TSTP Solution File: SEV302^5 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV302^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 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 : n003.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 04:12:43 EDT 2024
% Result : Theorem 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SEV302^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.11/0.15 % 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 : n003.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 19:02:38 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
% 0.15/0.38 % (16333)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.38 % (16328)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.15/0.38 % (16326)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.38 % (16332)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.38 % (16333)Instruction limit reached!
% 0.15/0.38 % (16333)------------------------------
% 0.15/0.38 % (16333)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (16333)Termination reason: Unknown
% 0.15/0.38 % (16333)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (16333)Memory used [KB]: 1023
% 0.15/0.38 % (16333)Time elapsed: 0.003 s
% 0.15/0.38 % (16333)Instructions burned: 4 (million)
% 0.15/0.38 % (16333)------------------------------
% 0.15/0.38 % (16333)------------------------------
% 0.15/0.39 % (16329)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.39 % (16329)Instruction limit reached!
% 0.15/0.39 % (16329)------------------------------
% 0.15/0.39 % (16329)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (16329)Termination reason: Unknown
% 0.15/0.39 % (16329)Termination phase: Property scanning
% 0.15/0.39
% 0.15/0.39 % (16329)Memory used [KB]: 1023
% 0.15/0.39 % (16329)Time elapsed: 0.003 s
% 0.15/0.39 % (16329)Instructions burned: 3 (million)
% 0.15/0.39 % (16329)------------------------------
% 0.15/0.39 % (16329)------------------------------
% 0.15/0.39 % (16331)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.15/0.39 % (16327)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.39 % (16332)Instruction limit reached!
% 0.15/0.39 % (16332)------------------------------
% 0.15/0.39 % (16332)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (16332)Termination reason: Unknown
% 0.15/0.39 % (16332)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (16332)Memory used [KB]: 5500
% 0.15/0.39 % (16332)Time elapsed: 0.012 s
% 0.15/0.39 % (16332)Instructions burned: 19 (million)
% 0.15/0.39 % (16332)------------------------------
% 0.15/0.39 % (16332)------------------------------
% 0.15/0.39 % (16331)Refutation not found, incomplete strategy
% 0.15/0.39 % (16331)------------------------------
% 0.15/0.39 % (16331)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (16331)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.39
% 0.15/0.40
% 0.15/0.40 % (16331)Memory used [KB]: 5500
% 0.15/0.40 % (16331)Time elapsed: 0.004 s
% 0.15/0.40 % (16331)Instructions burned: 3 (million)
% 0.15/0.40 % (16331)------------------------------
% 0.15/0.40 % (16331)------------------------------
% 0.15/0.40 % (16327)Instruction limit reached!
% 0.15/0.40 % (16327)------------------------------
% 0.15/0.40 % (16327)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (16327)Termination reason: Unknown
% 0.15/0.40 % (16327)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (16327)Memory used [KB]: 1023
% 0.15/0.40 % (16327)Time elapsed: 0.004 s
% 0.15/0.40 % (16327)Instructions burned: 6 (million)
% 0.15/0.40 % (16327)------------------------------
% 0.15/0.40 % (16327)------------------------------
% 0.15/0.40 % (16330)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.40 % (16330)Instruction limit reached!
% 0.15/0.40 % (16330)------------------------------
% 0.15/0.40 % (16330)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (16330)Termination reason: Unknown
% 0.15/0.40 % (16330)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (16330)Memory used [KB]: 895
% 0.15/0.40 % (16330)Time elapsed: 0.003 s
% 0.15/0.40 % (16330)Instructions burned: 2 (million)
% 0.15/0.40 % (16330)------------------------------
% 0.15/0.40 % (16330)------------------------------
% 0.15/0.40 % (16328)Instruction limit reached!
% 0.15/0.40 % (16328)------------------------------
% 0.15/0.40 % (16328)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (16328)Termination reason: Unknown
% 0.15/0.40 % (16328)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (16328)Memory used [KB]: 5500
% 0.15/0.40 % (16328)Time elapsed: 0.016 s
% 0.15/0.40 % (16328)Instructions burned: 28 (million)
% 0.15/0.40 % (16328)------------------------------
% 0.15/0.40 % (16328)------------------------------
% 0.15/0.40 % (16335)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.15/0.41 % (16334)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.15/0.41 % (16337)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.15/0.41 % (16336)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.41 % (16338)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.41 % (16336)Instruction limit reached!
% 0.15/0.41 % (16336)------------------------------
% 0.15/0.41 % (16336)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (16336)Termination reason: Unknown
% 0.15/0.41 % (16336)Termination phase: Function definition elimination
% 0.15/0.41
% 0.15/0.41 % (16336)Memory used [KB]: 1023
% 0.15/0.41 % (16336)Time elapsed: 0.004 s
% 0.15/0.41 % (16336)Instructions burned: 3 (million)
% 0.15/0.41 % (16336)------------------------------
% 0.15/0.41 % (16336)------------------------------
% 0.22/0.41 % (16339)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.41 % (16335)Instruction limit reached!
