).
% 0.23/0.49 thf(f348,plain,(
% 0.23/0.49 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK8 @ sK7))))) | ~spl0_1),
% 0.23/0.49 inference(binary_proxy_clausification,[],[f282])).
% 0.23/0.49 thf(f388,plain,(
% 0.23/0.49 ( ! [X0 : $i] : ((((sK10 @ X0 @ sK7) & (sK10 @ sK9 @ X0)) = $false)) ) | ~spl0_1),
% 0.23/0.49 inference(not_proxy_clausification,[],[f335])).
% 0.23/0.49 thf(f335,plain,(
% 0.23/0.49 ( ! [X0 : $i] : (((~ ((sK10 @ X0 @ sK7) & (sK10 @ sK9 @ X0))) = $true)) ) | ~spl0_1),
% 0.23/0.49 inference(boolean_simplification,[],[f332])).
% 0.23/0.49 thf(f332,plain,(
% 0.23/0.49 ( ! [X0 : $i] : (($true = (((sK10 @ X0 @ sK7) & (sK10 @ sK9 @ X0)) => $false))) ) | ~spl0_1),
% 0.23/0.49 inference(superposition,[],[f328,f300])).
% 0.23/0.49 thf(f300,plain,(
% 0.23/0.49 ($false = (sK10 @ sK9 @ sK7)) | ~spl0_1),
% 0.23/0.49 inference(boolean_simplification,[],[f299])).
% 0.23/0.49 thf(f299,plain,(
% 0.23/0.49 ($false = ($true => (sK10 @ sK9 @ sK7))) | ~spl0_1),
% 0.23/0.49 inference(backward_demodulation,[],[f291,f298])).
% 0.23/0.49 thf(f328,plain,(
% 0.23/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((sK10 @ X2 @ X1) & (sK10 @ X3 @ X2)) => (sK10 @ X3 @ X1)) = $true)) ) | ~spl0_1),
% 0.23/0.49 inference(beta_eta_normalization,[],[f327])).
% 0.23/0.49 thf(f327,plain,(
% 0.23/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((sK10 @ X2 @ X1) & (sK10 @ Y0 @ X2)) => (sK10 @ Y0 @ X1))) @ X3) = $true)) ) | ~spl0_1),
% 0.23/0.49 inference(pi_clausification,[],[f324])).
% 0.23/0.49 thf(f324,plain,(
% 0.23/0.49 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((sK10 @ X2 @ X1) & (sK10 @ Y0 @ X2)) => (sK10 @ Y0 @ X1)))))) ) | ~spl0_1),
% 0.23/0.49 inference(beta_eta_normalization,[],[f323])).
% 0.23/0.49 thf(f323,plain,(
% 0.23/0.49 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK10 @ Y0 @ X1) & (sK10 @ Y1 @ Y0)) => (sK10 @ Y1 @ X1))))) @ X2) = $true)) ) | ~spl0_1),
% 0.23/0.49 inference(pi_clausification,[],[f315])).
% 0.23/0.49 thf(f315,plain,(
% 0.23/0.49 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK10 @ Y0 @ X1) & (sK10 @ Y1 @ Y0)) => (sK10 @ Y1 @ X1)))))) = $true)) ) | ~spl0_1),
% 0.23/0.49 inference(beta_eta_normalization,[],[f314])).
% 0.23/0.49 thf(f314,plain,(
% 0.23/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK10 @ Y1 @ Y0) & (sK10 @ Y2 @ Y1)) => (sK10 @ Y2 @ Y0))))))) @ X1) = $true)) ) | ~spl0_1),
% 0.23/0.49 inference(pi_clausification,[],[f304])).
% 0.23/0.49 thf(f488,plain,(
% 0.23/0.49 ($true = (sK10 @ sK8 @ sK7)) | ~spl0_1),
% 0.23/0.49 inference(boolean_simplification,[],[f487])).
% 0.23/0.49 thf(f487,plain,(
% 0.23/0.49 (($true => (sK10 @ sK8 @ sK7)) = $true) | ~spl0_1),
% 0.23/0.49 inference(forward_demodulation,[],[f471,f302])).
% 0.23/0.49 thf(f471,plain,(
% 0.23/0.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK10 @ Y1 @ Y0)))))) => (sK10 @ sK8 @ sK7)) = $true) | ~spl0_1),
% 0.23/0.49 inference(boolean_simplification,[],[f469])).
