TSTP Solution File: SEU637^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU637^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n009.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 03:50:11 EDT 2024
% Result : Theorem 0.21s 0.49s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU637^2 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 16:48:08 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36 % (6311)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)
% 0.13/0.36 % (6311)Instruction limit reached!
% 0.13/0.36 % (6311)------------------------------
% 0.13/0.36 % (6311)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (6311)Termination reason: Unknown
% 0.13/0.36 % (6311)Termination phase: Property scanning
% 0.13/0.36
% 0.13/0.36 % (6311)Memory used [KB]: 1023
% 0.13/0.36 % (6311)Time elapsed: 0.003 s
% 0.13/0.36 % (6311)Instructions burned: 4 (million)
% 0.13/0.36 % (6311)------------------------------
% 0.13/0.36 % (6311)------------------------------
% 0.13/0.37 % (6310)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.37 % (6312)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)
% 0.13/0.37 % (6314)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)
% 0.13/0.37 % (6313)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37 % (6315)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)
% 0.13/0.37 % (6313)Instruction limit reached!
% 0.13/0.37 % (6313)------------------------------
% 0.13/0.37 % (6313)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (6314)Instruction limit reached!
% 0.13/0.37 % (6314)------------------------------
% 0.13/0.37 % (6314)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (6313)Termination reason: Unknown
% 0.13/0.37 % (6313)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (6313)Memory used [KB]: 895
% 0.13/0.37 % (6313)Time elapsed: 0.003 s
% 0.13/0.37 % (6313)Instructions burned: 2 (million)
% 0.13/0.37 % (6313)------------------------------
% 0.13/0.37 % (6313)------------------------------
% 0.13/0.37 % (6314)Termination reason: Unknown
% 0.13/0.37 % (6314)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (6314)Memory used [KB]: 895
% 0.13/0.37 % (6314)Time elapsed: 0.003 s
% 0.13/0.37 % (6314)Instructions burned: 2 (million)
% 0.13/0.37 % (6314)------------------------------
% 0.13/0.37 % (6314)------------------------------
% 0.13/0.37 % (6320)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)
% 0.13/0.37 % (6318)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)
% 0.13/0.37 % (6318)Instruction limit reached!
% 0.13/0.37 % (6318)------------------------------
% 0.13/0.37 % (6318)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (6318)Termination reason: Unknown
% 0.13/0.37 % (6318)Termination phase: Preprocessing 3
% 0.13/0.37
% 0.13/0.37 % (6318)Memory used [KB]: 1023
% 0.13/0.37 % (6318)Time elapsed: 0.003 s
% 0.13/0.37 % (6318)Instructions burned: 3 (million)
% 0.13/0.37 % (6318)------------------------------
% 0.13/0.37 % (6318)------------------------------
% 0.13/0.37 % (6317)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.38 % (6321)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)
% 0.13/0.38 % (6322)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)
% 0.13/0.38 % (6320)Instruction limit reached!
% 0.13/0.38 % (6320)------------------------------
% 0.13/0.38 % (6320)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (6320)Termination reason: Unknown
% 0.13/0.38 % (6320)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (6320)Memory used [KB]: 5756
% 0.13/0.38 % (6320)Time elapsed: 0.014 s
% 0.13/0.38 % (6320)Instructions burned: 37 (million)
% 0.13/0.38 % (6320)------------------------------
% 0.13/0.38 % (6320)------------------------------
% 0.13/0.38 % (6312)Instruction limit reached!
% 0.13/0.38 % (6312)------------------------------
% 0.13/0.38 % (6312)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (6312)Termination reason: Unknown
% 0.13/0.38 % (6312)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (6312)Memory used [KB]: 5628
% 0.13/0.38 % (6312)Time elapsed: 0.020 s
% 0.13/0.38 % (6312)Instructions burned: 27 (million)
% 0.13/0.38 % (6312)------------------------------
% 0.13/0.38 % (6312)------------------------------
% 0.13/0.38 % (6322)Instruction limit reached!
% 0.13/0.38 % (6322)------------------------------
% 0.13/0.38 % (6322)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (6322)Termination reason: Unknown
% 0.13/0.38 % (6322)Termination phase: Preprocessing 3
% 0.13/0.38
% 0.13/0.38 % (6322)Memory used [KB]: 1023
% 0.13/0.39 % (6322)Time elapsed: 0.004 s
% 0.13/0.39 % (6322)Instructions burned: 3 (million)
% 0.13/0.39 % (6322)------------------------------
% 0.13/0.39 % (6322)------------------------------
% 0.13/0.39 % (6324)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)
% 0.13/0.39 % (6317)Instruction limit reached!
% 0.13/0.39 % (6317)------------------------------
% 0.13/0.39 % (6317)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (6317)Termination reason: Unknown
% 0.13/0.39 % (6317)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (6317)Memory used [KB]: 5628
% 0.13/0.39 % (6317)Time elapsed: 0.016 s
% 0.13/0.39 % (6317)Instructions burned: 19 (million)
% 0.13/0.39 % (6317)------------------------------
% 0.13/0.39 % (6317)------------------------------
% 0.13/0.39 % (6329)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.13/0.39 % (6321)Instruction limit reached!
% 0.13/0.39 % (6321)------------------------------
% 0.13/0.39 % (6321)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (6321)Termination reason: Unknown
% 0.13/0.39 % (6321)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (6321)Memory used [KB]: 5628
% 0.13/0.39 % (6321)Time elapsed: 0.013 s
% 0.13/0.39 % (6321)Instructions burned: 16 (million)
% 0.13/0.39 % (6321)------------------------------
% 0.13/0.39 % (6321)------------------------------
% 0.13/0.39 % (6329)Instruction limit reached!
