TSTP Solution File: SEU696^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU696^2 : 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 : n019.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 03:50:49 EDT 2024
% Result : Theorem 0.21s 0.45s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU696^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14 % 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
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 15:40:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37 % (17106)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)
% 0.14/0.37 % (17104)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (17105)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)
% 0.14/0.37 % (17107)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (17108)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)
% 0.14/0.37 % (17110)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (17107)Instruction limit reached!
% 0.14/0.37 % (17107)------------------------------
% 0.14/0.37 % (17107)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (17107)Termination reason: Unknown
% 0.14/0.38 % (17107)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (17108)Instruction limit reached!
% 0.14/0.38 % (17108)------------------------------
% 0.14/0.38 % (17108)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (17108)Termination reason: Unknown
% 0.14/0.38 % (17108)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (17108)Memory used [KB]: 1023
% 0.14/0.38 % (17108)Time elapsed: 0.003 s
% 0.14/0.38 % (17108)Instructions burned: 2 (million)
% 0.14/0.38 % (17108)------------------------------
% 0.14/0.38 % (17108)------------------------------
% 0.14/0.38 % (17107)Memory used [KB]: 1023
% 0.14/0.38 % (17107)Time elapsed: 0.003 s
% 0.14/0.38 % (17107)Instructions burned: 2 (million)
% 0.14/0.38 % (17107)------------------------------
% 0.14/0.38 % (17107)------------------------------
% 0.14/0.38 % (17105)Instruction limit reached!
% 0.14/0.38 % (17105)------------------------------
% 0.14/0.38 % (17105)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (17105)Termination reason: Unknown
% 0.14/0.38 % (17105)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (17105)Memory used [KB]: 1023
% 0.14/0.38 % (17105)Time elapsed: 0.004 s
% 0.14/0.38 % (17105)Instructions burned: 4 (million)
% 0.14/0.38 % (17105)------------------------------
% 0.14/0.38 % (17105)------------------------------
% 0.14/0.38 % (17109)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)
% 0.14/0.39 % (17110)Instruction limit reached!
% 0.14/0.39 % (17110)------------------------------
% 0.14/0.39 % (17110)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (17110)Termination reason: Unknown
% 0.14/0.39 % (17110)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (17110)Memory used [KB]: 5628
% 0.14/0.39 % (17110)Time elapsed: 0.013 s
% 0.14/0.39 % (17110)Instructions burned: 18 (million)
% 0.14/0.39 % (17110)------------------------------
% 0.14/0.39 % (17110)------------------------------
% 0.14/0.39 % (17111)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)
% 0.14/0.39 % (17111)Instruction limit reached!
% 0.14/0.39 % (17111)------------------------------
% 0.14/0.39 % (17111)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (17111)Termination reason: Unknown
% 0.14/0.39 % (17111)Termination phase: Property scanning
% 0.14/0.39
% 0.14/0.39 % (17111)Memory used [KB]: 1023
% 0.14/0.39 % (17111)Time elapsed: 0.003 s
% 0.14/0.39 % (17111)Instructions burned: 3 (million)
% 0.14/0.39 % (17111)------------------------------
% 0.14/0.39 % (17111)------------------------------
% 0.14/0.39 % (17113)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.39 % (17112)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.39 % (17106)Instruction limit reached!
% 0.21/0.39 % (17106)------------------------------
% 0.21/0.39 % (17106)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (17106)Termination reason: Unknown
% 0.21/0.39 % (17106)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (17106)Memory used [KB]: 5628
% 0.21/0.39 % (17106)Time elapsed: 0.018 s
% 0.21/0.39 % (17106)Instructions burned: 27 (million)
% 0.21/0.39 % (17106)------------------------------
% 0.21/0.39 % (17106)------------------------------
% 0.21/0.39 % (17114)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.39 % (17114)Instruction limit reached!
% 0.21/0.39 % (17114)------------------------------
% 0.21/0.39 % (17114)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (17114)Termination reason: Unknown
% 0.21/0.39 % (17114)Termination phase: Property scanning
% 0.21/0.39
% 0.21/0.39 % (17114)Memory used [KB]: 1023
% 0.21/0.39 % (17114)Time elapsed: 0.004 s
% 0.21/0.39 % (17114)Instructions burned: 4 (million)
% 0.21/0.39 % (17114)------------------------------
% 0.21/0.39 % (17114)------------------------------
% 0.21/0.40 % (17113)Instruction limit reached!
% 0.21/0.40 % (17113)------------------------------
% 0.21/0.40 % (17113)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (17113)Termination reason: Unknown
% 0.21/0.40 % (17113)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (17113)Memory used [KB]: 5756
% 0.21/0.40 % (17113)Time elapsed: 0.009 s
% 0.21/0.40 % (17113)Instructions burned: 15 (million)
% 0.21/0.40 % (17113)------------------------------
% 0.21/0.40 % (17113)------------------------------
% 0.21/0.40 % (17115)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.21/0.40 % (17116)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.40 % (17117)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.41 % (17116)Instruction limit reached!
% 0.21/0.41 % (17116)------------------------------
% 0.21/0.41 % (17116)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (17116)Termination reason: Unknown
% 0.21/0.41 % (17116)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (17116)Memory used [KB]: 1023
% 0.21/0.41 % (17116)Time elapsed: 0.006 s
% 0.21/0.41 % (17116)Instructions burned: 8 (million)
% 0.21/0.41 % (17116)------------------------------
% 0.21/0.41 % (17116)------------------------------
% 0.21/0.41 % (17118)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.41 % (17118)Instruction limit reached!