% 0.23/0.49 thf(f469,plain,(
% 0.23/0.49 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK10 @ Y1 @ Y0)))))) & $true) => (sK10 @ sK8 @ sK7)) = $true) | ~spl0_1),
% 0.23/0.49 inference(superposition,[],[f460,f304])).
% 0.23/0.49 thf(f460,plain,(
% 0.23/0.49 ( ! [X1 : $i > $i > $o] : (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (X1 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X1 @ Y1 @ Y0) & (X1 @ Y2 @ Y1)) => (X1 @ Y2 @ Y0))))))))) => (X1 @ sK8 @ sK7)) = $true)) ) | ~spl0_1),
% 0.23/0.49 inference(beta_eta_normalization,[],[f459])).
% 0.23/0.49 thf(f459,plain,(
% 0.23/0.49 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK8 @ sK7))) @ X1) = $true)) ) | ~spl0_1),
% 0.23/0.49 inference(pi_clausification,[],[f348])).
% 0.23/0.49 thf(f243,plain,(
% 0.23/0.49 ~spl0_3 | ~spl0_5),
% 0.23/0.49 inference(avatar_contradiction_clause,[],[f242])).
% 0.23/0.49 thf(f242,plain,(
% 0.23/0.49 $false | (~spl0_3 | ~spl0_5)),
% 0.23/0.49 inference(trivial_inequality_removal,[],[f241])).
% 0.23/0.49 thf(f241,plain,(
% 0.23/0.49 ($false = $true) | (~spl0_3 | ~spl0_5)),
% 0.23/0.49 inference(forward_demodulation,[],[f224,f228])).
% 0.23/0.49 thf(f228,plain,(
% 0.23/0.49 ((sK2 @ sK3 @ sK4) = $false) | ~spl0_3),
% 0.23/0.49 inference(not_proxy_clausification,[],[f219])).
% 0.23/0.49 thf(f219,plain,(
% 0.23/0.49 ((~ (sK2 @ sK3 @ sK4)) = $true) | ~spl0_3),
% 0.23/0.49 inference(boolean_simplification,[],[f211])).
% 0.23/0.49 thf(f211,plain,(
% 0.23/0.49 (($true => (~ (sK2 @ sK3 @ sK4))) = $true) | ~spl0_3),
% 0.23/0.49 inference(superposition,[],[f156,f197])).
% 0.23/0.49 thf(f197,plain,(
% 0.23/0.49 ((sK2 @ sK4 @ sK3) = $true) | ~spl0_3),
% 0.23/0.49 inference(avatar_component_clause,[],[f196])).
% 0.23/0.49 thf(f196,plain,(
% 0.23/0.49 spl0_3 <=> ((sK2 @ sK4 @ sK3) = $true)),
% 0.23/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.23/0.49 thf(f156,plain,(
% 0.23/0.49 ( ! [X2 : $i,X1 : $i] : ((((sK2 @ X2 @ X1) => (~ (sK2 @ X1 @ X2))) = $true)) )),
% 0.23/0.49 inference(beta_eta_normalization,[],[f155])).
% 0.23/0.49 thf(f155,plain,(
% 0.23/0.49 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((sK2 @ Y0 @ X1) => (~ (sK2 @ X1 @ Y0)))) @ X2) = $true)) )),
% 0.23/0.49 inference(pi_clausification,[],[f154])).
% 0.23/0.49 thf(f154,plain,(
% 0.23/0.49 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0 @ X1) => (~ (sK2 @ X1 @ Y0))))) = $true)) )),
% 0.23/0.49 inference(beta_eta_normalization,[],[f153])).
% 0.23/0.49 thf(f153,plain,(
% 0.23/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1)))))) @ X1) = $true)) )),
% 0.23/0.49 inference(pi_clausification,[],[f152])).
% 0.23/0.49 thf(f152,plain,(
% 0.23/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1))))))) = $true)),
% 0.23/0.49 inference(boolean_simplification,[],[f151])).
% 0.23/0.49 thf(f151,plain,(
% 0.23/0.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1))))))) & $true) = $true)),
% 0.23/0.49 inference(backward_demodulation,[],[f144,f149])).
% 0.23/0.49 thf(f149,plain,(
% 0.23/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0)))))))) = $true)),
% 0.23/0.49 inference(binary_proxy_clausification,[],[f144])).
% 0.23/0.49 thf(f144,plain,(
% 0.23/0.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))))) = $true)),
% 0.23/0.49 inference(binary_proxy_clausification,[],[f142])).