% 0.13/0.39 % (6329)------------------------------
% 0.13/0.39 % (6329)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (6329)Termination reason: Unknown
% 0.13/0.39 % (6329)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (6329)Memory used [KB]: 1023
% 0.13/0.39 % (6329)Time elapsed: 0.004 s
% 0.13/0.40 % (6329)Instructions burned: 8 (million)
% 0.13/0.40 % (6329)------------------------------
% 0.13/0.40 % (6329)------------------------------
% 0.13/0.40 % (6331)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.13/0.40 % (6332)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)
% 0.13/0.40 % (6332)Instruction limit reached!
% 0.13/0.40 % (6332)------------------------------
% 0.13/0.40 % (6332)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.40 % (6332)Termination reason: Unknown
% 0.13/0.40 % (6332)Termination phase: Preprocessing 3
% 0.13/0.40
% 0.13/0.40 % (6332)Memory used [KB]: 1023
% 0.13/0.40 % (6332)Time elapsed: 0.004 s
% 0.13/0.40 % (6332)Instructions burned: 3 (million)
% 0.13/0.40 % (6332)------------------------------
% 0.13/0.40 % (6332)------------------------------
% 0.13/0.40 % (6334)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)
% 0.13/0.40 % (6337)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)
% 0.13/0.40 % (6337)Instruction limit reached!
% 0.13/0.40 % (6337)------------------------------
% 0.13/0.40 % (6337)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.40 % (6337)Termination reason: Unknown
% 0.13/0.40 % (6337)Termination phase: Preprocessing 3
% 0.13/0.40
% 0.13/0.40 % (6337)Memory used [KB]: 1023
% 0.13/0.40 % (6337)Time elapsed: 0.002 s
% 0.13/0.40 % (6337)Instructions burned: 3 (million)
% 0.13/0.40 % (6337)------------------------------
% 0.13/0.40 % (6337)------------------------------
% 0.13/0.40 % (6334)Instruction limit reached!
% 0.13/0.40 % (6334)------------------------------
% 0.13/0.40 % (6334)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.40 % (6334)Termination reason: Unknown
% 0.13/0.40 % (6334)Termination phase: Property scanning
% 0.13/0.40
% 0.13/0.40 % (6334)Memory used [KB]: 1023
% 0.13/0.40 % (6334)Time elapsed: 0.004 s
% 0.13/0.40 % (6334)Instructions burned: 4 (million)
% 0.13/0.40 % (6334)------------------------------
% 0.13/0.40 % (6334)------------------------------
% 0.13/0.41 % (6336)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)
% 0.13/0.41 % (6331)Instruction limit reached!
% 0.13/0.41 % (6331)------------------------------
% 0.13/0.41 % (6331)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.41 % (6331)Termination reason: Unknown
% 0.13/0.41 % (6331)Termination phase: Saturation
% 0.13/0.41
% 0.13/0.41 % (6331)Memory used [KB]: 5884
% 0.13/0.41 % (6331)Time elapsed: 0.013 s
% 0.13/0.41 % (6331)Instructions burned: 16 (million)
% 0.13/0.41 % (6331)------------------------------
% 0.13/0.41 % (6331)------------------------------
% 0.13/0.41 % (6336)Refutation not found, incomplete strategy
% 0.13/0.41 % (6336)------------------------------
% 0.13/0.41 % (6336)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.41 % (6336)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.41
% 0.13/0.41
% 0.13/0.41 % (6336)Memory used [KB]: 5500
% 0.13/0.41 % (6336)Time elapsed: 0.006 s
% 0.13/0.41 % (6336)Instructions burned: 6 (million)
% 0.13/0.41 % (6336)------------------------------
% 0.13/0.41 % (6336)------------------------------
% 0.13/0.41 % (6339)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)
% 0.13/0.42 % (6338)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.13/0.42 % (6339)Instruction limit reached!
% 0.13/0.42 % (6339)------------------------------
% 0.13/0.42 % (6339)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.42 % (6339)Termination reason: Unknown
% 0.13/0.42 % (6339)Termination phase: Saturation
% 0.13/0.42
% 0.13/0.42 % (6339)Memory used [KB]: 5756
% 0.13/0.42 % (6339)Time elapsed: 0.008 s
% 0.13/0.42 % (6339)Instructions burned: 19 (million)
% 0.13/0.42 % (6339)------------------------------
% 0.13/0.42 % (6339)------------------------------
% 0.13/0.42 % (6338)Instruction limit reached!
% 0.13/0.42 % (6338)------------------------------
% 0.13/0.42 % (6338)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.42 % (6338)Termination reason: Unknown
% 0.13/0.42 % (6338)Termination phase: Property scanning
% 0.13/0.42
% 0.13/0.42 % (6338)Memory used [KB]: 1023
% 0.13/0.42 % (6338)Time elapsed: 0.005 s
% 0.13/0.42 % (6340)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.13/0.42 % (6338)Instructions burned: 4 (million)
% 0.13/0.42 % (6338)------------------------------
% 0.13/0.42 % (6338)------------------------------
% 0.21/0.43 % (6342)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.21/0.43 % (6347)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.21/0.43 % (6341)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.44 % (6341)Instruction limit reached!
% 0.21/0.44 % (6341)------------------------------
% 0.21/0.44 % (6341)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (6341)Termination reason: Unknown
% 0.21/0.44 % (6341)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (6341)Memory used [KB]: 5500
% 0.21/0.44 % (6341)Time elapsed: 0.008 s
% 0.21/0.44 % (6341)Instructions burned: 7 (million)
% 0.21/0.44 % (6341)------------------------------
% 0.21/0.44 % (6341)------------------------------
% 0.21/0.44 % (6348)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.21/0.44 % (6347)Instruction limit reached!
% 0.21/0.44 % (6347)------------------------------
% 0.21/0.44 % (6347)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (6347)Termination reason: Unknown
% 0.21/0.44 % (6347)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (6347)Memory used [KB]: 5628
% 0.21/0.44 % (6347)Time elapsed: 0.014 s
% 0.21/0.44 % (6347)Instructions burned: 21 (million)
% 0.21/0.44 % (6347)------------------------------
% 0.21/0.44 % (6347)------------------------------
% 0.21/0.44 % (6348)Instruction limit reached!
