TSTP Solution File: SEU686^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU686^2 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n020.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 03:50:44 EDT 2024
% Result : Theorem 0.15s 0.38s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SEU686^2 : TPTP v8.2.0. Released v3.7.0.
% 0.05/0.11 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.30 % Computer : n020.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sun May 19 15:55:07 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.30 This is a TH0_THM_EQU_NAR problem
% 0.10/0.30 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.32 % (5486)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.15/0.32 % (5483)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.15/0.32 % (5482)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.32 % (5481)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.32 % (5484)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.32 % (5487)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.32 % (5485)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.32 % (5488)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.32 % (5484)Instruction limit reached!
% 0.15/0.32 % (5484)------------------------------
% 0.15/0.32 % (5484)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (5484)Termination reason: Unknown
% 0.15/0.32 % (5484)Termination phase: Property scanning
% 0.15/0.32
% 0.15/0.32 % (5485)Instruction limit reached!
% 0.15/0.32 % (5485)------------------------------
% 0.15/0.32 % (5485)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (5485)Termination reason: Unknown
% 0.15/0.32 % (5485)Termination phase: Property scanning
% 0.15/0.32
% 0.15/0.32 % (5485)Memory used [KB]: 1023
% 0.15/0.32 % (5485)Time elapsed: 0.003 s
% 0.15/0.32 % (5485)Instructions burned: 3 (million)
% 0.15/0.32 % (5485)------------------------------
% 0.15/0.32 % (5485)------------------------------
% 0.15/0.32 % (5484)Memory used [KB]: 1023
% 0.15/0.32 % (5484)Time elapsed: 0.003 s
% 0.15/0.32 % (5484)Instructions burned: 3 (million)
% 0.15/0.32 % (5484)------------------------------
% 0.15/0.32 % (5484)------------------------------
% 0.15/0.32 % (5488)Instruction limit reached!
% 0.15/0.32 % (5488)------------------------------
% 0.15/0.32 % (5488)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (5488)Termination reason: Unknown
% 0.15/0.32 % (5488)Termination phase: Property scanning
% 0.15/0.32
% 0.15/0.32 % (5488)Memory used [KB]: 1023
% 0.15/0.32 % (5488)Time elapsed: 0.003 s
% 0.15/0.32 % (5488)Instructions burned: 4 (million)
% 0.15/0.32 % (5488)------------------------------
% 0.15/0.32 % (5488)------------------------------
% 0.15/0.32 % (5482)Instruction limit reached!
% 0.15/0.32 % (5482)------------------------------
% 0.15/0.32 % (5482)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (5482)Termination reason: Unknown
% 0.15/0.32 % (5482)Termination phase: Property scanning
% 0.15/0.32
% 0.15/0.32 % (5482)Memory used [KB]: 1023
% 0.15/0.32 % (5482)Time elapsed: 0.004 s
% 0.15/0.32 % (5482)Instructions burned: 5 (million)
% 0.15/0.32 % (5482)------------------------------
% 0.15/0.32 % (5482)------------------------------
% 0.15/0.32 % (5486)Refutation not found, incomplete strategy
% 0.15/0.32 % (5486)------------------------------
% 0.15/0.32 % (5486)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (5486)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.32
% 0.15/0.32
% 0.15/0.32 % (5486)Memory used [KB]: 5500
% 0.15/0.32 % (5486)Time elapsed: 0.005 s
% 0.15/0.32 % (5486)Instructions burned: 7 (million)
% 0.15/0.32 % (5486)------------------------------
% 0.15/0.32 % (5486)------------------------------
% 0.15/0.33 % (5487)Instruction limit reached!
% 0.15/0.33 % (5487)------------------------------
% 0.15/0.33 % (5487)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (5487)Termination reason: Unknown
% 0.15/0.33 % (5487)Termination phase: Saturation
% 0.15/0.33
% 0.15/0.33 % (5487)Memory used [KB]: 5756
% 0.15/0.33 % (5487)Time elapsed: 0.010 s
% 0.15/0.33 % (5487)Instructions burned: 18 (million)
% 0.15/0.33 % (5487)------------------------------
% 0.15/0.33 % (5487)------------------------------
% 0.15/0.33 % (5483)Instruction limit reached!
% 0.15/0.33 % (5483)------------------------------
% 0.15/0.33 % (5483)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (5483)Termination reason: Unknown
% 0.15/0.33 % (5483)Termination phase: Saturation
% 0.15/0.33
% 0.15/0.33 % (5483)Memory used [KB]: 5756
% 0.15/0.33 % (5483)Time elapsed: 0.014 s
% 0.15/0.33 % (5483)Instructions burned: 28 (million)
% 0.15/0.33 % (5483)------------------------------
% 0.15/0.33 % (5483)------------------------------
% 0.15/0.33 % (5492)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.15/0.33 % (5490)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.15/0.33 % (5489)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.15/0.33 % (5491)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.34 % (5491)Instruction limit reached!