% 0.22/0.41 % (16335)------------------------------
% 0.22/0.41 % (16335)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (16335)Termination reason: Unknown
% 0.22/0.41 % (16335)Termination phase: Saturation
% 0.22/0.41
% 0.22/0.41 % (16335)Memory used [KB]: 5500
% 0.22/0.41 % (16335)Time elapsed: 0.009 s
% 0.22/0.41 % (16335)Instructions burned: 15 (million)
% 0.22/0.41 % (16335)------------------------------
% 0.22/0.41 % (16335)------------------------------
% 0.22/0.41 % (16338)Instruction limit reached!
% 0.22/0.41 % (16338)------------------------------
% 0.22/0.41 % (16338)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (16338)Termination reason: Unknown
% 0.22/0.41 % (16338)Termination phase: Saturation
% 0.22/0.41
% 0.22/0.41 % (16338)Memory used [KB]: 1023
% 0.22/0.41 % (16338)Time elapsed: 0.006 s
% 0.22/0.41 % (16338)Instructions burned: 8 (million)
% 0.22/0.41 % (16338)------------------------------
% 0.22/0.41 % (16338)------------------------------
% 0.22/0.42 % (16340)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)
% 0.22/0.42 % (16340)Instruction limit reached!
% 0.22/0.42 % (16340)------------------------------
% 0.22/0.42 % (16340)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (16340)Termination reason: Unknown
% 0.22/0.42 % (16340)Termination phase: Function definition elimination
% 0.22/0.42
% 0.22/0.42 % (16340)Memory used [KB]: 1023
% 0.22/0.42 % (16340)Time elapsed: 0.004 s
% 0.22/0.42 % (16340)Instructions burned: 4 (million)
% 0.22/0.42 % (16340)------------------------------
% 0.22/0.42 % (16340)------------------------------
% 0.22/0.42 % (16339)Instruction limit reached!
% 0.22/0.42 % (16339)------------------------------
% 0.22/0.42 % (16339)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (16339)Termination reason: Unknown
% 0.22/0.42 % (16339)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (16339)Memory used [KB]: 5884
% 0.22/0.42 % (16339)Time elapsed: 0.013 s
% 0.22/0.42 % (16339)Instructions burned: 17 (million)
% 0.22/0.42 % (16339)------------------------------
% 0.22/0.42 % (16339)------------------------------
% 0.22/0.42 % (16334)Instruction limit reached!
% 0.22/0.42 % (16334)------------------------------
% 0.22/0.42 % (16334)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (16334)Termination reason: Unknown
% 0.22/0.42 % (16334)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (16334)Memory used [KB]: 5628
% 0.22/0.42 % (16334)Time elapsed: 0.018 s
% 0.22/0.42 % (16334)Instructions burned: 37 (million)
% 0.22/0.42 % (16334)------------------------------
% 0.22/0.42 % (16334)------------------------------
% 0.22/0.43 % (16341)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)
% 0.22/0.43 % (16342)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)
% 0.22/0.43 % (16341)Instruction limit reached!
% 0.22/0.43 % (16341)------------------------------
% 0.22/0.43 % (16341)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (16341)Termination reason: Unknown
% 0.22/0.43 % (16341)Termination phase: Function definition elimination
% 0.22/0.43
% 0.22/0.43 % (16341)Memory used [KB]: 1023
% 0.22/0.43 % (16341)Time elapsed: 0.003 s
% 0.22/0.43 % (16341)Instructions burned: 3 (million)
% 0.22/0.43 % (16341)------------------------------
% 0.22/0.43 % (16341)------------------------------
% 0.22/0.43 % (16342)Instruction limit reached!
% 0.22/0.43 % (16342)------------------------------
% 0.22/0.43 % (16342)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (16342)Termination reason: Unknown
% 0.22/0.43 % (16342)Termination phase: Saturation
% 0.22/0.43
% 0.22/0.43 % (16342)Memory used [KB]: 5500
% 0.22/0.43 % (16342)Time elapsed: 0.006 s
% 0.22/0.43 % (16342)Instructions burned: 8 (million)
% 0.22/0.43 % (16342)------------------------------
% 0.22/0.43 % (16342)------------------------------
% 0.22/0.44 % (16343)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)
% 0.22/0.44 % (16343)Instruction limit reached!
% 0.22/0.44 % (16343)------------------------------
% 0.22/0.44 % (16343)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (16343)Termination reason: Unknown
% 0.22/0.44 % (16343)Termination phase: Saturation
% 0.22/0.44
% 0.22/0.44 % (16343)Memory used [KB]: 1023
% 0.22/0.44 % (16343)Time elapsed: 0.004 s
% 0.22/0.44 % (16343)Instructions burned: 5 (million)
% 0.22/0.44 % (16344)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.44 % (16343)------------------------------
% 0.22/0.44 % (16343)------------------------------
% 0.22/0.44 % (16346)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.44 % (16345)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)
% 0.22/0.44 % (16344)Instruction limit reached!
% 0.22/0.44 % (16344)------------------------------
% 0.22/0.44 % (16344)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (16344)Termination reason: Unknown
% 0.22/0.44 % (16344)Termination phase: Property scanning
% 0.22/0.44
% 0.22/0.44 % (16344)Memory used [KB]: 1023
% 0.22/0.44 % (16344)Time elapsed: 0.004 s
% 0.22/0.44 % (16344)Instructions burned: 5 (million)
% 0.22/0.44 % (16344)------------------------------
% 0.22/0.44 % (16344)------------------------------
% 0.22/0.44 % (16337)First to succeed.