% 0.21/0.44 % (6348)------------------------------
% 0.21/0.44 % (6348)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (6348)Termination reason: Unknown
% 0.21/0.44 % (6348)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (6348)Memory used [KB]: 5500
% 0.21/0.44 % (6348)Time elapsed: 0.005 s
% 0.21/0.44 % (6348)Instructions burned: 6 (million)
% 0.21/0.44 % (6348)------------------------------
% 0.21/0.44 % (6348)------------------------------
% 0.21/0.46 % (6349)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.46 % (6351)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.21/0.47 % (6349)Instruction limit reached!
% 0.21/0.47 % (6349)------------------------------
% 0.21/0.47 % (6349)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (6349)Termination reason: Unknown
% 0.21/0.47 % (6349)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (6349)Memory used [KB]: 1023
% 0.21/0.47 % (6349)Time elapsed: 0.007 s
% 0.21/0.47 % (6349)Instructions burned: 6 (million)
% 0.21/0.47 % (6349)------------------------------
% 0.21/0.47 % (6349)------------------------------
% 0.21/0.47 % (6350)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.21/0.48 % (6324)First to succeed.
% 0.21/0.49 % (6310)Instruction limit reached!
% 0.21/0.49 % (6310)------------------------------
% 0.21/0.49 % (6310)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49 % (6310)Termination reason: Unknown
% 0.21/0.49 % (6310)Termination phase: Saturation
% 0.21/0.49
% 0.21/0.49 % (6310)Memory used [KB]: 6396
% 0.21/0.49 % (6310)Time elapsed: 0.121 s
% 0.21/0.49 % (6310)Instructions burned: 183 (million)
% 0.21/0.49 % (6310)------------------------------
% 0.21/0.49 % (6310)------------------------------
% 0.21/0.49 % (6324)Refutation found. Thanks to Tanya!
% 0.21/0.49 % SZS status Theorem for theBenchmark
% 0.21/0.49 % SZS output start Proof for theBenchmark
% 0.21/0.49 thf(func_def_0, type, in: $i > $i > $o).
% 0.21/0.49 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.21/0.49 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 0.21/0.49 thf(func_def_11, type, singleton: $i > $o).
% 0.21/0.49 thf(func_def_26, type, ph1: !>[X0: $tType]:(X0)).
% 0.21/0.49 thf(func_def_27, type, sK2: $i > $o).
% 0.21/0.49 thf(f631,plain,(
% 0.21/0.49 $false),
% 0.21/0.49 inference(avatar_sat_refutation,[],[f331,f525,f628])).
% 0.21/0.49 thf(f628,plain,(
% 0.21/0.49 ~spl0_1),
% 0.21/0.49 inference(avatar_contradiction_clause,[],[f627])).
% 0.21/0.49 thf(f627,plain,(
% 0.21/0.49 $false | ~spl0_1),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f626])).
% 0.21/0.49 thf(f626,plain,(
% 0.21/0.49 ($true = $false) | ~spl0_1),
% 0.21/0.49 inference(backward_demodulation,[],[f144,f612])).
% 0.21/0.49 thf(f612,plain,(
% 0.21/0.49 ((in @ sK4 @ (dsetconstr @ sK3 @ sK2)) = $false) | ~spl0_1),
% 0.21/0.49 inference(backward_demodulation,[],[f540,f593])).
% 0.21/0.49 thf(f593,plain,(
% 0.21/0.49 (sK6 = sK4) | ~spl0_1),
% 0.21/0.49 inference(equality_proxy_clausification,[],[f571])).
% 0.21/0.49 thf(f571,plain,(
% 0.21/0.49 ((sK6 = sK4) = $true) | ~spl0_1),
% 0.21/0.49 inference(boolean_simplification,[],[f561])).
% 0.21/0.49 thf(f561,plain,(
% 0.21/0.49 ($true = ($true => (sK6 = sK4))) | ~spl0_1),
% 0.21/0.49 inference(superposition,[],[f99,f536])).
% 0.21/0.49 thf(f536,plain,(
% 0.21/0.49 ((in @ sK6 @ (setadjoin @ sK4 @ emptyset)) = $true) | ~spl0_1),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f534])).
% 0.21/0.49 thf(f534,plain,(
% 0.21/0.49 ($false = ((in @ sK6 @ (setadjoin @ sK4 @ emptyset)) => (in @ sK6 @ (dsetconstr @ sK3 @ sK2)))) | ~spl0_1),
% 0.21/0.49 inference(beta_eta_normalization,[],[f528])).
% 0.21/0.49 thf(f528,plain,(
% 0.21/0.49 (((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ sK2)))) @ sK6) = $false) | ~spl0_1),
% 0.21/0.49 inference(sigma_clausification,[],[f327])).
% 0.21/0.49 thf(f327,plain,(
% 0.21/0.49 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ sK2))))) = $false) | ~spl0_1),
% 0.21/0.49 inference(avatar_component_clause,[],[f326])).
% 0.21/0.49 thf(f326,plain,(
% 0.21/0.49 spl0_1 <=> ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ sK2))))) = $false)),
% 0.21/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.21/0.49 thf(f99,plain,(
% 0.21/0.49 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X2 @ (setadjoin @ X1 @ emptyset)) => (X2 = X1)))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f98])).
% 0.21/0.49 thf(f98,plain,(
% 0.21/0.49 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1))) @ X2))) )),
% 0.21/0.49 inference(pi_clausification,[],[f93])).
% 0.21/0.49 thf(f93,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1)))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f92])).
% 0.21/0.49 thf(f92,plain,(
% 0.21/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0))))) @ X1) = $true)) )),
% 0.21/0.49 inference(pi_clausification,[],[f89])).