% 0.15/0.34 % (5491)------------------------------
% 0.15/0.34 % (5491)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34 % (5491)Termination reason: Unknown
% 0.15/0.34 % (5491)Termination phase: Property scanning
% 0.15/0.34
% 0.15/0.34 % (5491)Memory used [KB]: 1023
% 0.15/0.34 % (5491)Time elapsed: 0.003 s
% 0.15/0.34 % (5491)Instructions burned: 4 (million)
% 0.15/0.34 % (5491)------------------------------
% 0.15/0.34 % (5491)------------------------------
% 0.15/0.34 % (5493)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.34 % (5493)Instruction limit reached!
% 0.15/0.34 % (5493)------------------------------
% 0.15/0.34 % (5493)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34 % (5493)Termination reason: Unknown
% 0.15/0.34 % (5493)Termination phase: Saturation
% 0.15/0.34
% 0.15/0.34 % (5493)Memory used [KB]: 1023
% 0.15/0.34 % (5493)Time elapsed: 0.004 s
% 0.15/0.34 % (5493)Instructions burned: 7 (million)
% 0.15/0.34 % (5493)------------------------------
% 0.15/0.34 % (5493)------------------------------
% 0.15/0.34 % (5494)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.15/0.34 % (5490)Instruction limit reached!
% 0.15/0.34 % (5490)------------------------------
% 0.15/0.34 % (5490)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34 % (5490)Termination reason: Unknown
% 0.15/0.34 % (5490)Termination phase: Saturation
% 0.15/0.34
% 0.15/0.34 % (5490)Memory used [KB]: 5756
% 0.15/0.34 % (5490)Time elapsed: 0.008 s
% 0.15/0.34 % (5490)Instructions burned: 15 (million)
% 0.15/0.34 % (5490)------------------------------
% 0.15/0.34 % (5490)------------------------------
% 0.15/0.34 % (5495)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)
% 0.15/0.35 % (5495)Instruction limit reached!
% 0.15/0.35 % (5495)------------------------------
% 0.15/0.35 % (5495)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.35 % (5495)Termination reason: Unknown
% 0.15/0.35 % (5495)Termination phase: Property scanning
% 0.15/0.35
% 0.15/0.35 % (5495)Memory used [KB]: 1023
% 0.15/0.35 % (5495)Time elapsed: 0.003 s
% 0.15/0.35 % (5495)Instructions burned: 4 (million)
% 0.15/0.35 % (5495)------------------------------
% 0.15/0.35 % (5495)------------------------------
% 0.15/0.35 % (5494)Instruction limit reached!
% 0.15/0.35 % (5494)------------------------------
% 0.15/0.35 % (5494)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.35 % (5494)Termination reason: Unknown
% 0.15/0.35 % (5494)Termination phase: Saturation
% 0.15/0.35
% 0.15/0.35 % (5494)Memory used [KB]: 6012
% 0.15/0.35 % (5494)Time elapsed: 0.010 s
% 0.15/0.35 % (5494)Instructions burned: 17 (million)
% 0.15/0.35 % (5494)------------------------------
% 0.15/0.35 % (5494)------------------------------
% 0.15/0.35 % (5496)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)
% 0.15/0.35 % (5496)Instruction limit reached!
% 0.15/0.35 % (5496)------------------------------
% 0.15/0.35 % (5496)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.35 % (5496)Termination reason: Unknown
% 0.15/0.35 % (5496)Termination phase: shuffling
% 0.15/0.35
% 0.15/0.35 % (5496)Memory used [KB]: 1023
% 0.15/0.35 % (5496)Time elapsed: 0.003 s
% 0.15/0.35 % (5496)Instructions burned: 3 (million)
% 0.15/0.35 % (5496)------------------------------
% 0.15/0.35 % (5496)------------------------------
% 0.15/0.35 % (5489)Instruction limit reached!
% 0.15/0.35 % (5489)------------------------------
% 0.15/0.35 % (5489)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.35 % (5489)Termination reason: Unknown
% 0.15/0.35 % (5489)Termination phase: Saturation
% 0.15/0.35
% 0.15/0.35 % (5489)Memory used [KB]: 5628
% 0.15/0.35 % (5489)Time elapsed: 0.018 s
% 0.15/0.35 % (5489)Instructions burned: 39 (million)
% 0.15/0.35 % (5489)------------------------------
% 0.15/0.35 % (5489)------------------------------
% 0.15/0.35 % (5497)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)
% 0.15/0.35 % (5498)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)
% 0.15/0.35 % (5498)Instruction limit reached!