% 0.22/0.45 % (16348)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)
% 0.22/0.45 % (16347)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.45 % (16348)Refutation not found, incomplete strategy
% 0.22/0.45 % (16348)------------------------------
% 0.22/0.45 % (16348)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (16348)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.45
% 0.22/0.45
% 0.22/0.45 % (16348)Memory used [KB]: 5500
% 0.22/0.45 % (16348)Time elapsed: 0.004 s
% 0.22/0.45 % (16348)Instructions burned: 4 (million)
% 0.22/0.45 % (16348)------------------------------
% 0.22/0.45 % (16348)------------------------------
% 0.22/0.45 % (16345)Instruction limit reached!
% 0.22/0.45 % (16345)------------------------------
% 0.22/0.45 % (16345)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (16345)Termination reason: Unknown
% 0.22/0.45 % (16345)Termination phase: Saturation
% 0.22/0.45
% 0.22/0.45 % (16345)Memory used [KB]: 5628
% 0.22/0.45 % (16345)Time elapsed: 0.014 s
% 0.22/0.45 % (16345)Instructions burned: 18 (million)
% 0.22/0.45 % (16345)------------------------------
% 0.22/0.45 % (16345)------------------------------
% 0.22/0.45 % (16349)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)
% 0.22/0.45 % (16347)Instruction limit reached!
% 0.22/0.45 % (16347)------------------------------
% 0.22/0.45 % (16347)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (16347)Termination reason: Unknown
% 0.22/0.45 % (16347)Termination phase: Property scanning
% 0.22/0.45
% 0.22/0.45 % (16347)Memory used [KB]: 1023
% 0.22/0.45 % (16347)Time elapsed: 0.004 s
% 0.22/0.45 % (16347)Instructions burned: 6 (million)
% 0.22/0.45 % (16347)------------------------------
% 0.22/0.45 % (16347)------------------------------
% 0.22/0.45 % (16337)Refutation found. Thanks to Tanya!
% 0.22/0.45 % SZS status Theorem for theBenchmark
% 0.22/0.45 % SZS output start Proof for theBenchmark
% 0.22/0.45 thf(func_def_0, type, cNAT: (($i > $o) > $o) > $o).
% 0.22/0.45 thf(func_def_1, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 0.22/0.45 thf(func_def_2, type, cZERO: ($i > $o) > $o).
% 0.22/0.45 thf(func_def_18, type, ph1: !>[X0: $tType]:(X0)).
% 0.22/0.45 thf(func_def_19, type, sK2: (($i > $o) > $o) > $o).
% 0.22/0.45 thf(func_def_20, type, sK3: ($i > $o) > $o).
% 0.22/0.45 thf(func_def_23, type, sK4: ($i > $o) > $o).
% 0.22/0.45 thf(func_def_24, type, sK5: (($i > $o) > $o) > $o).
% 0.22/0.45 thf(func_def_25, type, sK6: (($i > $o) > $o) > $o).
% 0.22/0.45 thf(f192,plain,(
% 0.22/0.45 $false),
% 0.22/0.45 inference(avatar_sat_refutation,[],[f87,f176,f191])).
% 0.22/0.45 thf(f191,plain,(
% 0.22/0.45 ~spl0_1),
% 0.22/0.45 inference(avatar_contradiction_clause,[],[f190])).
% 0.22/0.45 thf(f190,plain,(
% 0.22/0.45 $false | ~spl0_1),
% 0.22/0.45 inference(trivial_inequality_removal,[],[f189])).
% 0.22/0.45 thf(f189,plain,(
% 0.22/0.45 ($true = $false) | ~spl0_1),
% 0.22/0.45 inference(boolean_simplification,[],[f188])).
% 0.22/0.45 thf(f188,plain,(
% 0.22/0.45 ($true = ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK6 @ Y0) => (sK6 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))) & $false)) | ~spl0_1),
% 0.22/0.45 inference(backward_demodulation,[],[f185,f187])).
% 0.22/0.45 thf(f187,plain,(
% 0.22/0.45 ($false = (sK6 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ~spl0_1),
% 0.22/0.45 inference(boolean_simplification,[],[f186])).
% 0.22/0.45 thf(f186,plain,(
% 0.22/0.45 ($false = ($true => (sK6 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))) | ~spl0_1),
% 0.22/0.45 inference(backward_demodulation,[],[f183,f185])).
% 0.22/0.45 thf(f183,plain,(
% 0.22/0.45 ($false = (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK6 @ Y0) => (sK6 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))) & (sK6 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (sK6 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))) | ~spl0_1),
% 0.22/0.45 inference(beta_eta_normalization,[],[f179])).
% 0.22/0.45 thf(f179,plain,(
% 0.22/0.45 ($false = ((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))) @ sK6)) | ~spl0_1),
% 0.22/0.45 inference(sigma_clausification,[],[f46])).
% 0.22/0.45 thf(f46,plain,(
% 0.22/0.45 ($false = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))) | ~spl0_1),
% 0.22/0.45 inference(avatar_component_clause,[],[f45])).