% 0.21/0.41 % (17118)------------------------------
% 0.21/0.41 % (17118)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (17118)Termination reason: Unknown
% 0.21/0.41 % (17118)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (17118)Memory used [KB]: 1023
% 0.21/0.41 % (17118)Time elapsed: 0.004 s
% 0.21/0.41 % (17118)Instructions burned: 4 (million)
% 0.21/0.41 % (17119)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.41 % (17118)------------------------------
% 0.21/0.41 % (17118)------------------------------
% 0.21/0.41 % (17119)Instruction limit reached!
% 0.21/0.41 % (17119)------------------------------
% 0.21/0.41 % (17119)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (17119)Termination reason: Unknown
% 0.21/0.41 % (17119)Termination phase: shuffling
% 0.21/0.41
% 0.21/0.41 % (17119)Memory used [KB]: 1023
% 0.21/0.41 % (17119)Time elapsed: 0.003 s
% 0.21/0.41 % (17119)Instructions burned: 3 (million)
% 0.21/0.41 % (17119)------------------------------
% 0.21/0.41 % (17119)------------------------------
% 0.21/0.41 % (17112)Instruction limit reached!
% 0.21/0.41 % (17112)------------------------------
% 0.21/0.41 % (17112)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (17112)Termination reason: Unknown
% 0.21/0.41 % (17112)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (17112)Memory used [KB]: 5756
% 0.21/0.41 % (17112)Time elapsed: 0.023 s
% 0.21/0.41 % (17112)Instructions burned: 38 (million)
% 0.21/0.41 % (17112)------------------------------
% 0.21/0.41 % (17112)------------------------------
% 0.21/0.41 % (17117)Instruction limit reached!
% 0.21/0.41 % (17117)------------------------------
% 0.21/0.41 % (17117)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (17117)Termination reason: Unknown
% 0.21/0.41 % (17117)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (17117)Memory used [KB]: 6012
% 0.21/0.41 % (17117)Time elapsed: 0.012 s
% 0.21/0.41 % (17117)Instructions burned: 16 (million)
% 0.21/0.41 % (17117)------------------------------
% 0.21/0.41 % (17117)------------------------------
% 0.21/0.42 % (17120)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.42 % (17122)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.42 % (17121)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.42 % (17121)Instruction limit reached!
% 0.21/0.42 % (17121)------------------------------
% 0.21/0.42 % (17121)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (17121)Termination reason: Unknown
% 0.21/0.42 % (17121)Termination phase: Property scanning
% 0.21/0.42 % (17120)Refutation not found, incomplete strategy
% 0.21/0.42 % (17120)------------------------------
% 0.21/0.42 % (17120)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42
% 0.21/0.42 % (17121)Memory used [KB]: 1023
% 0.21/0.42 % (17121)Time elapsed: 0.003 s
% 0.21/0.42 % (17121)Instructions burned: 3 (million)
% 0.21/0.42 % (17121)------------------------------
% 0.21/0.42 % (17121)------------------------------
% 0.21/0.42 % (17120)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.42
% 0.21/0.42
% 0.21/0.42 % (17120)Memory used [KB]: 5500
% 0.21/0.42 % (17120)Time elapsed: 0.005 s
% 0.21/0.42 % (17120)Instructions burned: 6 (million)
% 0.21/0.42 % (17122)Instruction limit reached!
% 0.21/0.42 % (17122)------------------------------
% 0.21/0.42 % (17122)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (17122)Termination reason: Unknown
% 0.21/0.42 % (17122)Termination phase: Property scanning
% 0.21/0.42
% 0.21/0.42 % (17122)Memory used [KB]: 1023
% 0.21/0.42 % (17122)Time elapsed: 0.003 s
% 0.21/0.42 % (17122)Instructions burned: 4 (million)
% 0.21/0.42 % (17122)------------------------------
% 0.21/0.42 % (17122)------------------------------
% 0.21/0.42 % (17120)------------------------------
% 0.21/0.42 % (17120)------------------------------
% 0.21/0.43 % (17123)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.43 % (17124)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.44 % (17123)Instruction limit reached!
% 0.21/0.44 % (17123)------------------------------
% 0.21/0.44 % (17123)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (17123)Termination reason: Unknown
% 0.21/0.44 % (17123)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (17123)Memory used [KB]: 5628
% 0.21/0.44 % (17123)Time elapsed: 0.012 s
% 0.21/0.44 % (17123)Instructions burned: 18 (million)
% 0.21/0.44 % (17123)------------------------------
% 0.21/0.44 % (17123)------------------------------
% 0.21/0.44 % (17126)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)
% 0.21/0.44 % (17125)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.44 % (17127)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)
% 0.21/0.44 % (17126)Refutation not found, incomplete strategy
% 0.21/0.44 % (17126)------------------------------
% 0.21/0.44 % (17126)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (17126)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.44
% 0.21/0.44
% 0.21/0.44 % (17126)Memory used [KB]: 5500
% 0.21/0.44 % (17126)Time elapsed: 0.005 s
% 0.21/0.44 % (17126)Instructions burned: 7 (million)
% 0.21/0.44 % (17126)------------------------------
% 0.21/0.44 % (17126)------------------------------
% 0.21/0.44 % (17125)Instruction limit reached!
% 0.21/0.44 % (17125)------------------------------
% 0.21/0.44 % (17125)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (17125)Termination reason: Unknown
% 0.21/0.44 % (17125)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (17125)Memory used [KB]: 5500
% 0.21/0.44 % (17125)Time elapsed: 0.005 s
% 0.21/0.44 % (17125)Instructions burned: 6 (million)
% 0.21/0.44 % (17125)------------------------------
% 0.21/0.44 % (17125)------------------------------
% 0.21/0.45 % (17115)First to succeed.