% 0.15/0.35 % (5498)------------------------------
% 0.15/0.35 % (5498)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.35 % (5498)Termination reason: Unknown
% 0.15/0.35 % (5498)Termination phase: Property scanning
% 0.15/0.35
% 0.15/0.35 % (5498)Memory used [KB]: 1023
% 0.15/0.35 % (5498)Time elapsed: 0.003 s
% 0.15/0.35 % (5498)Instructions burned: 4 (million)
% 0.15/0.35 % (5498)------------------------------
% 0.15/0.35 % (5498)------------------------------
% 0.15/0.36 % (5497)Instruction limit reached!
% 0.15/0.36 % (5497)------------------------------
% 0.15/0.36 % (5497)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.36 % (5497)Termination reason: Unknown
% 0.15/0.36 % (5497)Termination phase: Saturation
% 0.15/0.36
% 0.15/0.36 % (5497)Memory used [KB]: 5500
% 0.15/0.36 % (5497)Time elapsed: 0.004 s
% 0.15/0.36 % (5497)Instructions burned: 7 (million)
% 0.15/0.36 % (5497)------------------------------
% 0.15/0.36 % (5497)------------------------------
% 0.15/0.36 % (5499)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.36 % (5499)Instruction limit reached!
% 0.15/0.36 % (5499)------------------------------
% 0.15/0.36 % (5499)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.36 % (5499)Termination reason: Unknown
% 0.15/0.36 % (5499)Termination phase: Property scanning
% 0.15/0.36
% 0.15/0.36 % (5499)Memory used [KB]: 1023
% 0.15/0.36 % (5499)Time elapsed: 0.003 s
% 0.15/0.36 % (5499)Instructions burned: 4 (million)
% 0.15/0.36 % (5499)------------------------------
% 0.15/0.36 % (5499)------------------------------
% 0.15/0.36 % (5500)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)
% 0.15/0.36 % (5501)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.15/0.36 % (5502)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.15/0.37 % (5502)Instruction limit reached!
% 0.15/0.37 % (5502)------------------------------
% 0.15/0.37 % (5502)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (5502)Termination reason: Unknown
% 0.15/0.37 % (5502)Termination phase: Property scanning
% 0.15/0.37
% 0.15/0.37 % (5502)Memory used [KB]: 1023
% 0.15/0.37 % (5502)Time elapsed: 0.004 s
% 0.15/0.37 % (5502)Instructions burned: 6 (million)
% 0.15/0.37 % (5502)------------------------------
% 0.15/0.37 % (5502)------------------------------
% 0.15/0.37 % (5492)First to succeed.
% 0.15/0.37 % (5503)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)
% 0.15/0.37 % (5504)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)
% 0.15/0.37 % (5500)Instruction limit reached!
% 0.15/0.37 % (5500)------------------------------
% 0.15/0.37 % (5500)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (5500)Termination reason: Unknown
% 0.15/0.37 % (5500)Termination phase: Saturation
% 0.15/0.37
% 0.15/0.37 % (5500)Memory used [KB]: 5756
% 0.15/0.37 % (5500)Time elapsed: 0.010 s
% 0.15/0.37 % (5500)Instructions burned: 19 (million)
% 0.15/0.37 % (5500)------------------------------
% 0.15/0.37 % (5500)------------------------------
% 0.15/0.37 % (5503)Refutation not found, incomplete strategy
% 0.15/0.37 % (5503)------------------------------
% 0.15/0.37 % (5503)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (5503)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.37
% 0.15/0.37
% 0.15/0.37 % (5503)Memory used [KB]: 5500
% 0.15/0.37 % (5503)Time elapsed: 0.028 s
% 0.15/0.37 % (5503)Instructions burned: 6 (million)
% 0.15/0.37 % (5503)------------------------------
% 0.15/0.37 % (5503)------------------------------
% 0.15/0.37 % (5505)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.15/0.38 % (5492)Refutation found. Thanks to Tanya!
% 0.15/0.38 % SZS status Theorem for theBenchmark
% 0.15/0.38 % SZS output start Proof for theBenchmark
% 0.15/0.38 thf(func_def_0, type, in: $i > $i > $o).
% 0.15/0.38 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.15/0.38 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 0.15/0.38 thf(func_def_4, type, subset: $i > $i > $o).
% 0.15/0.38 thf(func_def_5, type, kpair: $i > $i > $i).
% 0.15/0.38 thf(func_def_6, type, cartprod: $i > $i > $i).
% 0.15/0.38 thf(func_def_7, type, singleton: $i > $o).