% 0.23/0.49 thf(f142,plain,(
% 0.23/0.49 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) => (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y0 @ Y1)))))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0)))) & (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y1))))) => (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y0))))))))))))) = $false)),
% 0.23/0.49 inference(beta_eta_normalization,[],[f141])).
% 0.23/0.49 thf(f141,plain,(
% 0.23/0.49 (((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y1)))) => (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y2)))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y2 @ Y1)))) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y3 @ Y2))))) => (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y3 @ Y1)))))))))))))) @ sK2) = $false)),
% 0.23/0.49 inference(sigma_clausification,[],[f138])).
% 0.23/0.49 thf(f138,plain,(
% 0.23/0.49 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y1)))) => (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y2)))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y2 @ Y1)))) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y3 @ Y2))))) => (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y3 @ Y1))))))))))))))) = $false)),
% 0.23/0.49 inference(not_proxy_clausification,[],[f137])).
% 0.23/0.49 thf(f137,plain,(
% 0.23/0.49 ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y1)))) => (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y2)))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y2 @ Y1)))) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y3 @ Y2))))) => (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y3 @ Y1)))))))))))))))) = $true)),
% 0.23/0.49 inference(beta_eta_normalization,[],[f136])).
% 0.23/0.49 thf(f136,plain,(
% 0.23/0.49 ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((^[Y1 : $i > $i > $o]: (((^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => (~ (Y2 @ Y3 @ Y4)))))))) @ Y1) & ((^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) @ Y1))) @ Y0) => ((^[Y1 : $i > $i > $o]: (((^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => (~ (Y2 @ Y3 @ Y4)))))))) @ Y1) & ((^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) @ Y1))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((((^[Y5 : $i > $i > $o]: ((^[Y6 : $i > $i > $o]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y5 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))))) @ Y1 @ Y4) & ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y8 @ Y6))))))))) @ Y4)) => (Y4 @ Y2 @ Y3))))))))) @ Y0)))))) = $true)),
% 0.23/0.49 inference(definition_unfolding,[],[f118,f127,f127,f123])).
% 0.23/0.49 thf(f123,plain,(
% 0.23/0.49 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))))) @ Y0 @ Y3) & ((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y5) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y7 @ Y5))))))))) @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.23/0.49 inference(definition_unfolding,[],[f113,f110,f104])).
% 0.23/0.49 thf(f104,plain,(
% 0.23/0.49 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.23/0.49 inference(cnf_transformation,[],[f47])).
% 0.23/0.49 thf(f47,plain,(
% 0.23/0.49 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.23/0.49 inference(fool_elimination,[],[f46])).
% 0.23/0.49 thf(f46,plain,(
% 0.23/0.49 (trans = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)))))),
% 0.23/0.49 inference(rectify,[],[f13])).
% 0.23/0.49 thf(f13,axiom,(
% 0.23/0.49 (trans = (^[X0 : $i > $i > $o] : (! [X2,X3,X5] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X5)) => (X0 @ X2 @ X5)))))),
% 0.23/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive)).
% 0.23/0.49 thf(f110,plain,(
% 0.23/0.49 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))))),
% 0.23/0.49 inference(cnf_transformation,[],[f70])).
% 0.23/0.49 thf(f70,plain,(
% 0.23/0.49 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))))),
% 0.23/0.49 inference(fool_elimination,[],[f69])).
% 0.23/0.49 thf(f69,plain,(
% 0.23/0.49 (subrel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))))),
% 0.23/0.49 inference(rectify,[],[f1])).
% 0.23/0.49 thf(f1,axiom,(
% 0.23/0.49 (subrel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))))),
% 0.23/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subrel)).
% 0.23/0.49 thf(f113,plain,(
% 0.23/0.49 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((subrel @ Y0 @ Y3) & (trans @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.23/0.49 inference(cnf_transformation,[],[f59])).
% 0.23/0.49 thf(f59,plain,(
% 0.23/0.49 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((subrel @ Y0 @ Y3) & (trans @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.23/0.49 inference(fool_elimination,[],[f58])).
% 0.23/0.49 thf(f58,plain,(
% 0.23/0.49 ((^[X0 : $i > $i > $o, X1 : $i, X2 : $i] : (! [X3 : $i > $i > $o] : (((trans @ X3) & (subrel @ X0 @ X3)) => (X3 @ X1 @ X2)))) = tc)),
% 0.23/0.49 inference(rectify,[],[f14])).