% 0.22/0.45 thf(f45,plain,(
% 0.22/0.45 spl0_1 <=> ($false = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))))),
% 0.22/0.45 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.22/0.45 thf(f185,plain,(
% 0.22/0.45 ($true = ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK6 @ Y0) => (sK6 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))) & (sK6 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))) | ~spl0_1),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f183])).
% 0.22/0.45 thf(f176,plain,(
% 0.22/0.45 ~spl0_5),
% 0.22/0.45 inference(avatar_contradiction_clause,[],[f175])).
% 0.22/0.45 thf(f175,plain,(
% 0.22/0.45 $false | ~spl0_5),
% 0.22/0.45 inference(trivial_inequality_removal,[],[f174])).
% 0.22/0.45 thf(f174,plain,(
% 0.22/0.45 ($true = $false) | ~spl0_5),
% 0.22/0.45 inference(boolean_simplification,[],[f173])).
% 0.22/0.45 thf(f173,plain,(
% 0.22/0.45 ((~ $true) = $true) | ~spl0_5),
% 0.22/0.45 inference(forward_demodulation,[],[f166,f152])).
% 0.22/0.45 thf(f152,plain,(
% 0.22/0.45 ($true = (sK5 @ sK4)) | ~spl0_5),
% 0.22/0.45 inference(boolean_simplification,[],[f151])).
% 0.22/0.45 thf(f151,plain,(
% 0.22/0.45 ($true = ($true => (sK5 @ sK4))) | ~spl0_5),
% 0.22/0.45 inference(forward_demodulation,[],[f150,f131])).
% 0.22/0.45 thf(f131,plain,(
% 0.22/0.45 ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK5 @ Y0) => (sK5 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))) = $true) | ~spl0_5),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f125])).
% 0.22/0.45 thf(f125,plain,(
% 0.22/0.45 ($true = ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK5 @ Y0) => (sK5 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))) & (sK5 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))) | ~spl0_5),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f115])).
% 0.22/0.45 thf(f115,plain,(
% 0.22/0.45 ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK5 @ Y0) => (sK5 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))) & (sK5 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (sK5 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK4 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))) & (Y0 @ Y1))))))) = $false) | ~spl0_5),
% 0.22/0.45 inference(beta_eta_normalization,[],[f111])).
% 0.22/0.45 thf(f111,plain,(
% 0.22/0.45 ($false = ((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((sK4 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))))) @ sK5)) | ~spl0_5),
% 0.22/0.45 inference(sigma_clausification,[],[f110])).
% 0.22/0.45 thf(f110,plain,(
% 0.22/0.45 ($false = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((sK4 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))))))) | ~spl0_5),
% 0.22/0.45 inference(boolean_simplification,[],[f109])).
% 0.22/0.45 thf(f109,plain,(
% 0.22/0.45 ($false = ($true & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((sK4 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))))) | ~spl0_5),
% 0.22/0.45 inference(backward_demodulation,[],[f95,f108])).
% 0.22/0.45 thf(f108,plain,(
% 0.22/0.45 ((sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK4 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))) & (Y0 @ Y1)))))) = $true) | ~spl0_5),
% 0.22/0.45 inference(boolean_simplification,[],[f107])).
% 0.22/0.45 thf(f107,plain,(
% 0.22/0.45 ($true = ($true => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK4 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))) & (Y0 @ Y1)))))))) | ~spl0_5),
% 0.22/0.45 inference(forward_demodulation,[],[f106,f102])).
% 0.22/0.45 thf(f102,plain,(
% 0.22/0.45 ($true = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK4))))) | ~spl0_5),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f96])).
% 0.22/0.45 thf(f96,plain,(
% 0.22/0.45 ($true = ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK4)))) & (sK2 @ sK4))) | ~spl0_5),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f94])).
% 0.22/0.45 thf(f94,plain,(
% 0.22/0.45 ($false = (((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK4)))) & (sK2 @ sK4)) => ((sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK4 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))) & (Y0 @ Y1)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((sK4 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))))))))) | ~spl0_5),
% 0.22/0.45 inference(beta_eta_normalization,[],[f93])).
% 0.22/0.45 thf(f93,plain,(
% 0.22/0.45 ($false = ((^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) & (sK2 @ Y0)) => ((sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3)))))))))))) @ sK4)) | ~spl0_5),
% 0.22/0.45 inference(sigma_clausification,[],[f86])).
% 0.22/0.45 thf(f86,plain,(
% 0.22/0.45 ($false = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) & (sK2 @ Y0)) => ((sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3)))))))))))))) | ~spl0_5),
% 0.22/0.45 inference(avatar_component_clause,[],[f85])).
% 0.22/0.45 thf(f85,plain,(
% 0.22/0.45 spl0_5 <=> ($false = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) & (sK2 @ Y0)) => ((sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))))))))),
% 0.22/0.45 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.22/0.45 thf(f106,plain,(
% 0.22/0.45 ($true = ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK4)))) => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK4 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))) & (Y0 @ Y1)))))))) | ~spl0_5),
% 0.22/0.45 inference(boolean_simplification,[],[f105])).
% 0.22/0.45 thf(f105,plain,(
% 0.22/0.45 ($true = ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK4)))) => ($true => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK4 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))) & (Y0 @ Y1))))))))) | ~spl0_5),
% 0.22/0.45 inference(superposition,[],[f38,f104])).