% 0.15/0.38 thf(func_def_9, type, ex1: $i > ($i > $o) > $o).
% 0.15/0.38 thf(func_def_10, type, breln: $i > $i > $i > $o).
% 0.15/0.38 thf(func_def_11, type, func: $i > $i > $i > $o).
% 0.15/0.38 thf(func_def_12, type, ap: $i > $i > $i > $i > $i).
% 0.15/0.38 thf(func_def_32, type, ph1: !>[X0: $tType]:(X0)).
% 0.15/0.38 thf(f209,plain,(
% 0.15/0.38 $false),
% 0.15/0.38 inference(subsumption_resolution,[],[f205,f141])).
% 0.15/0.38 thf(f141,plain,(
% 0.15/0.38 ((ap @ sK3 @ sK2 @ sK4 @ sK5) != sK6)),
% 0.15/0.38 inference(equality_proxy_clausification,[],[f122])).
% 0.15/0.38 thf(f122,plain,(
% 0.15/0.38 (((ap @ sK3 @ sK2 @ sK4 @ sK5) = sK6) = $false)),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f100])).
% 0.15/0.38 thf(f100,plain,(
% 0.15/0.38 (((in @ (kpair @ sK5 @ sK6) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ sK5) = sK6)) = $false)),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f99])).
% 0.15/0.38 thf(f99,plain,(
% 0.15/0.38 (((in @ sK6 @ sK2) => ((in @ (kpair @ sK5 @ sK6) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ sK5) = sK6))) = $false)),
% 0.15/0.38 inference(beta_eta_normalization,[],[f98])).
% 0.15/0.38 thf(f98,plain,(
% 0.15/0.38 (((^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ sK5) = Y0)))) @ sK6) = $false)),
% 0.15/0.38 inference(sigma_clausification,[],[f97])).
% 0.15/0.38 thf(f97,plain,(
% 0.15/0.38 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ sK5) = Y0))))))),
% 0.15/0.38 inference(boolean_simplification,[],[f96])).
% 0.15/0.38 thf(f96,plain,(
% 0.15/0.38 ($false = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ sK5) = Y0)))))))),
% 0.15/0.38 inference(backward_demodulation,[],[f93,f95])).
% 0.15/0.38 thf(f95,plain,(
% 0.15/0.38 ((in @ sK5 @ sK3) = $true)),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f93])).
% 0.15/0.38 thf(f93,plain,(
% 0.15/0.38 ($false = ((in @ sK5 @ sK3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ sK5) = Y0)))))))),
% 0.15/0.38 inference(beta_eta_normalization,[],[f92])).
% 0.15/0.38 thf(f92,plain,(
% 0.15/0.38 (((^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ (kpair @ Y0 @ Y1) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ Y0) = Y1))))))) @ sK5) = $false)),
% 0.15/0.38 inference(sigma_clausification,[],[f86])).
% 0.15/0.38 thf(f86,plain,(
% 0.15/0.38 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ (kpair @ Y0 @ Y1) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ Y0) = Y1)))))))))),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f85])).
% 0.15/0.38 thf(f85,plain,(
% 0.15/0.38 ($false = (((subset @ sK4 @ (cartprod @ sK3 @ sK2)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK4)))) & (in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK4))))))))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ (kpair @ Y0 @ Y1) @ sK4) => ((ap @ sK3 @ sK2 @ sK4 @ Y0) = Y1))))))))))),
% 0.15/0.38 inference(beta_eta_normalization,[],[f84])).
% 0.15/0.38 thf(f84,plain,(
% 0.15/0.38 ($false = ((^[Y0 : $i]: (((subset @ Y0 @ (cartprod @ sK3 @ sK2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & (in @ Y2 @ (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => ((ap @ sK3 @ sK2 @ Y0 @ Y1) = Y2)))))))))) @ sK4))),
% 0.15/0.38 inference(sigma_clausification,[],[f83])).
% 0.15/0.38 thf(f83,plain,(
% 0.15/0.38 ((!! @ $i @ (^[Y0 : $i]: (((subset @ Y0 @ (cartprod @ sK3 @ sK2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & (in @ Y2 @ (dsetconstr @ sK2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK2) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => ((ap @ sK3 @ sK2 @ Y0 @ Y1) = Y2))))))))))) = $false)),
% 0.15/0.38 inference(beta_eta_normalization,[],[f82])).
% 0.15/0.38 thf(f82,plain,(
% 0.15/0.38 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ sK2)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ sK2 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1)))) & (in @ Y3 @ (dsetconstr @ sK2 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ sK2) => ((in @ (kpair @ Y2 @ Y3) @ Y1) => ((ap @ Y0 @ sK2 @ Y1 @ Y2) = Y3)))))))))))) @ sK3))),
% 0.15/0.38 inference(sigma_clausification,[],[f81])).