% 0.23/0.49 thf(f14,axiom,(
% 0.23/0.49 ((^[X0 : $i > $i > $o, X2 : $i, X3 : $i] : (! [X1 : $i > $i > $o] : (((trans @ X1) & (subrel @ X0 @ X1)) => (X1 @ X2 @ X3)))) = tc)),
% 0.23/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure)).
% 0.23/0.49 thf(f127,plain,(
% 0.23/0.49 (so = (^[Y0 : $i > $i > $o]: (((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) => (~ (Y1 @ Y2 @ Y3)))))))) @ Y0) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) @ Y0))))),
% 0.23/0.49 inference(definition_unfolding,[],[f92,f93,f104])).
% 0.23/0.49 thf(f93,plain,(
% 0.23/0.49 (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (~ (Y0 @ Y1 @ Y2)))))))))),
% 0.23/0.49 inference(cnf_transformation,[],[f86])).
% 0.23/0.49 thf(f86,plain,(
% 0.23/0.49 (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (~ (Y0 @ Y1 @ Y2)))))))))),
% 0.23/0.49 inference(fool_elimination,[],[f85])).
% 0.23/0.49 thf(f85,plain,(
% 0.23/0.49 (asymm = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X1 @ X2) => ~(X0 @ X2 @ X1)))))),
% 0.23/0.49 inference(rectify,[],[f11])).
% 0.23/0.49 thf(f11,axiom,(
% 0.23/0.49 (asymm = (^[X0 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X2 @ X3) => ~(X0 @ X3 @ X2)))))),
% 0.23/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',asymmetric)).
% 0.23/0.49 thf(f92,plain,(
% 0.23/0.49 (so = (^[Y0 : $i > $i > $o]: ((asymm @ Y0) & (trans @ Y0))))),
% 0.23/0.49 inference(cnf_transformation,[],[f41])).
% 0.23/0.49 thf(f41,plain,(
% 0.23/0.49 (so = (^[Y0 : $i > $i > $o]: ((asymm @ Y0) & (trans @ Y0))))),
% 0.23/0.49 inference(fool_elimination,[],[f40])).
% 0.23/0.49 thf(f40,plain,(
% 0.23/0.49 ((^[X0 : $i > $i > $o] : ((trans @ X0) & (asymm @ X0))) = so)),
% 0.23/0.49 inference(rectify,[],[f18])).
% 0.23/0.49 thf(f18,axiom,(
% 0.23/0.49 ((^[X0 : $i > $i > $o] : ((trans @ X0) & (asymm @ X0))) = so)),
% 0.23/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',strict_order)).
% 0.23/0.49 thf(f118,plain,(
% 0.23/0.49 ($true = (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((so @ Y0) => (so @ (tc @ Y0)))))))),
% 0.23/0.49 inference(cnf_transformation,[],[f57])).
% 0.23/0.49 thf(f57,plain,(
% 0.23/0.49 ($true = (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((so @ Y0) => (so @ (tc @ Y0)))))))),
% 0.23/0.49 inference(fool_elimination,[],[f56])).
% 0.23/0.49 thf(f56,plain,(
% 0.23/0.49 ~! [X0 : $i > $i > $o] : ((so @ X0) => (so @ (tc @ X0)))),
% 0.23/0.49 inference(rectify,[],[f31])).
% 0.23/0.49 thf(f31,negated_conjecture,(
% 0.23/0.49 ~! [X0 : $i > $i > $o] : ((so @ X0) => (so @ (tc @ X0)))),
% 0.23/0.49 inference(negated_conjecture,[],[f30])).
% 0.23/0.49 thf(f30,conjecture,(
% 0.23/0.49 ! [X0 : $i > $i > $o] : ((so @ X0) => (so @ (tc @ X0)))),
% 0.23/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure_of_strict_order_is_strict_order)).
% 0.23/0.49 thf(f224,plain,(
% 0.23/0.49 ((sK2 @ sK3 @ sK4) = $true) | ~spl0_5),
% 0.23/0.49 inference(avatar_component_clause,[],[f223])).
% 0.23/0.49 thf(f223,plain,(
% 0.23/0.49 spl0_5 <=> ((sK2 @ sK3 @ sK4) = $true)),
% 0.23/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.23/0.49 thf(f238,plain,(
% 0.23/0.49 ~spl0_4),
% 0.23/0.49 inference(avatar_contradiction_clause,[],[f237])).
% 0.23/0.49 thf(f237,plain,(
% 0.23/0.49 $false | ~spl0_4),
% 0.23/0.49 inference(trivial_inequality_removal,[],[f236])).