% 0.21/0.49 thf(f89,plain,(
% 0.21/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) = $true)),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f56])).
% 0.21/0.49 thf(f56,plain,(
% 0.21/0.49 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f53])).
% 0.21/0.49 thf(f53,plain,(
% 0.21/0.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))) = $false)),
% 0.21/0.49 inference(boolean_simplification,[],[f52])).
% 0.21/0.49 thf(f52,plain,(
% 0.21/0.49 (($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))) = $false)),
% 0.21/0.49 inference(backward_demodulation,[],[f47,f51])).
% 0.21/0.49 thf(f51,plain,(
% 0.21/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (Y2 @ Y1)))))))) = $true)),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f47])).
% 0.21/0.49 thf(f47,plain,(
% 0.21/0.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))) = $false)),
% 0.21/0.49 inference(boolean_simplification,[],[f46])).
% 0.21/0.49 thf(f46,plain,(
% 0.21/0.49 ($false = ($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))),
% 0.21/0.49 inference(backward_demodulation,[],[f43,f45])).
% 0.21/0.49 thf(f45,plain,(
% 0.21/0.49 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))))),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f43])).
% 0.21/0.49 thf(f43,plain,(
% 0.21/0.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))) = $false)),
% 0.21/0.49 inference(boolean_simplification,[],[f42])).
% 0.21/0.49 thf(f42,plain,(
% 0.21/0.49 ($false = ($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))),
% 0.21/0.49 inference(backward_demodulation,[],[f37,f41])).
% 0.21/0.49 thf(f41,plain,(
% 0.21/0.49 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))))),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f37])).
% 0.21/0.49 thf(f37,plain,(
% 0.21/0.49 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))),
% 0.21/0.49 inference(not_proxy_clausification,[],[f36])).
% 0.21/0.49 thf(f36,plain,(
% 0.21/0.49 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))) = $true)),
% 0.21/0.49 inference(beta_eta_normalization,[],[f35])).
% 0.21/0.49 thf(f35,plain,(
% 0.21/0.49 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))))))))))))))))) = $true)),
% 0.21/0.49 inference(definition_unfolding,[],[f33,f29,f30,f34,f27,f32,f31,f28])).
% 0.21/0.49 thf(f28,plain,(
% 0.21/0.49 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f20])).
% 0.21/0.49 thf(f20,plain,(
% 0.21/0.49 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 0.21/0.49 inference(fool_elimination,[],[f19])).
% 0.21/0.49 thf(f19,plain,(
% 0.21/0.49 ((^[X0 : $i] : (? [X1] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 0.21/0.49 inference(rectify,[],[f7])).
% 0.21/0.49 thf(f7,axiom,(
% 0.21/0.49 ((^[X0 : $i] : (? [X2] : ((in @ X2 @ X0) & ((setadjoin @ X2 @ emptyset) = X0)))) = singleton)),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)).
% 0.21/0.49 thf(f31,plain,(
% 0.21/0.49 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f16])).
% 0.21/0.49 thf(f16,plain,(
% 0.21/0.49 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f15])).
% 0.21/0.49 thf(f15,plain,(
% 0.21/0.49 (eqinunit = ! [X0,X1] : ((X0 = X1) => (in @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 0.21/0.49 inference(rectify,[],[f6])).
% 0.21/0.49 thf(f6,axiom,(
% 0.21/0.49 (eqinunit = ! [X2,X3] : ((X2 = X3) => (in @ X2 @ (setadjoin @ X3 @ emptyset))))),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit)).
% 0.21/0.49 thf(f32,plain,(
% 0.21/0.49 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f18])).
% 0.21/0.49 thf(f18,plain,(
% 0.21/0.49 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 0.21/0.49 inference(fool_elimination,[],[f17])).
% 0.21/0.49 thf(f17,plain,(
% 0.21/0.49 (uniqinunit = ! [X0,X1] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 0.21/0.49 inference(rectify,[],[f5])).
% 0.21/0.49 thf(f5,axiom,(
% 0.21/0.49 (uniqinunit = ! [X2,X3] : ((in @ X2 @ (setadjoin @ X3 @ emptyset)) => (X2 = X3)))),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit)).
% 0.21/0.49 thf(f27,plain,(
% 0.21/0.49 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f26])).
% 0.21/0.49 thf(f26,plain,(
% 0.21/0.49 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f25])).
% 0.21/0.49 thf(f25,plain,(
% 0.21/0.49 (setext = ! [X0,X1] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X3] : ((in @ X3 @ X1) => (in @ X3 @ X0)) => (X0 = X1))))),
% 0.21/0.49 inference(rectify,[],[f4])).
% 0.21/0.49 thf(f4,axiom,(
% 0.21/0.49 (setext = ! [X0,X4] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X4)) => (! [X2] : ((in @ X2 @ X4) => (in @ X2 @ X0)) => (X0 = X4))))),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext)).
% 0.21/0.49 thf(f34,plain,(
% 0.21/0.49 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y1)))))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f14])).
% 0.21/0.49 thf(f14,plain,(
% 0.21/0.49 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y1)))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f13])).
% 0.21/0.49 thf(f13,plain,(
% 0.21/0.49 (dsetconstrER = ! [X0 : $i > $o,X1,X2] : ((in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X1)))),
% 0.21/0.49 inference(rectify,[],[f3])).
% 0.21/0.49 thf(f3,axiom,(
% 0.21/0.49 (dsetconstrER = ! [X1 : $i > $o,X2,X0] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)))),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER)).
% 0.21/0.49 thf(f30,plain,(
% 0.21/0.49 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y2 @ Y0)))))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f24])).
% 0.21/0.49 thf(f24,plain,(
% 0.21/0.49 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y2 @ Y0)))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f23])).
% 0.21/0.49 thf(f23,plain,(
% 0.21/0.49 (dsetconstrEL = ! [X0,X1 : $i > $o,X2] : ((in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X0 @ X2)))),
% 0.21/0.49 inference(rectify,[],[f2])).