% 0.22/0.45 thf(f104,plain,(
% 0.22/0.45 ($true = (sK2 @ sK4)) | ~spl0_5),
% 0.22/0.45 inference(boolean_simplification,[],[f103])).
% 0.22/0.45 thf(f103,plain,(
% 0.22/0.45 ($true = ($true & (sK2 @ sK4))) | ~spl0_5),
% 0.22/0.45 inference(backward_demodulation,[],[f96,f102])).
% 0.22/0.45 thf(f38,plain,(
% 0.22/0.45 ( ! [X1 : ($i > $o) > $o] : ((((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ X1)))) => ((sK2 @ X1) => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((X1 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))) & (Y0 @ Y1)))))))) = $true)) )),
% 0.22/0.45 inference(beta_eta_normalization,[],[f37])).
% 0.22/0.45 thf(f37,plain,(
% 0.22/0.45 ( ! [X1 : ($i > $o) > $o] : (($true = ((^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))) @ X1))) )),
% 0.22/0.45 inference(pi_clausification,[],[f36])).
% 0.22/0.45 thf(f36,plain,(
% 0.22/0.45 ($true = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))))))))),
% 0.22/0.45 inference(boolean_simplification,[],[f35])).
% 0.22/0.45 thf(f35,plain,(
% 0.22/0.45 ($true = ($true & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))))))),
% 0.22/0.45 inference(backward_demodulation,[],[f28,f34])).
% 0.22/0.45 thf(f34,plain,(
% 0.22/0.45 ($true = (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f28])).
% 0.22/0.45 thf(f28,plain,(
% 0.22/0.45 ($true = ((sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))))))),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f26])).
% 0.22/0.45 thf(f26,plain,(
% 0.22/0.45 ($false = (((sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))))) => (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))))) & (sK2 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))) & (sK2 @ Y1)) => ((sK2 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y1 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4)))))))))))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) & (sK2 @ Y0))) => (sK2 @ Y0))))))),
% 0.22/0.45 inference(beta_eta_normalization,[],[f25])).
% 0.22/0.45 thf(f25,plain,(
% 0.22/0.45 ($false = ((^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))) => ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))))) & (Y0 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y4 @ (^[Y7 : $i]: ((Y5 @ Y7) & (~ (Y6 = Y7))))) & (Y5 @ Y6))))))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4))))) => (Y3 @ Y2)))) & (Y0 @ Y2)) => ((Y0 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y4 @ (^[Y7 : $i]: ((Y5 @ Y7) & (~ (Y6 = Y7))))) & (Y5 @ Y6))))))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4))))) => (Y3 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y2 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5)))))))))))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))) & (Y0 @ Y1))) => (Y0 @ Y1)))))) @ sK2))),
% 0.22/0.45 inference(sigma_clausification,[],[f22])).
% 0.22/0.45 thf(f22,plain,(
% 0.22/0.45 ($false = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))) => ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))))) & (Y0 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y4 @ (^[Y7 : $i]: ((Y5 @ Y7) & (~ (Y6 = Y7))))) & (Y5 @ Y6))))))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4))))) => (Y3 @ Y2)))) & (Y0 @ Y2)) => ((Y0 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y4 @ (^[Y7 : $i]: ((Y5 @ Y7) & (~ (Y6 = Y7))))) & (Y5 @ Y6))))))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4))))) => (Y3 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y2 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5)))))))))))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))) & (Y0 @ Y1))) => (Y0 @ Y1))))))))),
% 0.22/0.45 inference(not_proxy_clausification,[],[f21])).
% 0.22/0.45 thf(f21,plain,(
% 0.22/0.45 ($true = (~ (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))) => ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))))) & (Y0 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y4 @ (^[Y7 : $i]: ((Y5 @ Y7) & (~ (Y6 = Y7))))) & (Y5 @ Y6))))))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4))))) => (Y3 @ Y2)))) & (Y0 @ Y2)) => ((Y0 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y4 @ (^[Y7 : $i]: ((Y5 @ Y7) & (~ (Y6 = Y7))))) & (Y5 @ Y6))))))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4))))) => (Y3 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y2 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5)))))))))))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))) & (Y0 @ Y1))) => (Y0 @ Y1)))))))))),
% 0.22/0.45 inference(beta_eta_normalization,[],[f20])).