% 0.23/0.49 thf(f236,plain,(
% 0.23/0.49 ($false = $true) | ~spl0_4),
% 0.23/0.49 inference(beta_eta_normalization,[],[f235])).
% 0.23/0.49 thf(f235,plain,(
% 0.23/0.49 ($false = ((^[Y0 : $i]: ($true)) @ sK6)) | ~spl0_4),
% 0.23/0.49 inference(sigma_clausification,[],[f234])).
% 0.23/0.49 thf(f234,plain,(
% 0.23/0.49 ((!! @ $i @ (^[Y0 : $i]: ($true))) = $false) | ~spl0_4),
% 0.23/0.49 inference(beta_eta_normalization,[],[f233])).
% 0.23/0.49 thf(f233,plain,(
% 0.23/0.49 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ($true)))) @ sK5)) | ~spl0_4),
% 0.23/0.49 inference(sigma_clausification,[],[f200])).
% 0.23/0.49 thf(f200,plain,(
% 0.23/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ($true))))) = $false) | ~spl0_4),
% 0.23/0.49 inference(avatar_component_clause,[],[f199])).
% 0.23/0.49 thf(f199,plain,(
% 0.23/0.49 spl0_4 <=> ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ($true))))) = $false)),
% 0.23/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.23/0.49 thf(f225,plain,(
% 0.23/0.49 spl0_4 | spl0_5 | ~spl0_2),
% 0.23/0.49 inference(avatar_split_clause,[],[f221,f165,f223,f199])).
% 0.23/0.49 thf(f165,plain,(
% 0.23/0.49 spl0_2 <=> ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) => (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y0 @ Y1)))))))))) = $false)),
% 0.23/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.23/0.49 thf(f221,plain,(
% 0.23/0.49 ((sK2 @ sK3 @ sK4) = $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ($true))))) = $false) | ~spl0_2),
% 0.23/0.49 inference(binary_proxy_clausification,[],[f207])).
% 0.23/0.49 thf(f207,plain,(
% 0.23/0.49 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ($true))))) => (sK2 @ sK3 @ sK4))) | ~spl0_2),
% 0.23/0.49 inference(boolean_simplification,[],[f206])).
% 0.23/0.49 thf(f206,plain,(
% 0.23/0.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK2 @ Y1 @ Y0)))))) => (sK2 @ sK3 @ sK4)) = $true) | ~spl0_2),
% 0.23/0.49 inference(boolean_simplification,[],[f205])).
% 0.23/0.49 thf(f205,plain,(
% 0.23/0.49 ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK2 @ Y1 @ Y0)))))) & $true) => (sK2 @ sK3 @ sK4))) | ~spl0_2),
% 0.23/0.49 inference(superposition,[],[f193,f149])).
% 0.23/0.49 thf(f193,plain,(
% 0.23/0.49 ( ! [X1 : $i > $i > $o] : (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (X1 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X1 @ Y1 @ Y0) & (X1 @ Y2 @ Y1)) => (X1 @ Y2 @ Y0))))))))) => (X1 @ sK3 @ sK4)) = $true)) ) | ~spl0_2),
% 0.23/0.49 inference(beta_eta_normalization,[],[f192])).
% 0.23/0.49 thf(f192,plain,(
% 0.23/0.49 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK3 @ sK4))) @ X1) = $true)) ) | ~spl0_2),
% 0.23/0.49 inference(pi_clausification,[],[f185])).
% 0.23/0.49 thf(f185,plain,(
% 0.23/0.49 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK3 @ sK4)))) = $true) | ~spl0_2),
% 0.23/0.49 inference(not_proxy_clausification,[],[f182])).
% 0.23/0.49 thf(f182,plain,(
% 0.23/0.49 ($false = (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK3 @ sK4)))))) | ~spl0_2),
% 0.23/0.49 inference(boolean_simplification,[],[f181])).
% 0.23/0.49 thf(f181,plain,(
% 0.23/0.49 (($true => (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK3 @ sK4)))))) = $false) | ~spl0_2),
% 0.23/0.49 inference(backward_demodulation,[],[f177,f180])).
% 0.23/0.49 thf(f180,plain,(
% 0.23/0.49 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK4 @ sK3)))) = $true) | ~spl0_2),
% 0.23/0.49 inference(binary_proxy_clausification,[],[f177])).
% 0.23/0.49 thf(f177,plain,(
% 0.23/0.49 (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK4 @ sK3)))) => (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK3 @ sK4)))))) = $false) | ~spl0_2),
% 0.23/0.49 inference(beta_eta_normalization,[],[f176])).