% 0.21/0.45 % (17128)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.21/0.45 % (17128)Instruction limit reached!
% 0.21/0.45 % (17128)------------------------------
% 0.21/0.45 % (17128)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (17128)Termination reason: Unknown
% 0.21/0.45 % (17128)Termination phase: Property scanning
% 0.21/0.45
% 0.21/0.45 % (17128)Memory used [KB]: 1023
% 0.21/0.45 % (17128)Time elapsed: 0.004 s
% 0.21/0.45 % (17128)Instructions burned: 5 (million)
% 0.21/0.45 % (17128)------------------------------
% 0.21/0.45 % (17128)------------------------------
% 0.21/0.45 % (17115)Refutation found. Thanks to Tanya!
% 0.21/0.45 % SZS status Theorem for theBenchmark
% 0.21/0.45 % SZS output start Proof for theBenchmark
% 0.21/0.45 thf(func_def_0, type, in: $i > $i > $o).
% 0.21/0.45 thf(func_def_1, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.21/0.45 thf(func_def_2, type, func: $i > $i > $i > $o).
% 0.21/0.45 thf(func_def_3, type, ap: $i > $i > $i > $i > $i).
% 0.21/0.45 thf(func_def_6, type, lam: $i > $i > ($i > $i) > $i).
% 0.21/0.45 thf(func_def_24, type, ph1: !>[X0: $tType]:(X0)).
% 0.21/0.45 thf(f197,plain,(
% 0.21/0.45 $false),
% 0.21/0.45 inference(subsumption_resolution,[],[f193,f90])).
% 0.21/0.45 thf(f90,plain,(
% 0.21/0.45 (sK3 != (dpsetconstr @ sK4 @ sK2 @ (^[Y0 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y0)))))),
% 0.21/0.45 inference(equality_proxy_clausification,[],[f85])).
% 0.21/0.45 thf(f85,plain,(
% 0.21/0.45 ($false = (sK3 = (dpsetconstr @ sK4 @ sK2 @ (^[Y0 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y0))))))),
% 0.21/0.45 inference(boolean_simplification,[],[f84])).
% 0.21/0.45 thf(f84,plain,(
% 0.21/0.45 ($false = ($true => (sK3 = (dpsetconstr @ sK4 @ sK2 @ (^[Y0 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y0)))))))),
% 0.21/0.45 inference(backward_demodulation,[],[f81,f83])).
% 0.21/0.45 thf(f83,plain,(
% 0.21/0.45 ($true = (func @ sK4 @ sK2 @ sK3))),
% 0.21/0.45 inference(binary_proxy_clausification,[],[f81])).
% 0.21/0.45 thf(f81,plain,(
% 0.21/0.45 ($false = ((func @ sK4 @ sK2 @ sK3) => (sK3 = (dpsetconstr @ sK4 @ sK2 @ (^[Y0 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y0)))))))),
% 0.21/0.45 inference(beta_eta_normalization,[],[f80])).
% 0.21/0.45 thf(f80,plain,(
% 0.21/0.45 ($false = ((^[Y0 : $i]: ((func @ Y0 @ sK2 @ sK3) => (sK3 = (dpsetconstr @ Y0 @ sK2 @ (^[Y1 : $i]: (= @ (ap @ Y0 @ sK2 @ sK3 @ Y1))))))) @ sK4))),
% 0.21/0.45 inference(sigma_clausification,[],[f79])).
% 0.21/0.45 thf(f79,plain,(
% 0.21/0.45 ($false = (!! @ $i @ (^[Y0 : $i]: ((func @ Y0 @ sK2 @ sK3) => (sK3 = (dpsetconstr @ Y0 @ sK2 @ (^[Y1 : $i]: (= @ (ap @ Y0 @ sK2 @ sK3 @ Y1)))))))))),
% 0.21/0.45 inference(beta_eta_normalization,[],[f78])).
% 0.21/0.45 thf(f78,plain,(
% 0.21/0.45 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((func @ Y1 @ sK2 @ Y0) => (Y0 = (dpsetconstr @ Y1 @ sK2 @ (^[Y2 : $i]: (= @ (ap @ Y1 @ sK2 @ Y0 @ Y2))))))))) @ sK3) = $false)),
% 0.21/0.45 inference(sigma_clausification,[],[f77])).
% 0.21/0.45 thf(f77,plain,(
% 0.21/0.45 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((func @ Y1 @ sK2 @ Y0) => (Y0 = (dpsetconstr @ Y1 @ sK2 @ (^[Y2 : $i]: (= @ (ap @ Y1 @ sK2 @ Y0 @ Y2)))))))))))),
% 0.21/0.45 inference(beta_eta_normalization,[],[f76])).
% 0.21/0.45 thf(f76,plain,(
% 0.21/0.45 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (Y1 = (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: (= @ (ap @ Y2 @ Y0 @ Y1 @ Y3))))))))))) @ sK2))),
% 0.21/0.45 inference(sigma_clausification,[],[f75])).
% 0.21/0.45 thf(f75,plain,(
% 0.21/0.45 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (Y1 = (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: (= @ (ap @ Y2 @ Y0 @ Y1 @ Y3)))))))))))))),
% 0.21/0.45 inference(boolean_simplification,[],[f74])).
% 0.21/0.45 thf(f74,plain,(
% 0.21/0.45 ($false = ($true => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (Y1 = (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: (= @ (ap @ Y2 @ Y0 @ Y1 @ Y3))))))))))))))),
% 0.21/0.45 inference(backward_demodulation,[],[f59,f73])).