% 0.21/0.49 thf(f2,axiom,(
% 0.21/0.49 (dsetconstrEL = ! [X2,X1 : $i > $o,X0] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)))),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL)).
% 0.21/0.49 thf(f29,plain,(
% 0.21/0.49 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f22])).
% 0.21/0.49 thf(f22,plain,(
% 0.21/0.49 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f21])).
% 0.21/0.49 thf(f21,plain,(
% 0.21/0.49 (! [X0 : $i > $o,X1,X2] : ((in @ X1 @ X2) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))))) = dsetconstrI)),
% 0.21/0.49 inference(rectify,[],[f1])).
% 0.21/0.49 thf(f1,axiom,(
% 0.21/0.49 (! [X1 : $i > $o,X2,X0] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))) = dsetconstrI)),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI)).
% 0.21/0.49 thf(f33,plain,(
% 0.21/0.49 ($true = (~ (dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (singleton @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))))))))))))))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f12])).
% 0.21/0.49 thf(f12,plain,(
% 0.21/0.49 ($true = (~ (dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (singleton @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))))))))))))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f11])).
% 0.21/0.49 thf(f11,plain,(
% 0.21/0.49 ~(dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => ! [X0,X1 : $i > $o] : (! [X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X4] : ((in @ X4 @ X0) & (X1 @ X4)) => (singleton @ (dsetconstr @ X0 @ (^[X5 : $i] : (X1 @ X5))))))))))))),
% 0.21/0.49 inference(rectify,[],[f9])).
% 0.21/0.49 thf(f9,negated_conjecture,(
% 0.21/0.49 ~(dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => ! [X0,X1 : $i > $o] : (! [X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X2] : ((in @ X2 @ X0) & (X1 @ X2)) => (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))))))))),
% 0.21/0.49 inference(negated_conjecture,[],[f8])).
% 0.21/0.49 thf(f8,conjecture,(
% 0.21/0.49 dsetconstrI => (dsetconstrEL => (dsetconstrER => (setext => (uniqinunit => (eqinunit => ! [X0,X1 : $i > $o] : (! [X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X2] : ((in @ X2 @ X0) & (X1 @ X2)) => (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2)))))))))))),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop)).
% 0.21/0.49 thf(f540,plain,(
% 0.21/0.49 ((in @ sK6 @ (dsetconstr @ sK3 @ sK2)) = $false) | ~spl0_1),
% 0.21/0.49 inference(boolean_simplification,[],[f539])).
% 0.21/0.49 thf(f539,plain,(
% 0.21/0.49 (($true => (in @ sK6 @ (dsetconstr @ sK3 @ sK2))) = $false) | ~spl0_1),
% 0.21/0.49 inference(backward_demodulation,[],[f534,f536])).
% 0.21/0.49 thf(f144,plain,(
% 0.21/0.49 ((in @ sK4 @ (dsetconstr @ sK3 @ sK2)) = $true)),
% 0.21/0.49 inference(boolean_simplification,[],[f141])).
% 0.21/0.49 thf(f141,plain,(
% 0.21/0.49 (($true => (in @ sK4 @ (dsetconstr @ sK3 @ sK2))) = $true)),
% 0.21/0.49 inference(superposition,[],[f136,f124])).
% 0.21/0.49 thf(f124,plain,(
% 0.21/0.49 ($true = (sK2 @ sK4))),
% 0.21/0.49 inference(boolean_simplification,[],[f123])).
% 0.21/0.49 thf(f123,plain,(
% 0.21/0.49 ($true = ((sK2 @ sK4) & $true))),
% 0.21/0.49 inference(backward_demodulation,[],[f118,f121])).
% 0.21/0.49 thf(f121,plain,(
% 0.21/0.49 ($true = (in @ sK4 @ sK3))),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f118])).
% 0.21/0.49 thf(f118,plain,(
% 0.21/0.49 ($true = ((sK2 @ sK4) & (in @ sK4 @ sK3)))),
% 0.21/0.49 inference(beta_eta_normalization,[],[f117])).
% 0.21/0.49 thf(f117,plain,(
% 0.21/0.49 ($true = ((^[Y0 : $i]: ((sK2 @ Y0) & (in @ Y0 @ sK3))) @ sK4))),
% 0.21/0.49 inference(sigma_clausification,[],[f114])).
% 0.21/0.49 thf(f114,plain,(
% 0.21/0.49 ($true = (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (in @ Y0 @ sK3)))))),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f110])).
% 0.21/0.49 thf(f110,plain,(
% 0.21/0.49 ($false = ((?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (in @ Y0 @ sK3)))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK3 @ sK2)) & (in @ Y0 @ (dsetconstr @ sK3 @ sK2)))))))),
% 0.21/0.49 inference(boolean_simplification,[],[f109])).
% 0.21/0.49 thf(f109,plain,(
% 0.21/0.49 ($false = ($true => ((?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (in @ Y0 @ sK3)))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK3 @ sK2)) & (in @ Y0 @ (dsetconstr @ sK3 @ sK2))))))))),
% 0.21/0.49 inference(backward_demodulation,[],[f104,f108])).
% 0.21/0.49 thf(f108,plain,(
% 0.21/0.49 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => ((sK2 @ Y0) => ((sK2 @ Y1) => (Y0 = Y1))))))))) = $true)),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f104])).
% 0.21/0.49 thf(f104,plain,(
% 0.21/0.49 ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => ((sK2 @ Y0) => ((sK2 @ Y1) => (Y0 = Y1))))))))) => ((?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (in @ Y0 @ sK3)))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK3 @ sK2)) & (in @ Y0 @ (dsetconstr @ sK3 @ sK2))))))))),
% 0.21/0.49 inference(beta_eta_normalization,[],[f103])).