% 0.15/0.38 thf(f81,plain,(
% 0.15/0.38 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ sK2)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ sK2 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1)))) & (in @ Y3 @ (dsetconstr @ sK2 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ sK2) => ((in @ (kpair @ Y2 @ Y3) @ Y1) => ((ap @ Y0 @ sK2 @ Y1 @ Y2) = Y3))))))))))))))),
% 0.15/0.38 inference(beta_eta_normalization,[],[f80])).
% 0.15/0.38 thf(f80,plain,(
% 0.15/0.38 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4)))))))))))))) @ sK2) = $false)),
% 0.15/0.38 inference(sigma_clausification,[],[f67])).
% 0.15/0.38 thf(f67,plain,(
% 0.15/0.38 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))))),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f49])).
% 0.15/0.38 thf(f49,plain,(
% 0.15/0.38 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y3 @ (ap @ Y0 @ Y1 @ Y2 @ Y3)) @ Y2))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4)))))))))))))))))),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f48])).
% 0.15/0.38 thf(f48,plain,(
% 0.15/0.38 (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)) & (in @ Y2 @ (dsetconstr @ Y0 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y3 @ (ap @ Y0 @ Y1 @ Y2 @ Y3)) @ Y2))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))))) = $false)),
% 0.15/0.38 inference(boolean_simplification,[],[f47])).
% 0.15/0.38 thf(f47,plain,(
% 0.15/0.38 (($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)) & (in @ Y2 @ (dsetconstr @ Y0 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y3 @ (ap @ Y0 @ Y1 @ Y2 @ Y3)) @ Y2))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4)))))))))))))))))) = $false)),
% 0.15/0.38 inference(backward_demodulation,[],[f42,f46])).
% 0.15/0.38 thf(f46,plain,(
% 0.15/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y1 @ Y2 @ Y3) @ Y1))))))))))))),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f42])).
% 0.15/0.38 thf(f42,plain,(
% 0.15/0.38 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y1 @ Y2 @ Y3) @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)) & (in @ Y2 @ (dsetconstr @ Y0 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y3 @ (ap @ Y0 @ Y1 @ Y2 @ Y3)) @ Y2))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4)))))))))))))))))))),
% 0.15/0.38 inference(not_proxy_clausification,[],[f41])).
% 0.15/0.38 thf(f41,plain,(
% 0.15/0.38 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y1 @ Y2 @ Y3) @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)) & (in @ Y2 @ (dsetconstr @ Y0 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y3 @ (ap @ Y0 @ Y1 @ Y2 @ Y3)) @ Y2))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))))))))),
% 0.15/0.38 inference(beta_eta_normalization,[],[f40])).
% 0.15/0.38 thf(f40,plain,(
% 0.15/0.38 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (((setadjoin @ Y10 @ emptyset) = Y9) & (in @ Y10 @ Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y1 @ Y2 @ Y3) @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((setadjoin @ Y5 @ emptyset) = Y4) & (in @ Y5 @ Y4))))) @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (((setadjoin @ Y10 @ emptyset) = Y9) & (in @ Y10 @ Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y3 @ (ap @ Y0 @ Y1 @ Y2 @ Y3)) @ Y2))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (((setadjoin @ Y10 @ emptyset) = Y9) & (in @ Y10 @ Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))))))))),
% 0.15/0.38 inference(definition_unfolding,[],[f34,f37,f38,f39,f36])).
% 0.15/0.38 thf(f36,plain,(
% 0.15/0.38 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((setadjoin @ Y7 @ emptyset) = Y6) & (in @ Y7 @ Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 0.15/0.38 inference(definition_unfolding,[],[f27,f32,f35])).
% 0.15/0.38 thf(f35,plain,(
% 0.15/0.38 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.15/0.38 inference(definition_unfolding,[],[f30,f29])).
% 0.15/0.38 thf(f29,plain,(
% 0.15/0.38 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f20])).
% 0.15/0.38 thf(f20,plain,(
% 0.15/0.38 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 0.15/0.38 inference(fool_elimination,[],[f19])).
% 0.15/0.38 thf(f19,plain,(
% 0.15/0.38 (singleton = (^[X0 : $i] : (? [X1] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))))),
% 0.15/0.38 inference(rectify,[],[f1])).
% 0.15/0.38 thf(f1,axiom,(
% 0.15/0.38 (singleton = (^[X0 : $i] : (? [X1] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))))),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton)).
% 0.15/0.38 thf(f30,plain,(
% 0.15/0.38 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f26])).