% 0.21/0.45 thf(f73,plain,(
% 0.21/0.45 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y4 : $i]: (= @ (Y2 @ Y4)))) @ Y3)))))))))))))),
% 0.21/0.45 inference(binary_proxy_clausification,[],[f59])).
% 0.21/0.45 thf(f59,plain,(
% 0.21/0.45 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y4 : $i]: (= @ (Y2 @ Y4)))) @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (Y1 = (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: (= @ (ap @ Y2 @ Y0 @ Y1 @ Y3))))))))))))))),
% 0.21/0.45 inference(binary_proxy_clausification,[],[f46])).
% 0.21/0.45 thf(f46,plain,(
% 0.21/0.45 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y3 @ Y4) = (ap @ Y1 @ Y2 @ Y0 @ Y4))))) => (Y0 = Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y4 : $i]: (= @ (Y2 @ Y4)))) @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (Y1 = (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: (= @ (ap @ Y2 @ Y0 @ Y1 @ Y3)))))))))))))))),
% 0.21/0.45 inference(binary_proxy_clausification,[],[f33])).
% 0.21/0.45 thf(f33,plain,(
% 0.21/0.45 ($false = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y0 @ Y3) @ Y1)))) => (func @ Y2 @ Y1 @ (dpsetconstr @ Y2 @ Y1 @ (^[Y3 : $i]: (= @ (Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y3 @ Y4) = (ap @ Y1 @ Y2 @ Y0 @ Y4))))) => (Y0 = Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y4 : $i]: (= @ (Y2 @ Y4)))) @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (Y1 = (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: (= @ (ap @ Y2 @ Y0 @ Y1 @ Y3))))))))))))))))),
% 0.21/0.45 inference(binary_proxy_clausification,[],[f30])).
% 0.21/0.45 thf(f30,plain,(
% 0.21/0.45 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y1 @ Y2 @ Y3) @ Y1))))))))))) => ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y0 @ Y3) @ Y1)))) => (func @ Y2 @ Y1 @ (dpsetconstr @ Y2 @ Y1 @ (^[Y3 : $i]: (= @ (Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y3 @ Y4) = (ap @ Y1 @ Y2 @ Y0 @ Y4))))) => (Y0 = Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y4 : $i]: (= @ (Y2 @ Y4)))) @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (Y1 = (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: (= @ (ap @ Y2 @ Y0 @ Y1 @ Y3)))))))))))))))))),
% 0.21/0.45 inference(not_proxy_clausification,[],[f29])).
% 0.21/0.45 thf(f29,plain,(
% 0.21/0.45 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y1 @ Y2 @ Y3) @ Y1))))))))))) => ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y0 @ Y3) @ Y1)))) => (func @ Y2 @ Y1 @ (dpsetconstr @ Y2 @ Y1 @ (^[Y3 : $i]: (= @ (Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y3 @ Y4) = (ap @ Y1 @ Y2 @ Y0 @ Y4))))) => (Y0 = Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y4 : $i]: (= @ (Y2 @ Y4)))) @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (Y1 = (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: (= @ (ap @ Y2 @ Y0 @ Y1 @ Y3))))))))))))))))) = $true)),
% 0.21/0.45 inference(beta_eta_normalization,[],[f28])).
% 0.21/0.45 thf(f28,plain,(
% 0.21/0.45 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y1 @ Y2 @ Y3) @ Y1))))))))))) => ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y0 @ Y3) @ Y1)))) => (func @ Y2 @ Y1 @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (dpsetconstr @ Y3 @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6) = Y7)))))))))) @ Y2 @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y3 @ Y4) = (ap @ Y1 @ Y2 @ Y0 @ Y4))))) => (Y0 = Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i > $i]: (dpsetconstr @ Y4 @ Y5 @ (^[Y7 : $i]: ((^[Y8 : $i]: ((Y6 @ Y7) = Y8)))))))))) @ Y0 @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) @ Y3)))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (Y1 = ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (dpsetconstr @ Y3 @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6) = Y7)))))))))) @ Y2 @ Y0 @ (^[Y3 : $i]: (ap @ Y2 @ Y0 @ Y1 @ Y3)))))))))))))))))),
% 0.21/0.45 inference(definition_unfolding,[],[f20,f23,f26,f22,f27,f25])).
% 0.21/0.45 thf(f25,plain,(
% 0.21/0.45 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))),
% 0.21/0.45 inference(cnf_transformation,[],[f11])).
% 0.21/0.45 thf(f11,plain,(
% 0.21/0.45 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))),
% 0.21/0.45 inference(fool_elimination,[],[f2])).
% 0.21/0.45 thf(f2,axiom,(
% 0.21/0.45 ((^[X0 : $i, X1 : $i, X2 : $i > $i] : (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : (((X2 @ X3) = X4))))) = lam)),
% 0.21/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam)).
% 0.21/0.45 thf(f27,plain,(
% 0.21/0.45 (beta1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i > $i]: (dpsetconstr @ Y4 @ Y5 @ (^[Y7 : $i]: ((^[Y8 : $i]: ((Y6 @ Y7) = Y8)))))))))) @ Y0 @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) @ Y3)))))))))))))),
% 0.21/0.45 inference(definition_unfolding,[],[f24,f25])).
% 0.21/0.45 thf(f24,plain,(
% 0.21/0.45 (beta1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) @ Y3)))))))))))))),
% 0.21/0.45 inference(cnf_transformation,[],[f17])).
% 0.21/0.45 thf(f17,plain,(
% 0.21/0.45 (beta1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (lam @ Y0 @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) @ Y3)))))))))))))),
% 0.21/0.45 inference(fool_elimination,[],[f16])).