% 0.21/0.49 thf(f103,plain,(
% 0.21/0.49 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((sK2 @ Y1) => ((sK2 @ Y2) => (Y1 = Y2))))))))) => ((?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) & (in @ Y1 @ Y0)))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ Y0 @ sK2)) & (in @ Y1 @ (dsetconstr @ Y0 @ sK2)))))))) @ sK3) = $false)),
% 0.21/0.49 inference(sigma_clausification,[],[f101])).
% 0.21/0.49 thf(f101,plain,(
% 0.21/0.49 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((sK2 @ Y1) => ((sK2 @ Y2) => (Y1 = Y2))))))))) => ((?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) & (in @ Y1 @ Y0)))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ Y0 @ sK2)) & (in @ Y1 @ (dsetconstr @ Y0 @ sK2))))))))) = $false)),
% 0.21/0.49 inference(beta_eta_normalization,[],[f100])).
% 0.21/0.49 thf(f100,plain,(
% 0.21/0.49 ($false = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) @ sK2))),
% 0.21/0.49 inference(sigma_clausification,[],[f97])).
% 0.21/0.49 thf(f97,plain,(
% 0.21/0.49 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))),
% 0.21/0.49 inference(boolean_simplification,[],[f96])).
% 0.21/0.49 thf(f96,plain,(
% 0.21/0.49 (($true => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))) = $false)),
% 0.21/0.49 inference(backward_demodulation,[],[f91,f95])).
% 0.21/0.49 thf(f95,plain,(
% 0.21/0.49 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f91])).
% 0.21/0.49 thf(f91,plain,(
% 0.21/0.49 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))) = $false)),
% 0.21/0.49 inference(boolean_simplification,[],[f90])).
% 0.21/0.49 thf(f90,plain,(
% 0.21/0.49 (($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))) = $false)),
% 0.21/0.49 inference(backward_demodulation,[],[f56,f89])).
% 0.21/0.49 thf(f136,plain,(
% 0.21/0.49 ( ! [X0 : $i > $o] : (($true = ((X0 @ sK4) => (in @ sK4 @ (dsetconstr @ sK3 @ X0))))) )),
% 0.21/0.49 inference(boolean_simplification,[],[f131])).
% 0.21/0.49 thf(f131,plain,(
% 0.21/0.49 ( ! [X0 : $i > $o] : (($true = ($true => ((X0 @ sK4) => (in @ sK4 @ (dsetconstr @ sK3 @ X0)))))) )),
% 0.21/0.49 inference(superposition,[],[f77,f121])).
% 0.21/0.49 thf(f77,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((in @ X2 @ X1) => ((X3 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ X3)))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f76])).
% 0.21/0.49 thf(f76,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ Y0))))) @ X3))) )),
% 0.21/0.49 inference(pi_clausification,[],[f75])).
% 0.21/0.49 thf(f75,plain,(
% 0.21/0.49 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ Y0)))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f74])).
% 0.21/0.49 thf(f74,plain,(
% 0.21/0.49 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ Y1))))))) @ X2))) )),
% 0.21/0.49 inference(pi_clausification,[],[f73])).
% 0.21/0.49 thf(f73,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ Y1)))))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f72])).
% 0.21/0.49 thf(f72,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2))))))))) @ X1))) )),
% 0.21/0.49 inference(pi_clausification,[],[f41])).
% 0.21/0.49 thf(f525,plain,(
% 0.21/0.49 ~spl0_2),
% 0.21/0.49 inference(avatar_contradiction_clause,[],[f524])).
% 0.21/0.49 thf(f524,plain,(
% 0.21/0.49 $false | ~spl0_2),
% 0.21/0.49 inference(subsumption_resolution,[],[f509,f447])).
% 0.21/0.49 thf(f447,plain,(
% 0.21/0.49 (sK5 != sK4) | ~spl0_2),
% 0.21/0.49 inference(equality_proxy_clausification,[],[f444])).
% 0.21/0.49 thf(f444,plain,(
% 0.21/0.49 ($false = (sK5 = sK4)) | ~spl0_2),
% 0.21/0.49 inference(not_proxy_clausification,[],[f443])).
% 0.21/0.49 thf(f443,plain,(
% 0.21/0.49 ($true = (~ (sK5 = sK4))) | ~spl0_2),
% 0.21/0.49 inference(boolean_simplification,[],[f431])).
% 0.21/0.49 thf(f431,plain,(
% 0.21/0.49 (((sK5 = sK4) => $false) = $true) | ~spl0_2),
% 0.21/0.49 inference(superposition,[],[f112,f424])).
% 0.21/0.49 thf(f424,plain,(
% 0.21/0.49 ($false = (in @ sK5 @ (setadjoin @ sK4 @ emptyset))) | ~spl0_2),
% 0.21/0.49 inference(boolean_simplification,[],[f423])).
% 0.21/0.49 thf(f423,plain,(
% 0.21/0.49 (($true => (in @ sK5 @ (setadjoin @ sK4 @ emptyset))) = $false) | ~spl0_2),
% 0.21/0.49 inference(backward_demodulation,[],[f414,f419])).
% 0.21/0.49 thf(f419,plain,(
% 0.21/0.49 ($true = (in @ sK5 @ (dsetconstr @ sK3 @ sK2))) | ~spl0_2),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f414])).
% 0.21/0.49 thf(f414,plain,(
% 0.21/0.49 (((in @ sK5 @ (dsetconstr @ sK3 @ sK2)) => (in @ sK5 @ (setadjoin @ sK4 @ emptyset))) = $false) | ~spl0_2),
% 0.21/0.49 inference(beta_eta_normalization,[],[f411])).
% 0.21/0.49 thf(f411,plain,(
% 0.21/0.49 (((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset)))) @ sK5) = $false) | ~spl0_2),
% 0.21/0.49 inference(sigma_clausification,[],[f353])).