% 0.22/0.45 thf(f20,plain,(
% 0.22/0.45 ($true = (~ (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ (^[Y2 : $i]: (Y1 @ Y2)))))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((^[Y2 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ ((^[Y5 : ($i > $o) > $o]: ((^[Y6 : $i > $o]: (?? @ $i @ (^[Y7 : $i]: ((Y5 @ (^[Y8 : $i]: ((Y6 @ Y8) & (~ (Y7 = Y8))))) & (Y6 @ Y7))))))) @ Y4))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ (^[Y5 : $i]: (Y4 @ Y5))))))) => (Y3 @ Y2))))) @ Y1) => ((Y0 @ Y1) => (Y0 @ ((^[Y2 : ($i > $o) > $o]: ((^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))) @ Y1))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((((((^[Y2 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ ((^[Y5 : ($i > $o) > $o]: ((^[Y6 : $i > $o]: (?? @ $i @ (^[Y7 : $i]: ((Y5 @ (^[Y8 : $i]: ((Y6 @ Y8) & (~ (Y7 = Y8))))) & (Y6 @ Y7))))))) @ Y4))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ (^[Y5 : $i]: (Y4 @ Y5))))))) => (Y3 @ Y2))))) @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3)))))) & (Y0 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((((^[Y3 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y4 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y5 : ($i > $o) > $o]: ((Y4 @ Y5) => (Y4 @ ((^[Y6 : ($i > $o) > $o]: ((^[Y7 : $i > $o]: (?? @ $i @ (^[Y8 : $i]: ((Y6 @ (^[Y9 : $i]: ((Y7 @ Y9) & (~ (Y8 = Y9))))) & (Y7 @ Y8))))))) @ Y5))))) & (Y4 @ (^[Y5 : $i > $o]: (~ (?? @ $i @ (^[Y6 : $i]: (Y5 @ Y6))))))) => (Y4 @ Y3))))) @ Y2) & (Y0 @ Y2)) => ((Y0 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))) @ Y2)) & ((^[Y3 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y4 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y5 : ($i > $o) > $o]: ((Y4 @ Y5) => (Y4 @ ((^[Y6 : ($i > $o) > $o]: ((^[Y7 : $i > $o]: (?? @ $i @ (^[Y8 : $i]: ((Y6 @ (^[Y9 : $i]: ((Y7 @ Y9) & (~ (Y8 = Y9))))) & (Y7 @ Y8))))))) @ Y5))))) & (Y4 @ (^[Y5 : $i > $o]: (~ (?? @ $i @ (^[Y6 : $i]: (Y5 @ Y6))))))) => (Y4 @ Y3))))) @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))) @ Y2))))))) => (((^[Y2 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ ((^[Y5 : ($i > $o) > $o]: ((^[Y6 : $i > $o]: (?? @ $i @ (^[Y7 : $i]: ((Y5 @ (^[Y8 : $i]: ((Y6 @ Y8) & (~ (Y7 = Y8))))) & (Y6 @ Y7))))))) @ Y4))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ (^[Y5 : $i]: (Y4 @ Y5))))))) => (Y3 @ Y2))))) @ Y1) & (Y0 @ Y1))) => (Y0 @ Y1)))))))))),
% 0.22/0.45 inference(definition_unfolding,[],[f15,f18,f19,f17,f19,f18,f18,f19,f17,f19,f17,f19])).
% 0.22/0.45 thf(f17,plain,(
% 0.22/0.45 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))),
% 0.22/0.45 inference(cnf_transformation,[],[f14])).
% 0.22/0.45 thf(f14,plain,(
% 0.22/0.45 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))),
% 0.22/0.45 inference(fool_elimination,[],[f13])).
% 0.22/0.45 thf(f13,plain,(
% 0.22/0.45 (cSUCC = (^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2] : ((X1 @ X2) & (X0 @ (^[X3 : $i] : ((X2 != X3) & (X1 @ X3))))))))),
% 0.22/0.45 inference(rectify,[],[f2])).
% 0.22/0.45 thf(f2,axiom,(
% 0.22/0.45 (cSUCC = (^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1] : ((X0 @ X1) & (X2 @ (^[X3 : $i] : ((X1 != X3) & (X0 @ X3))))))))),
% 0.22/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSUCC_def)).
% 0.22/0.45 thf(f19,plain,(
% 0.22/0.45 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))) @ Y2))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))))),
% 0.22/0.45 inference(definition_unfolding,[],[f16,f17,f18])).
% 0.22/0.45 thf(f16,plain,(
% 0.22/0.45 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
% 0.22/0.45 inference(cnf_transformation,[],[f12])).
% 0.22/0.45 thf(f12,plain,(
% 0.22/0.45 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
% 0.22/0.45 inference(fool_elimination,[],[f11])).
% 0.22/0.45 thf(f11,plain,(
% 0.22/0.45 ((^[X0 : ($i > $o) > $o] : (! [X1 : (($i > $o) > $o) > $o] : (((X1 @ cZERO) & ! [X2 : ($i > $o) > $o] : ((X1 @ X2) => (X1 @ (cSUCC @ X2)))) => (X1 @ X0)))) = cNAT)),
% 0.22/0.45 inference(rectify,[],[f3])).
% 0.22/0.45 thf(f3,axiom,(
% 0.22/0.45 ((^[X2 : ($i > $o) > $o] : (! [X0 : (($i > $o) > $o) > $o] : (((X0 @ cZERO) & ! [X1 : ($i > $o) > $o] : ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) => (X0 @ X2)))) = cNAT)),
% 0.22/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cNAT_def)).
% 0.22/0.45 thf(f18,plain,(
% 0.22/0.45 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.22/0.45 inference(cnf_transformation,[],[f10])).
% 0.22/0.45 thf(f10,plain,(
% 0.22/0.45 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.22/0.45 inference(fool_elimination,[],[f9])).
% 0.22/0.45 thf(f9,plain,(
% 0.22/0.45 (cZERO = (^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))))),
% 0.22/0.45 inference(rectify,[],[f1])).
% 0.22/0.45 thf(f1,axiom,(
% 0.22/0.45 (cZERO = (^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))))),
% 0.22/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cZERO_def)).