% 0.21/0.45 thf(f16,plain,(
% 0.21/0.45 (! [X0 : $i > $i,X1,X2] : (! [X3] : ((in @ X3 @ X2) => (in @ (X0 @ X3) @ X1)) => ! [X4] : ((in @ X4 @ X2) => ((X0 @ X4) = (ap @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[X5 : $i] : (X0 @ X5))) @ X4)))) = beta1)),
% 0.21/0.45 inference(rectify,[],[f5])).
% 0.21/0.45 thf(f5,axiom,(
% 0.21/0.45 (! [X2 : $i > $i,X1,X0] : (! [X3] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X3] : ((in @ X3 @ X0) => ((X2 @ X3) = (ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : $i] : (X2 @ X4))) @ X3)))) = beta1)),
% 0.21/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta1)).
% 0.21/0.45 thf(f22,plain,(
% 0.21/0.45 (funcext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y3 @ Y4) = (ap @ Y1 @ Y2 @ Y0 @ Y4))))) => (Y0 = Y3)))))))))))))),
% 0.21/0.45 inference(cnf_transformation,[],[f15])).
% 0.21/0.45 thf(f15,plain,(
% 0.21/0.45 (funcext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y3 @ Y4) = (ap @ Y1 @ Y2 @ Y0 @ Y4))))) => (Y0 = Y3)))))))))))))),
% 0.21/0.45 inference(fool_elimination,[],[f14])).
% 0.21/0.45 thf(f14,plain,(
% 0.21/0.45 (! [X0,X1,X2] : ((func @ X1 @ X0 @ X2) => ! [X3] : ((func @ X1 @ X0 @ X3) => (! [X4] : ((in @ X4 @ X1) => ((ap @ X1 @ X0 @ X3 @ X4) = (ap @ X1 @ X0 @ X2 @ X4))) => (X2 = X3)))) = funcext)),
% 0.21/0.45 inference(rectify,[],[f4])).
% 0.21/0.45 thf(f4,axiom,(
% 0.21/0.45 (! [X1,X0,X2] : ((func @ X0 @ X1 @ X2) => ! [X5] : ((func @ X0 @ X1 @ X5) => (! [X3] : ((in @ X3 @ X0) => ((ap @ X0 @ X1 @ X2 @ X3) = (ap @ X0 @ X1 @ X5 @ X3))) => (X2 = X5)))) = funcext)),
% 0.21/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcext)).
% 0.21/0.45 thf(f26,plain,(
% 0.21/0.45 (lamp = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y0 @ Y3) @ Y1)))) => (func @ Y2 @ Y1 @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (dpsetconstr @ Y3 @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6) = Y7)))))))))) @ Y2 @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))),
% 0.21/0.45 inference(definition_unfolding,[],[f21,f25])).
% 0.21/0.45 thf(f21,plain,(
% 0.21/0.45 (lamp = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y0 @ Y3) @ Y1)))) => (func @ Y2 @ Y1 @ (lam @ Y2 @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))),
% 0.21/0.45 inference(cnf_transformation,[],[f10])).
% 0.21/0.45 thf(f10,plain,(
% 0.21/0.45 (lamp = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y0 @ Y3) @ Y1)))) => (func @ Y2 @ Y1 @ (lam @ Y2 @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))),
% 0.21/0.45 inference(fool_elimination,[],[f9])).
% 0.21/0.45 thf(f9,plain,(
% 0.21/0.45 (! [X0,X1,X2 : $i > $i] : (! [X3] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (func @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : $i] : (X2 @ X4))))) = lamp)),
% 0.21/0.45 inference(rectify,[],[f3])).
% 0.21/0.45 thf(f3,axiom,(
% 0.21/0.45 (! [X0,X1,X2 : $i > $i] : (! [X3] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (func @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X3 : $i] : (X2 @ X3))))) = lamp)),
% 0.21/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamp)).
% 0.21/0.45 thf(f23,plain,(
% 0.21/0.45 (app = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y1 @ Y2 @ Y3) @ Y1))))))))))))),
% 0.21/0.45 inference(cnf_transformation,[],[f13])).
% 0.21/0.45 thf(f13,plain,(
% 0.21/0.45 (app = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y1 @ Y2 @ Y3) @ Y1))))))))))))),
% 0.21/0.45 inference(fool_elimination,[],[f12])).
% 0.21/0.45 thf(f12,plain,(
% 0.21/0.45 (! [X0,X1,X2] : ((func @ X2 @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => (in @ (ap @ X2 @ X1 @ X0 @ X3) @ X1))) = app)),
% 0.21/0.45 inference(rectify,[],[f1])).
% 0.21/0.45 thf(f1,axiom,(
% 0.21/0.45 (! [X2,X1,X0] : ((func @ X0 @ X1 @ X2) => ! [X3] : ((in @ X3 @ X0) => (in @ (ap @ X0 @ X1 @ X2 @ X3) @ X1))) = app)),
% 0.21/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app)).
% 0.21/0.45 thf(f20,plain,(
% 0.21/0.45 ((~ (app => (lamp => (funcext => (beta1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (Y1 = (lam @ Y2 @ Y0 @ (^[Y3 : $i]: (ap @ Y2 @ Y0 @ Y1 @ Y3)))))))))))))))) = $true)),
% 0.21/0.45 inference(cnf_transformation,[],[f19])).