% 0.21/0.49 thf(f353,plain,(
% 0.21/0.49 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset))))) = $false) | ~spl0_2),
% 0.21/0.49 inference(not_proxy_clausification,[],[f330])).
% 0.21/0.49 thf(f330,plain,(
% 0.21/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset)))))) = $true) | ~spl0_2),
% 0.21/0.49 inference(avatar_component_clause,[],[f329])).
% 0.21/0.49 thf(f329,plain,(
% 0.21/0.49 spl0_2 <=> ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset)))))) = $true)),
% 0.21/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.21/0.49 thf(f112,plain,(
% 0.21/0.49 ( ! [X2 : $i,X1 : $i] : ((((X2 = X1) => (in @ X2 @ (setadjoin @ X1 @ emptyset))) = $true)) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f111])).
% 0.21/0.49 thf(f111,plain,(
% 0.21/0.49 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((Y0 = X1) => (in @ Y0 @ (setadjoin @ X1 @ emptyset)))) @ X2))) )),
% 0.21/0.49 inference(pi_clausification,[],[f106])).
% 0.21/0.49 thf(f106,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((Y0 = X1) => (in @ Y0 @ (setadjoin @ X1 @ emptyset))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f105])).
% 0.21/0.49 thf(f105,plain,(
% 0.21/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))) @ X1) = $true)) )),
% 0.21/0.49 inference(pi_clausification,[],[f95])).
% 0.21/0.49 thf(f509,plain,(
% 0.21/0.49 (sK5 = sK4) | ~spl0_2),
% 0.21/0.49 inference(equality_proxy_clausification,[],[f489])).
% 0.21/0.49 thf(f489,plain,(
% 0.21/0.49 ($true = (sK4 = sK5)) | ~spl0_2),
% 0.21/0.49 inference(boolean_simplification,[],[f488])).
% 0.21/0.49 thf(f488,plain,(
% 0.21/0.49 ($true = ($true => (sK4 = sK5))) | ~spl0_2),
% 0.21/0.49 inference(backward_demodulation,[],[f429,f482])).
% 0.21/0.49 thf(f482,plain,(
% 0.21/0.49 ((in @ sK5 @ sK3) = $true) | ~spl0_2),
% 0.21/0.49 inference(boolean_simplification,[],[f472])).
% 0.21/0.49 thf(f472,plain,(
% 0.21/0.49 (($true => (in @ sK5 @ sK3)) = $true) | ~spl0_2),
% 0.21/0.49 inference(superposition,[],[f63,f419])).
% 0.21/0.49 thf(f63,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ (dsetconstr @ X1 @ X2)) => (in @ X3 @ X1)))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f62])).
% 0.21/0.49 thf(f62,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X1 @ X2)) => (in @ Y0 @ X1))) @ X3) = $true)) )),
% 0.21/0.49 inference(pi_clausification,[],[f55])).
% 0.21/0.49 thf(f55,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X1 @ X2)) => (in @ Y0 @ X1)))) = $true)) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f54])).
% 0.21/0.49 thf(f54,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X1 @ Y0)) => (in @ Y1 @ X1))))) @ X2))) )),
% 0.21/0.49 inference(pi_clausification,[],[f49])).
% 0.21/0.49 thf(f49,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X1 @ Y0)) => (in @ Y1 @ X1)))))) = $true)) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f48])).
% 0.21/0.49 thf(f48,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0))))))) @ X1))) )),
% 0.21/0.49 inference(pi_clausification,[],[f45])).
% 0.21/0.49 thf(f429,plain,(
% 0.21/0.49 (((in @ sK5 @ sK3) => (sK4 = sK5)) = $true) | ~spl0_2),
% 0.21/0.49 inference(boolean_simplification,[],[f425])).
% 0.21/0.49 thf(f425,plain,(
% 0.21/0.49 ($true = ((in @ sK5 @ sK3) => ($true => (sK4 = sK5)))) | ~spl0_2),
% 0.21/0.49 inference(superposition,[],[f221,f422])).
% 0.21/0.49 thf(f422,plain,(
% 0.21/0.49 ($true = (sK2 @ sK5)) | ~spl0_2),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f421])).
% 0.21/0.49 thf(f421,plain,(
% 0.21/0.49 ($true = $false) | ($true = (sK2 @ sK5)) | ~spl0_2),
% 0.21/0.49 inference(boolean_simplification,[],[f420])).
% 0.21/0.49 thf(f420,plain,(
% 0.21/0.49 ($true = (sK2 @ sK5)) | ($false = ($false => (in @ sK5 @ (setadjoin @ sK4 @ emptyset)))) | ~spl0_2),
% 0.21/0.49 inference(superposition,[],[f414,f71])).
% 0.21/0.49 thf(f71,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($false = (in @ X2 @ (dsetconstr @ X1 @ X3))) | ((X3 @ X2) = $true)) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f70])).
% 0.21/0.49 thf(f70,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((in @ X2 @ (dsetconstr @ X1 @ X3)) => (X3 @ X2)))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f69])).
% 0.21/0.49 thf(f69,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((in @ X2 @ (dsetconstr @ X1 @ Y0)) => (Y0 @ X2))) @ X3))) )),
% 0.21/0.49 inference(pi_clausification,[],[f68])).
% 0.21/0.49 thf(f68,plain,(
% 0.21/0.49 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X2 @ (dsetconstr @ X1 @ Y0)) => (Y0 @ X2)))) = $true)) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f67])).
% 0.21/0.49 thf(f67,plain,(
% 0.21/0.49 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ (dsetconstr @ X1 @ Y1)) => (Y1 @ Y0))))) @ X2))) )),
% 0.21/0.49 inference(pi_clausification,[],[f66])).
% 0.21/0.49 thf(f66,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ (dsetconstr @ X1 @ Y1)) => (Y1 @ Y0)))))) = $true)) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f65])).
% 0.21/0.49 thf(f65,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (Y2 @ Y1))))))) @ X1))) )),
% 0.21/0.49 inference(pi_clausification,[],[f51])).