% 0.15/0.38 thf(f26,plain,(
% 0.15/0.38 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.15/0.38 inference(fool_elimination,[],[f25])).
% 0.15/0.38 thf(f25,plain,(
% 0.15/0.38 ((^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))) = ex1)),
% 0.15/0.38 inference(rectify,[],[f2])).
% 0.15/0.38 thf(f2,axiom,(
% 0.15/0.38 ((^[X0 : $i, X2 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X1 : $i] : (X2 @ X1))))) = ex1)),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1)).
% 0.15/0.38 thf(f32,plain,(
% 0.15/0.38 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f24])).
% 0.15/0.38 thf(f24,plain,(
% 0.15/0.38 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.15/0.38 inference(fool_elimination,[],[f23])).
% 0.15/0.38 thf(f23,plain,(
% 0.15/0.38 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))))),
% 0.15/0.38 inference(rectify,[],[f3])).
% 0.15/0.38 thf(f3,axiom,(
% 0.15/0.38 (breln = (^[X0 : $i, X3 : $i, X4 : $i] : (subset @ X4 @ (cartprod @ X0 @ X3))))),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln)).
% 0.15/0.38 thf(f27,plain,(
% 0.15/0.38 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f18])).
% 0.15/0.38 thf(f18,plain,(
% 0.15/0.38 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 0.15/0.38 inference(fool_elimination,[],[f17])).
% 0.15/0.38 thf(f17,plain,(
% 0.15/0.38 (func = (^[X0 : $i, X1 : $i, X2 : $i] : (! [X3] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))) & (breln @ X0 @ X1 @ X2))))),
% 0.15/0.38 inference(rectify,[],[f4])).
% 0.15/0.38 thf(f4,axiom,(
% 0.15/0.38 (func = (^[X0 : $i, X3 : $i, X5 : $i] : (! [X1] : ((in @ X1 @ X0) => (ex1 @ X3 @ (^[X6 : $i] : (in @ (kpair @ X1 @ X6) @ X5)))) & (breln @ X0 @ X3 @ X5))))),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',func)).
% 0.15/0.38 thf(f39,plain,(
% 0.15/0.38 (funcGraphProp1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (((setadjoin @ Y10 @ emptyset) = Y9) & (in @ Y10 @ Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y3 @ (ap @ Y0 @ Y1 @ Y2 @ Y3)) @ Y2))))))))))))),
% 0.15/0.38 inference(definition_unfolding,[],[f28,f36])).
% 0.15/0.38 thf(f28,plain,(
% 0.15/0.38 (funcGraphProp1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y3 @ (ap @ Y0 @ Y1 @ Y2 @ Y3)) @ Y2))))))))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f14])).
% 0.15/0.38 thf(f14,plain,(
% 0.15/0.38 (funcGraphProp1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y3 @ (ap @ Y0 @ Y1 @ Y2 @ Y3)) @ Y2))))))))))))),
% 0.15/0.38 inference(fool_elimination,[],[f13])).
% 0.15/0.38 thf(f13,plain,(
% 0.15/0.38 (! [X0,X1,X2] : ((func @ X2 @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => (in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0))) = funcGraphProp1)),
% 0.15/0.38 inference(rectify,[],[f7])).
% 0.15/0.38 thf(f7,axiom,(
% 0.15/0.38 (! [X7,X3,X0] : ((func @ X0 @ X3 @ X7) => ! [X1] : ((in @ X1 @ X0) => (in @ (kpair @ X1 @ (ap @ X0 @ X3 @ X7 @ X1)) @ X7))) = funcGraphProp1)),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1)).
% 0.15/0.38 thf(f38,plain,(
% 0.15/0.38 (ex1E2 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((setadjoin @ Y5 @ emptyset) = Y4) & (in @ Y5 @ Y4))))) @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))))),
% 0.15/0.38 inference(definition_unfolding,[],[f33,f35])).
% 0.15/0.38 thf(f33,plain,(
% 0.15/0.38 (ex1E2 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f22])).
% 0.15/0.38 thf(f22,plain,(
% 0.15/0.38 (ex1E2 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))))),
% 0.15/0.38 inference(fool_elimination,[],[f21])).
% 0.15/0.38 thf(f21,plain,(
% 0.15/0.38 (ex1E2 = ! [X0 : $i > $o,X1] : ((ex1 @ X1 @ (^[X2 : $i] : (X0 @ X2))) => ! [X3] : ((in @ X3 @ X1) => ! [X4] : ((in @ X4 @ X1) => ((X0 @ X3) => ((X0 @ X4) => (X3 = X4)))))))),
% 0.15/0.38 inference(rectify,[],[f6])).