% 0.21/0.45 thf(f19,plain,(
% 0.21/0.45 ((~ (app => (lamp => (funcext => (beta1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (Y1 = (lam @ Y2 @ Y0 @ (^[Y3 : $i]: (ap @ Y2 @ Y0 @ Y1 @ Y3)))))))))))))))) = $true)),
% 0.21/0.45 inference(fool_elimination,[],[f18])).
% 0.21/0.45 thf(f18,plain,(
% 0.21/0.45 ~(app => (lamp => (funcext => (beta1 => ! [X0,X1,X2] : ((func @ X0 @ X2 @ X1) => (X1 = (lam @ X0 @ X2 @ (^[X3 : $i] : (ap @ X0 @ X2 @ X1 @ X3)))))))))),
% 0.21/0.45 inference(rectify,[],[f7])).
% 0.21/0.45 thf(f7,negated_conjecture,(
% 0.21/0.45 ~(app => (lamp => (funcext => (beta1 => ! [X0,X2,X1] : ((func @ X0 @ X1 @ X2) => (X2 = (lam @ X0 @ X1 @ (^[X3 : $i] : (ap @ X0 @ X1 @ X2 @ X3)))))))))),
% 0.21/0.45 inference(negated_conjecture,[],[f6])).
% 0.21/0.45 thf(f6,conjecture,(
% 0.21/0.45 app => (lamp => (funcext => (beta1 => ! [X0,X2,X1] : ((func @ X0 @ X1 @ X2) => (X2 = (lam @ X0 @ X1 @ (^[X3 : $i] : (ap @ X0 @ X1 @ X2 @ X3))))))))),
% 0.21/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eta1)).
% 0.21/0.45 thf(f193,plain,(
% 0.21/0.45 (sK3 = (dpsetconstr @ sK4 @ sK2 @ (^[Y0 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y0)))))),
% 0.21/0.45 inference(equality_proxy_clausification,[],[f190])).
% 0.21/0.45 thf(f190,plain,(
% 0.21/0.45 ($true = ((dpsetconstr @ sK4 @ sK2 @ (^[Y0 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y0)))) = sK3))),
% 0.21/0.45 inference(boolean_simplification,[],[f189])).
% 0.21/0.45 thf(f189,plain,(
% 0.21/0.45 (($true => ((dpsetconstr @ sK4 @ sK2 @ (^[Y0 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y0)))) = sK3)) = $true)),
% 0.21/0.45 inference(forward_demodulation,[],[f187,f83])).
% 0.21/0.45 thf(f187,plain,(
% 0.21/0.45 (((func @ sK4 @ sK2 @ sK3) => ((dpsetconstr @ sK4 @ sK2 @ (^[Y0 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y0)))) = sK3)) = $true)),
% 0.21/0.45 inference(boolean_simplification,[],[f179])).
% 0.21/0.45 thf(f179,plain,(
% 0.21/0.45 ($true = ((func @ sK4 @ sK2 @ sK3) => ($true => ((dpsetconstr @ sK4 @ sK2 @ (^[Y0 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y0)))) = sK3))))),
% 0.21/0.45 inference(superposition,[],[f175,f121])).
% 0.21/0.45 thf(f121,plain,(
% 0.21/0.45 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((ap @ sK4 @ sK2 @ sK3 @ Y0) = (ap @ sK4 @ sK2 @ (dpsetconstr @ sK4 @ sK2 @ (^[Y1 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y1)))) @ Y0))))))),
% 0.21/0.45 inference(boolean_simplification,[],[f118])).
% 0.21/0.45 thf(f118,plain,(
% 0.21/0.45 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((ap @ sK4 @ sK2 @ sK3 @ Y0) = (ap @ sK4 @ sK2 @ (dpsetconstr @ sK4 @ sK2 @ (^[Y1 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y1)))) @ Y0)))))) = $true)),
% 0.21/0.45 inference(superposition,[],[f115,f89])).
% 0.21/0.45 thf(f89,plain,(
% 0.21/0.45 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => (in @ (ap @ sK4 @ sK2 @ sK3 @ Y0) @ sK2)))))),
% 0.21/0.45 inference(boolean_simplification,[],[f87])).
% 0.21/0.45 thf(f87,plain,(
% 0.21/0.45 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => (in @ (ap @ sK4 @ sK2 @ sK3 @ Y0) @ sK2))))))),
% 0.21/0.45 inference(superposition,[],[f44,f83])).
% 0.21/0.45 thf(f44,plain,(
% 0.21/0.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((func @ X1 @ X2 @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ (ap @ X1 @ X2 @ X3 @ Y0) @ X2))))) = $true)) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f43])).
% 0.21/0.45 thf(f43,plain,(
% 0.21/0.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((func @ X1 @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (ap @ X1 @ X2 @ Y0 @ Y1) @ X2)))))) @ X3) = $true)) )),
% 0.21/0.45 inference(pi_clausification,[],[f42])).
% 0.21/0.45 thf(f42,plain,(
% 0.21/0.45 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((func @ X1 @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (ap @ X1 @ X2 @ Y0 @ Y1) @ X2))))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f41])).
% 0.21/0.45 thf(f41,plain,(
% 0.21/0.45 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((func @ X1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (ap @ X1 @ Y0 @ Y1 @ Y2) @ Y0)))))))) @ X2))) )),
% 0.21/0.45 inference(pi_clausification,[],[f40])).
% 0.21/0.45 thf(f40,plain,(
% 0.21/0.45 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((func @ X1 @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (ap @ X1 @ Y0 @ Y1 @ Y2) @ Y0))))))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f39])).
% 0.21/0.45 thf(f39,plain,(
% 0.21/0.45 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y1 @ Y2 @ Y3) @ Y1)))))))))) @ X1))) )),
% 0.21/0.45 inference(pi_clausification,[],[f34])).