% 0.21/0.49 thf(f221,plain,(
% 0.21/0.49 ( ! [X1 : $i] : ((((in @ X1 @ sK3) => ((sK2 @ X1) => (sK4 = X1))) = $true)) )),
% 0.21/0.49 inference(boolean_simplification,[],[f220])).
% 0.21/0.49 thf(f220,plain,(
% 0.21/0.49 ( ! [X1 : $i] : ((((in @ X1 @ sK3) => ($true => ((sK2 @ X1) => (sK4 = X1)))) = $true)) )),
% 0.21/0.49 inference(forward_demodulation,[],[f218,f124])).
% 0.21/0.49 thf(f218,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK3) => ((sK2 @ sK4) => ((sK2 @ X1) => (sK4 = X1)))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f216])).
% 0.21/0.49 thf(f216,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK3) => ((sK2 @ sK4) => ((sK2 @ Y0) => (sK4 = Y0))))) @ X1))) )),
% 0.21/0.49 inference(pi_clausification,[],[f185])).
% 0.21/0.49 thf(f185,plain,(
% 0.21/0.49 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((sK2 @ sK4) => ((sK2 @ Y0) => (sK4 = Y0)))))))),
% 0.21/0.49 inference(boolean_simplification,[],[f184])).
% 0.21/0.49 thf(f184,plain,(
% 0.21/0.49 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((sK2 @ sK4) => ((sK2 @ Y0) => (sK4 = Y0))))))))),
% 0.21/0.49 inference(superposition,[],[f168,f121])).
% 0.21/0.49 thf(f168,plain,(
% 0.21/0.49 ( ! [X1 : $i] : ((((in @ X1 @ sK3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((sK2 @ X1) => ((sK2 @ Y0) => (X1 = Y0))))))) = $true)) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f167])).
% 0.21/0.49 thf(f167,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => ((sK2 @ Y0) => ((sK2 @ Y1) => (Y0 = Y1)))))))) @ X1))) )),
% 0.21/0.49 inference(pi_clausification,[],[f108])).
% 0.21/0.49 thf(f331,plain,(
% 0.21/0.49 spl0_1 | spl0_2),
% 0.21/0.49 inference(avatar_split_clause,[],[f324,f329,f326])).
% 0.21/0.49 thf(f324,plain,(
% 0.21/0.49 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ sK2))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset)))))) = $true)),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f180])).
% 0.21/0.49 thf(f180,plain,(
% 0.21/0.49 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ sK2))))) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset))))))))),
% 0.21/0.49 inference(boolean_simplification,[],[f173])).
% 0.21/0.49 thf(f173,plain,(
% 0.21/0.49 ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK4 @ emptyset)) => (in @ Y0 @ (dsetconstr @ sK3 @ sK2))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK3 @ sK2)) => (in @ Y0 @ (setadjoin @ sK4 @ emptyset))))) => $false)))),
% 0.21/0.49 inference(superposition,[],[f82,f159])).
% 0.21/0.49 thf(f159,plain,(
% 0.21/0.49 ($false = ((setadjoin @ sK4 @ emptyset) = (dsetconstr @ sK3 @ sK2)))),
% 0.21/0.49 inference(boolean_simplification,[],[f149])).
% 0.21/0.49 thf(f149,plain,(
% 0.21/0.49 ($false = (((setadjoin @ sK4 @ emptyset) = (dsetconstr @ sK3 @ sK2)) & $true))),
% 0.21/0.49 inference(superposition,[],[f120,f144])).
% 0.21/0.49 thf(f120,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (((((setadjoin @ X1 @ emptyset) = (dsetconstr @ sK3 @ sK2)) & (in @ X1 @ (dsetconstr @ sK3 @ sK2))) = $false)) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f119])).
% 0.21/0.49 thf(f119,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK3 @ sK2)) & (in @ Y0 @ (dsetconstr @ sK3 @ sK2)))) @ X1))) )),
% 0.21/0.49 inference(pi_clausification,[],[f116])).
% 0.21/0.49 thf(f116,plain,(
% 0.21/0.49 ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK3 @ sK2)) & (in @ Y0 @ (dsetconstr @ sK3 @ sK2))))) = $false)),
% 0.21/0.49 inference(boolean_simplification,[],[f115])).
% 0.21/0.49 thf(f115,plain,(
% 0.21/0.49 ($false = ($true => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK3 @ sK2)) & (in @ Y0 @ (dsetconstr @ sK3 @ sK2)))))))),
% 0.21/0.49 inference(backward_demodulation,[],[f110,f114])).
% 0.21/0.49 thf(f82,plain,(
% 0.21/0.49 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (X2 = X1))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f81])).
% 0.21/0.49 thf(f81,plain,(
% 0.21/0.49 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1)))) @ X2))) )),
% 0.21/0.49 inference(pi_clausification,[],[f80])).
% 0.21/0.49 thf(f80,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1))))) = $true)) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f79])).
% 0.21/0.49 thf(f79,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) @ X1))) )),
% 0.21/0.49 inference(pi_clausification,[],[f57])).
% 0.21/0.49 thf(f57,plain,(
% 0.21/0.49 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f53])).
% 0.21/0.49 % SZS output end Proof for theBenchmark
% 0.21/0.49 % (6324)------------------------------
% 0.21/0.49 % (6324)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49 % (6324)Termination reason: Refutation
% 0.21/0.49
% 0.21/0.49 % (6324)Memory used [KB]: 6268
% 0.21/0.49 % (6324)Time elapsed: 0.101 s
% 0.21/0.49 % (6324)Instructions burned: 128 (million)
% 0.21/0.49 % (6324)------------------------------
% 0.21/0.49 % (6324)------------------------------
% 0.21/0.49 % (6306)Success in time 0.122 s
% 0.21/0.49 % Vampire---4.8 exiting
%------------------------------------------------------------------------------