% 0.22/0.45 thf(f15,plain,(
% 0.22/0.45 ($true = (~ (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ cZERO) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((cNAT @ Y1) => ((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((cNAT @ cZERO) & (Y0 @ cZERO)) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((cNAT @ Y2) & (Y0 @ Y2)) => ((Y0 @ (cSUCC @ Y2)) & (cNAT @ (cSUCC @ Y2))))))) => ((cNAT @ Y1) & (Y0 @ Y1))) => (Y0 @ Y1)))))))))),
% 0.22/0.45 inference(cnf_transformation,[],[f8])).
% 0.22/0.45 thf(f8,plain,(
% 0.22/0.45 ($true = (~ (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ cZERO) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((cNAT @ Y1) => ((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((cNAT @ cZERO) & (Y0 @ cZERO)) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((cNAT @ Y2) & (Y0 @ Y2)) => ((Y0 @ (cSUCC @ Y2)) & (cNAT @ (cSUCC @ Y2))))))) => ((cNAT @ Y1) & (Y0 @ Y1))) => (Y0 @ Y1)))))))))),
% 0.22/0.45 inference(fool_elimination,[],[f7])).
% 0.22/0.45 thf(f7,plain,(
% 0.22/0.45 ~! [X0 : (($i > $o) > $o) > $o] : ((! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) & (X0 @ cZERO)) => ! [X2 : ($i > $o) > $o] : (((! [X3 : ($i > $o) > $o] : (((X0 @ X3) & (cNAT @ X3)) => ((cNAT @ (cSUCC @ X3)) & (X0 @ (cSUCC @ X3)))) & (X0 @ cZERO) & (cNAT @ cZERO)) => ((X0 @ X2) & (cNAT @ X2))) => (X0 @ X2)))),
% 0.22/0.45 inference(rectify,[],[f5])).
% 0.22/0.45 thf(f5,negated_conjecture,(
% 0.22/0.45 ~! [X0 : (($i > $o) > $o) > $o] : ((! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) & (X0 @ cZERO)) => ! [X4 : ($i > $o) > $o] : (((! [X1 : ($i > $o) > $o] : (((X0 @ X1) & (cNAT @ X1)) => ((cNAT @ (cSUCC @ X1)) & (X0 @ (cSUCC @ X1)))) & (X0 @ cZERO) & (cNAT @ cZERO)) => ((X0 @ X4) & (cNAT @ X4))) => (X0 @ X4)))),
% 0.22/0.45 inference(negated_conjecture,[],[f4])).
% 0.22/0.45 thf(f4,conjecture,(
% 0.22/0.45 ! [X0 : (($i > $o) > $o) > $o] : ((! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) & (X0 @ cZERO)) => ! [X4 : ($i > $o) > $o] : (((! [X1 : ($i > $o) > $o] : (((X0 @ X1) & (cNAT @ X1)) => ((cNAT @ (cSUCC @ X1)) & (X0 @ (cSUCC @ X1)))) & (X0 @ cZERO) & (cNAT @ cZERO)) => ((X0 @ X4) & (cNAT @ X4))) => (X0 @ X4)))),
% 0.22/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX6102_B)).
% 0.22/0.45 thf(f95,plain,(
% 0.22/0.45 (((sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK4 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))) & (Y0 @ Y1)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((sK4 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))))))) = $false) | ~spl0_5),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f94])).
% 0.22/0.45 thf(f150,plain,(
% 0.22/0.45 (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK5 @ Y0) => (sK5 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))) => (sK5 @ sK4)) = $true) | ~spl0_5),
% 0.22/0.45 inference(boolean_simplification,[],[f145])).
% 0.22/0.45 thf(f145,plain,(
% 0.22/0.45 ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK5 @ Y0) => (sK5 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))) & $true) => (sK5 @ sK4)) = $true) | ~spl0_5),
% 0.22/0.45 inference(superposition,[],[f136,f133])).
% 0.22/0.45 thf(f133,plain,(
% 0.22/0.45 ($true = (sK5 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ~spl0_5),
% 0.22/0.45 inference(boolean_simplification,[],[f132])).
% 0.22/0.45 thf(f132,plain,(
% 0.22/0.45 ($true = ($true & (sK5 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))) | ~spl0_5),
% 0.22/0.45 inference(backward_demodulation,[],[f125,f131])).
% 0.22/0.45 thf(f136,plain,(
% 0.22/0.45 ( ! [X1 : (($i > $o) > $o) > $o] : (($true = (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))) & (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (X1 @ sK4)))) ) | ~spl0_5),
% 0.22/0.45 inference(beta_eta_normalization,[],[f134])).
% 0.22/0.45 thf(f134,plain,(
% 0.22/0.45 ( ! [X1 : (($i > $o) > $o) > $o] : (($true = ((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK4))) @ X1))) ) | ~spl0_5),
% 0.22/0.45 inference(pi_clausification,[],[f102])).
% 0.22/0.45 thf(f166,plain,(
% 0.22/0.45 ($true = (~ (sK5 @ sK4))) | ~spl0_5),
% 0.22/0.45 inference(boolean_simplification,[],[f160])).
% 0.22/0.45 thf(f160,plain,(
% 0.22/0.45 ($true = ((sK5 @ sK4) => $false)) | ~spl0_5),
% 0.22/0.45 inference(superposition,[],[f141,f124])).