% 0.15/0.38 thf(f6,axiom,(
% 0.15/0.38 (ex1E2 = ! [X2 : $i > $o,X0] : ((ex1 @ X0 @ (^[X1 : $i] : (X2 @ X1))) => ! [X1] : ((in @ X1 @ X0) => ! [X6] : ((in @ X6 @ X0) => ((X2 @ X1) => ((X2 @ X6) => (X1 = X6)))))))),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2)).
% 0.15/0.38 thf(f37,plain,(
% 0.15/0.38 (app = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (((setadjoin @ Y10 @ emptyset) = Y9) & (in @ Y10 @ Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y1 @ Y2 @ Y3) @ Y1))))))))))))),
% 0.15/0.38 inference(definition_unfolding,[],[f31,f36])).
% 0.15/0.38 thf(f31,plain,(
% 0.15/0.38 (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))))))))))))),
% 0.15/0.38 inference(cnf_transformation,[],[f12])).
% 0.15/0.38 thf(f12,plain,(
% 0.15/0.38 (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))))))))))))),
% 0.15/0.38 inference(fool_elimination,[],[f11])).
% 0.15/0.38 thf(f11,plain,(
% 0.15/0.38 (! [X0,X1,X2] : ((func @ X2 @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => (in @ (ap @ X2 @ X1 @ X0 @ X3) @ X1))) = app)),
% 0.15/0.38 inference(rectify,[],[f5])).
% 0.15/0.38 thf(f5,axiom,(
% 0.15/0.38 (! [X7,X3,X0] : ((func @ X0 @ X3 @ X7) => ! [X1] : ((in @ X1 @ X0) => (in @ (ap @ X0 @ X3 @ X7 @ X1) @ X3))) = app)),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',app)).
% 0.15/0.38 thf(f34,plain,(
% 0.15/0.38 ((~ (app => (ex1E2 => (funcGraphProp1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))))))) = $true)),
% 0.15/0.38 inference(cnf_transformation,[],[f16])).
% 0.15/0.38 thf(f16,plain,(
% 0.15/0.38 ((~ (app => (ex1E2 => (funcGraphProp1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))))))) = $true)),
% 0.15/0.38 inference(fool_elimination,[],[f15])).
% 0.15/0.38 thf(f15,plain,(
% 0.15/0.38 ~(app => (ex1E2 => (funcGraphProp1 => ! [X0,X1,X2] : ((func @ X1 @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => ! [X4] : ((in @ X4 @ X2) => ((in @ (kpair @ X3 @ X4) @ X0) => ((ap @ X1 @ X2 @ X0 @ X3) = X4))))))))),
% 0.15/0.38 inference(rectify,[],[f9])).
% 0.15/0.38 thf(f9,negated_conjecture,(
% 0.15/0.38 ~(app => (ex1E2 => (funcGraphProp1 => ! [X7,X0,X3] : ((func @ X0 @ X3 @ X7) => ! [X1] : ((in @ X1 @ X0) => ! [X6] : ((in @ X6 @ X3) => ((in @ (kpair @ X1 @ X6) @ X7) => ((ap @ X0 @ X3 @ X7 @ X1) = X6))))))))),
% 0.15/0.38 inference(negated_conjecture,[],[f8])).
% 0.15/0.38 thf(f8,conjecture,(
% 0.15/0.38 app => (ex1E2 => (funcGraphProp1 => ! [X7,X0,X3] : ((func @ X0 @ X3 @ X7) => ! [X1] : ((in @ X1 @ X0) => ! [X6] : ((in @ X6 @ X3) => ((in @ (kpair @ X1 @ X6) @ X7) => ((ap @ X0 @ X3 @ X7 @ X1) = X6)))))))),
% 0.15/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2)).
% 0.15/0.38 thf(f205,plain,(
% 0.15/0.38 ((ap @ sK3 @ sK2 @ sK4 @ sK5) = sK6)),
% 0.15/0.38 inference(equality_proxy_clausification,[],[f202])).
% 0.15/0.38 thf(f202,plain,(
% 0.15/0.38 ((sK6 = (ap @ sK3 @ sK2 @ sK4 @ sK5)) = $true)),
% 0.15/0.38 inference(boolean_simplification,[],[f201])).
% 0.15/0.38 thf(f201,plain,(
% 0.15/0.38 ($true = ($true => (sK6 = (ap @ sK3 @ sK2 @ sK4 @ sK5))))),
% 0.15/0.38 inference(forward_demodulation,[],[f200,f134])).
% 0.15/0.38 thf(f134,plain,(
% 0.15/0.38 ($true = (in @ (ap @ sK3 @ sK2 @ sK4 @ sK5) @ sK2))),
% 0.15/0.38 inference(boolean_simplification,[],[f133])).