% 0.23/0.49 thf(f176,plain,(
% 0.23/0.49 ($false = ((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ Y0 @ sK3)))) => (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ sK3 @ Y0))))))) @ sK4)) | ~spl0_2),
% 0.23/0.49 inference(sigma_clausification,[],[f173])).
% 0.23/0.49 thf(f173,plain,(
% 0.23/0.49 ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ Y0 @ sK3)))) => (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ sK3 @ Y0)))))))) = $false) | ~spl0_2),
% 0.23/0.49 inference(beta_eta_normalization,[],[f172])).
% 0.23/0.49 thf(f172,plain,(
% 0.23/0.49 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) => (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y0 @ Y1))))))))) @ sK3)) | ~spl0_2),
% 0.23/0.49 inference(sigma_clausification,[],[f166])).
% 0.23/0.49 thf(f166,plain,(
% 0.23/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) => (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y0 @ Y1)))))))))) = $false) | ~spl0_2),
% 0.23/0.49 inference(avatar_component_clause,[],[f165])).
% 0.23/0.49 thf(f201,plain,(
% 0.23/0.49 spl0_3 | spl0_4 | ~spl0_2),
% 0.23/0.49 inference(avatar_split_clause,[],[f194,f165,f199,f196])).
% 0.23/0.49 thf(f194,plain,(
% 0.23/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ($true))))) = $false) | ((sK2 @ sK4 @ sK3) = $true) | ~spl0_2),
% 0.23/0.49 inference(binary_proxy_clausification,[],[f191])).
% 0.23/0.49 thf(f191,plain,(
% 0.23/0.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ($true))))) => (sK2 @ sK4 @ sK3)) = $true) | ~spl0_2),
% 0.23/0.49 inference(boolean_simplification,[],[f190])).
% 0.23/0.49 thf(f190,plain,(
% 0.23/0.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK2 @ Y1 @ Y0)))))) => (sK2 @ sK4 @ sK3)) = $true) | ~spl0_2),
% 0.23/0.49 inference(boolean_simplification,[],[f189])).
% 0.23/0.49 thf(f189,plain,(
% 0.23/0.49 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK2 @ Y1 @ Y0)))))) & $true) => (sK2 @ sK4 @ sK3)) = $true) | ~spl0_2),
% 0.23/0.49 inference(superposition,[],[f184,f149])).
% 0.23/0.49 thf(f184,plain,(
% 0.23/0.49 ( ! [X1 : $i > $i > $o] : (($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (X1 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X1 @ Y1 @ Y0) & (X1 @ Y2 @ Y1)) => (X1 @ Y2 @ Y0))))))))) => (X1 @ sK4 @ sK3)))) ) | ~spl0_2),
% 0.23/0.49 inference(beta_eta_normalization,[],[f183])).
% 0.23/0.49 thf(f183,plain,(
% 0.23/0.49 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK4 @ sK3))) @ X1) = $true)) ) | ~spl0_2),
% 0.23/0.49 inference(pi_clausification,[],[f180])).
% 0.23/0.49 thf(f167,plain,(
% 0.23/0.49 spl0_1 | spl0_2),
% 0.23/0.49 inference(avatar_split_clause,[],[f160,f165,f162])).
% 0.23/0.49 thf(f160,plain,(
% 0.23/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) => (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y0 @ Y1)))))))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0)))) & (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y1))))) => (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y0))))))))))))),
% 0.23/0.49 inference(binary_proxy_clausification,[],[f143])).
% 0.23/0.49 thf(f143,plain,(
% 0.23/0.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) => (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y0 @ Y1)))))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y0)))) & (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y1))))) => (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y0)))))))))))) = $false)),
% 0.23/0.49 inference(binary_proxy_clausification,[],[f142])).
% 0.23/0.49 % SZS output end Proof for theBenchmark
% 0.23/0.49 % (32549)------------------------------
% 0.23/0.49 % (32549)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.49 % (32549)Termination reason: Refutation
% 0.23/0.49
% 0.23/0.49 % (32549)Memory used [KB]: 6268
% 0.23/0.49 % (32549)Time elapsed: 0.064 s
% 0.23/0.49 % (32549)Instructions burned: 93 (million)
% 0.23/0.49 % (32549)------------------------------
% 0.23/0.49 % (32549)------------------------------
% 0.23/0.49 % (32537)Success in time 0.106 s
% 0.23/0.49 % Vampire---4.8 exiting
%------------------------------------------------------------------------------