% 0.21/0.45 thf(f34,plain,(
% 0.21/0.45 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y1 @ Y2 @ Y3) @ Y1))))))))))) = $true)),
% 0.21/0.45 inference(binary_proxy_clausification,[],[f30])).
% 0.21/0.45 thf(f115,plain,(
% 0.21/0.45 ( ! [X2 : $i,X3 : $i > $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ (X3 @ Y0) @ X2)))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((X3 @ Y0) = (ap @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[Y1 : $i]: (= @ (X3 @ Y1)))) @ Y0)))))) = $true)) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f114])).
% 0.21/0.45 thf(f114,plain,(
% 0.21/0.45 ( ! [X2 : $i,X3 : $i > $i,X1 : $i] : ((((^[Y0 : $i > $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (Y0 @ Y1) @ X2)))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((Y0 @ Y1) = (ap @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[Y2 : $i]: (= @ (Y0 @ Y2)))) @ Y1))))))) @ X3) = $true)) )),
% 0.21/0.45 inference(pi_clausification,[],[f107])).
% 0.21/0.45 thf(f107,plain,(
% 0.21/0.45 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $i) @ (^[Y0 : $i > $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (Y0 @ Y1) @ X2)))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((Y0 @ Y1) = (ap @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[Y2 : $i]: (= @ (Y0 @ Y2)))) @ Y1)))))))) = $true)) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f106])).
% 0.21/0.45 thf(f106,plain,(
% 0.21/0.45 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (Y1 @ Y2) @ Y0)))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y1 @ Y2) = (ap @ X1 @ Y0 @ (dpsetconstr @ X1 @ Y0 @ (^[Y3 : $i]: (= @ (Y1 @ Y3)))) @ Y2))))))))) @ X2))) )),
% 0.21/0.45 inference(pi_clausification,[],[f99])).
% 0.21/0.45 thf(f99,plain,(
% 0.21/0.45 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (Y1 @ Y2) @ Y0)))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y1 @ Y2) = (ap @ X1 @ Y0 @ (dpsetconstr @ X1 @ Y0 @ (^[Y3 : $i]: (= @ (Y1 @ Y3)))) @ Y2)))))))))) = $true)) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f98])).
% 0.21/0.45 thf(f98,plain,(
% 0.21/0.45 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y2 @ Y3) @ Y1)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y2 @ Y3) = (ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y4 : $i]: (= @ (Y2 @ Y4)))) @ Y3))))))))))) @ X1) = $true)) )),
% 0.21/0.45 inference(pi_clausification,[],[f73])).
% 0.21/0.45 thf(f175,plain,(
% 0.21/0.45 ( ! [X1 : $i] : (($true = ((func @ sK4 @ sK2 @ X1) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((ap @ sK4 @ sK2 @ X1 @ Y0) = (ap @ sK4 @ sK2 @ (dpsetconstr @ sK4 @ sK2 @ (^[Y1 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y1)))) @ Y0))))) => ((dpsetconstr @ sK4 @ sK2 @ (^[Y0 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y0)))) = X1))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f172])).
% 0.21/0.45 thf(f172,plain,(
% 0.21/0.45 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((func @ sK4 @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((ap @ sK4 @ sK2 @ Y0 @ Y1) = (ap @ sK4 @ sK2 @ (dpsetconstr @ sK4 @ sK2 @ (^[Y2 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y2)))) @ Y1))))) => ((dpsetconstr @ sK4 @ sK2 @ (^[Y1 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y1)))) = Y0)))) @ X1))) )),
% 0.21/0.45 inference(pi_clausification,[],[f103])).
% 0.21/0.45 thf(f103,plain,(
% 0.21/0.45 ($true = (!! @ $i @ (^[Y0 : $i]: ((func @ sK4 @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((ap @ sK4 @ sK2 @ Y0 @ Y1) = (ap @ sK4 @ sK2 @ (dpsetconstr @ sK4 @ sK2 @ (^[Y2 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y2)))) @ Y1))))) => ((dpsetconstr @ sK4 @ sK2 @ (^[Y1 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y1)))) = Y0))))))),
% 0.21/0.45 inference(boolean_simplification,[],[f101])).
% 0.21/0.45 thf(f101,plain,(
% 0.21/0.45 (($true => (!! @ $i @ (^[Y0 : $i]: ((func @ sK4 @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((ap @ sK4 @ sK2 @ Y0 @ Y1) = (ap @ sK4 @ sK2 @ (dpsetconstr @ sK4 @ sK2 @ (^[Y2 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y2)))) @ Y1))))) => ((dpsetconstr @ sK4 @ sK2 @ (^[Y1 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y1)))) = Y0)))))) = $true)),
% 0.21/0.45 inference(superposition,[],[f70,f94])).
% 0.21/0.45 thf(f94,plain,(
% 0.21/0.45 ($true = (func @ sK4 @ sK2 @ (dpsetconstr @ sK4 @ sK2 @ (^[Y0 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y0))))))),
% 0.21/0.45 inference(boolean_simplification,[],[f93])).
% 0.21/0.45 thf(f93,plain,(
% 0.21/0.45 ($true = ($true => (func @ sK4 @ sK2 @ (dpsetconstr @ sK4 @ sK2 @ (^[Y0 : $i]: (= @ (ap @ sK4 @ sK2 @ sK3 @ Y0)))))))),
% 0.21/0.45 inference(superposition,[],[f57,f89])).