% 0.22/0.45 thf(f124,plain,(
% 0.22/0.45 ($false = (sK5 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK4 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))) & (Y0 @ Y1))))))) | ~spl0_5),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f115])).
% 0.22/0.45 thf(f141,plain,(
% 0.22/0.45 ( ! [X1 : ($i > $o) > $o] : ((((sK5 @ X1) => (sK5 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((X1 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))) & (Y0 @ Y1))))))) = $true)) ) | ~spl0_5),
% 0.22/0.45 inference(beta_eta_normalization,[],[f140])).
% 0.22/0.45 thf(f140,plain,(
% 0.22/0.45 ( ! [X1 : ($i > $o) > $o] : (($true = ((^[Y0 : ($i > $o) > $o]: ((sK5 @ Y0) => (sK5 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))))) @ X1))) ) | ~spl0_5),
% 0.22/0.45 inference(pi_clausification,[],[f131])).
% 0.22/0.45 thf(f87,plain,(
% 0.22/0.45 spl0_5 | spl0_1),
% 0.22/0.45 inference(avatar_split_clause,[],[f83,f45,f85])).
% 0.22/0.45 thf(f83,plain,(
% 0.22/0.45 ($false = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))) | ($false = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) & (sK2 @ Y0)) => ((sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))))))))),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f70])).
% 0.22/0.45 thf(f70,plain,(
% 0.22/0.45 ($false = ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) & (sK2 @ Y0)) => ((sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3)))))))))))))))),
% 0.22/0.45 inference(not_proxy_clausification,[],[f66])).
% 0.22/0.45 thf(f66,plain,(
% 0.22/0.45 ($true = (~ ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) & (sK2 @ Y0)) => ((sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))))))))))),
% 0.22/0.45 inference(boolean_simplification,[],[f65])).
% 0.22/0.45 thf(f65,plain,(
% 0.22/0.45 ($true = (((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) & (sK2 @ Y0)) => ((sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3)))))))))))))) => $false))),
% 0.22/0.45 inference(boolean_simplification,[],[f64])).
% 0.22/0.45 thf(f64,plain,(
% 0.22/0.45 ($true = (((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) & (sK2 @ Y0)) => ((sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3)))))))))))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK3)))) & $false)))),
% 0.22/0.45 inference(backward_demodulation,[],[f61,f63])).
% 0.22/0.45 thf(f63,plain,(
% 0.22/0.45 ($false = (sK2 @ sK3))),
% 0.22/0.45 inference(boolean_simplification,[],[f62])).
% 0.22/0.45 thf(f62,plain,(
% 0.22/0.45 (($true => (sK2 @ sK3)) = $false)),
% 0.22/0.45 inference(backward_demodulation,[],[f56,f61])).
% 0.22/0.45 thf(f56,plain,(
% 0.22/0.45 ($false = ((((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) & (sK2 @ Y0)) => ((sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3)))))))))))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK3)))) & (sK2 @ sK3))) => (sK2 @ sK3)))),
% 0.22/0.45 inference(boolean_simplification,[],[f55])).
% 0.22/0.45 thf(f55,plain,(
% 0.22/0.45 ((((((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))) & $true) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) & (sK2 @ Y0)) => ((sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3)))))))))))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK3)))) & (sK2 @ sK3))) => (sK2 @ sK3)) = $false)),
% 0.22/0.45 inference(forward_demodulation,[],[f54,f34])).
% 0.22/0.45 thf(f54,plain,(
% 0.22/0.45 ((((((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))) & (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) & (sK2 @ Y0)) => ((sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3)))))))))))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK3)))) & (sK2 @ sK3))) => (sK2 @ sK3)) = $false)),
% 0.22/0.45 inference(beta_eta_normalization,[],[f53])).
% 0.22/0.45 thf(f53,plain,(
% 0.22/0.45 ($false = ((^[Y0 : ($i > $o) > $o]: (((((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))))) & (sK2 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))) & (sK2 @ Y1)) => ((sK2 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y1 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4)))))))))))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) & (sK2 @ Y0))) => (sK2 @ Y0))) @ sK3))),
% 0.22/0.45 inference(sigma_clausification,[],[f27])).
% 0.22/0.45 thf(f27,plain,(
% 0.22/0.45 ($false = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))))) & (sK2 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))) & (sK2 @ Y1)) => ((sK2 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y1 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4)))))))))))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) & (sK2 @ Y0))) => (sK2 @ Y0)))))),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f26])).
% 0.22/0.45 thf(f61,plain,(
% 0.22/0.45 ($true = (((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) & (sK2 @ Y0)) => ((sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))) & (Y3 @ Y4))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3)))))))))))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK3)))) & (sK2 @ sK3))))),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f56])).
% 0.22/0.45 % SZS output end Proof for theBenchmark
% 0.22/0.45 % (16337)------------------------------
% 0.22/0.45 % (16337)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (16337)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (16337)Memory used [KB]: 6140
% 0.22/0.45 % (16337)Time elapsed: 0.043 s
% 0.22/0.45 % (16337)Instructions burned: 67 (million)
% 0.22/0.45 % (16337)------------------------------
% 0.22/0.45 % (16337)------------------------------
% 0.22/0.45 % (16325)Success in time 0.073 s
% 0.22/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------