% 0.21/0.45 thf(f57,plain,(
% 0.21/0.45 ( ! [X2 : $i,X3 : $i,X1 : $i > $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (X1 @ Y0) @ X2)))) => (func @ X3 @ X2 @ (dpsetconstr @ X3 @ X2 @ (^[Y0 : $i]: (= @ (X1 @ Y0)))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f56])).
% 0.21/0.45 thf(f56,plain,(
% 0.21/0.45 ( ! [X2 : $i,X3 : $i,X1 : $i > $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (X1 @ Y1) @ X2)))) => (func @ Y0 @ X2 @ (dpsetconstr @ Y0 @ X2 @ (^[Y1 : $i]: (= @ (X1 @ Y1))))))) @ X3))) )),
% 0.21/0.45 inference(pi_clausification,[],[f55])).
% 0.21/0.45 thf(f55,plain,(
% 0.21/0.45 ( ! [X2 : $i,X1 : $i > $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (X1 @ Y1) @ X2)))) => (func @ Y0 @ X2 @ (dpsetconstr @ Y0 @ X2 @ (^[Y1 : $i]: (= @ (X1 @ Y1)))))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f54])).
% 0.21/0.45 thf(f54,plain,(
% 0.21/0.45 ( ! [X2 : $i,X1 : $i > $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ (X1 @ Y2) @ Y0)))) => (func @ Y1 @ Y0 @ (dpsetconstr @ Y1 @ Y0 @ (^[Y2 : $i]: (= @ (X1 @ Y2))))))))) @ X2) = $true)) )),
% 0.21/0.45 inference(pi_clausification,[],[f53])).
% 0.21/0.45 thf(f53,plain,(
% 0.21/0.45 ( ! [X1 : $i > $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ (X1 @ Y2) @ Y0)))) => (func @ Y1 @ Y0 @ (dpsetconstr @ Y1 @ Y0 @ (^[Y2 : $i]: (= @ (X1 @ Y2)))))))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f52])).
% 0.21/0.45 thf(f52,plain,(
% 0.21/0.45 ( ! [X1 : $i > $i] : (($true = ((^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y0 @ Y3) @ Y1)))) => (func @ Y2 @ Y1 @ (dpsetconstr @ Y2 @ Y1 @ (^[Y3 : $i]: (= @ (Y0 @ Y3))))))))))) @ X1))) )),
% 0.21/0.45 inference(pi_clausification,[],[f47])).
% 0.21/0.45 thf(f47,plain,(
% 0.21/0.45 ($true = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y0 @ Y3) @ Y1)))) => (func @ Y2 @ Y1 @ (dpsetconstr @ Y2 @ Y1 @ (^[Y3 : $i]: (= @ (Y0 @ Y3)))))))))))))),
% 0.21/0.45 inference(binary_proxy_clausification,[],[f33])).
% 0.21/0.45 thf(f70,plain,(
% 0.21/0.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((func @ X2 @ X3 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((func @ X2 @ X3 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((ap @ X2 @ X3 @ Y0 @ Y1) = (ap @ X2 @ X3 @ X1 @ Y1))))) => (X1 = Y0)))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f69])).
% 0.21/0.45 thf(f69,plain,(
% 0.21/0.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((func @ X2 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((func @ X2 @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((ap @ X2 @ Y0 @ Y1 @ Y2) = (ap @ X2 @ Y0 @ X1 @ Y2))))) => (X1 = Y1))))))) @ X3))) )),
% 0.21/0.45 inference(pi_clausification,[],[f68])).
% 0.21/0.45 thf(f68,plain,(
% 0.21/0.45 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((func @ X2 @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((func @ X2 @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((ap @ X2 @ Y0 @ Y1 @ Y2) = (ap @ X2 @ Y0 @ X1 @ Y2))))) => (X1 = Y1)))))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f67])).
% 0.21/0.45 thf(f67,plain,(
% 0.21/0.45 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((func @ Y0 @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ap @ Y0 @ Y1 @ Y2 @ Y3) = (ap @ Y0 @ Y1 @ X1 @ Y3))))) => (X1 = Y2))))))))) @ X2) = $true)) )),
% 0.21/0.45 inference(pi_clausification,[],[f66])).
% 0.21/0.45 thf(f66,plain,(
% 0.21/0.45 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((func @ Y0 @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ap @ Y0 @ Y1 @ Y2 @ Y3) = (ap @ Y0 @ Y1 @ X1 @ Y3))))) => (X1 = Y2)))))))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f65])).
% 0.21/0.45 thf(f65,plain,(
% 0.21/0.45 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y3 @ Y4) = (ap @ Y1 @ Y2 @ Y0 @ Y4))))) => (Y0 = Y3))))))))))) @ X1) = $true)) )),
% 0.21/0.45 inference(pi_clausification,[],[f60])).
% 0.21/0.45 thf(f60,plain,(
% 0.21/0.45 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((func @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y3 @ Y4) = (ap @ Y1 @ Y2 @ Y0 @ Y4))))) => (Y0 = Y3)))))))))))))),
% 0.21/0.45 inference(binary_proxy_clausification,[],[f46])).
% 0.21/0.45 % SZS output end Proof for theBenchmark
% 0.21/0.45 % (17115)------------------------------
% 0.21/0.45 % (17115)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (17115)Termination reason: Refutation
% 0.21/0.45
% 0.21/0.45 % (17115)Memory used [KB]: 6012
% 0.21/0.45 % (17115)Time elapsed: 0.054 s
% 0.21/0.45 % (17115)Instructions burned: 77 (million)
% 0.21/0.45 % (17115)------------------------------
% 0.21/0.45 % (17115)------------------------------
% 0.21/0.45 % (17103)Success in time 0.096 s
% 0.21/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------