% 0.15/0.38 thf(f133,plain,(
% 0.15/0.38 ($true = ($true => (in @ (ap @ sK3 @ sK2 @ sK4 @ sK5) @ sK2)))),
% 0.15/0.38 inference(superposition,[],[f131,f95])).
% 0.15/0.38 thf(f131,plain,(
% 0.15/0.38 ( ! [X1 : $i] : ((((in @ X1 @ sK3) => (in @ (ap @ sK3 @ sK2 @ sK4 @ X1) @ sK2)) = $true)) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f128])).
% 0.15/0.38 thf(f128,plain,(
% 0.15/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (ap @ sK3 @ sK2 @ sK4 @ Y0) @ sK2))) @ X1) = $true)) )),
% 0.15/0.38 inference(pi_clausification,[],[f111])).
% 0.15/0.38 thf(f111,plain,(
% 0.15/0.38 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (ap @ sK3 @ sK2 @ sK4 @ Y0) @ sK2)))) = $true)),
% 0.15/0.38 inference(boolean_simplification,[],[f109])).
% 0.15/0.38 thf(f109,plain,(
% 0.15/0.38 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (ap @ sK3 @ sK2 @ sK4 @ Y0) @ sK2))))) = $true)),
% 0.15/0.38 inference(superposition,[],[f65,f87])).
% 0.15/0.38 thf(f87,plain,(
% 0.15/0.38 ($true = ((subset @ sK4 @ (cartprod @ sK3 @ sK2)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK4)))) & (in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK4))))))))))))),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f85])).
% 0.15/0.38 thf(f65,plain,(
% 0.15/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((subset @ X3 @ (cartprod @ X1 @ X2)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X3)))) & (in @ Y1 @ (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X3))))))))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ (ap @ X1 @ X2 @ X3 @ Y0) @ X2))))) = $true)) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f64])).
% 0.15/0.38 thf(f64,plain,(
% 0.15/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((subset @ Y0 @ (cartprod @ X1 @ X2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & (in @ Y2 @ (dsetconstr @ X2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (ap @ X1 @ X2 @ Y0 @ Y1) @ X2)))))) @ X3) = $true)) )),
% 0.15/0.38 inference(pi_clausification,[],[f63])).
% 0.15/0.38 thf(f63,plain,(
% 0.15/0.38 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((subset @ Y0 @ (cartprod @ X1 @ X2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & (in @ Y2 @ (dsetconstr @ X2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (ap @ X1 @ X2 @ Y0 @ Y1) @ X2))))))))) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f62])).
% 0.15/0.38 thf(f62,plain,(
% 0.15/0.38 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ Y1 @ (cartprod @ X1 @ Y0)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1)))) & (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (ap @ X1 @ Y0 @ Y1 @ Y2) @ Y0)))))))) @ X2))) )),
% 0.15/0.38 inference(pi_clausification,[],[f61])).
% 0.15/0.38 thf(f61,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ Y1 @ (cartprod @ X1 @ Y0)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1)))) & (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (ap @ X1 @ Y0 @ Y1 @ Y2) @ Y0))))))))))) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f60])).
% 0.15/0.38 thf(f60,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (ap @ Y0 @ Y1 @ Y2 @ Y3) @ Y1)))))))))) @ X1))) )),
% 0.15/0.38 inference(pi_clausification,[],[f46])).
% 0.15/0.38 thf(f200,plain,(
% 0.15/0.38 (((in @ (ap @ sK3 @ sK2 @ sK4 @ sK5) @ sK2) => (sK6 = (ap @ sK3 @ sK2 @ sK4 @ sK5))) = $true)),
% 0.15/0.38 inference(boolean_simplification,[],[f190])).
% 0.15/0.38 thf(f190,plain,(
% 0.15/0.38 ($true = ((in @ (ap @ sK3 @ sK2 @ sK4 @ sK5) @ sK2) => ($true => (sK6 = (ap @ sK3 @ sK2 @ sK4 @ sK5)))))),
% 0.15/0.38 inference(superposition,[],[f187,f144])).
% 0.15/0.38 thf(f144,plain,(
% 0.15/0.38 ($true = (in @ (kpair @ sK5 @ (ap @ sK3 @ sK2 @ sK4 @ sK5)) @ sK4))),
% 0.15/0.38 inference(boolean_simplification,[],[f143])).
% 0.15/0.38 thf(f143,plain,(
% 0.15/0.38 ($true = ($true => (in @ (kpair @ sK5 @ (ap @ sK3 @ sK2 @ sK4 @ sK5)) @ sK4)))),
% 0.15/0.38 inference(superposition,[],[f140,f95])).
% 0.15/0.38 thf(f140,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK3) => (in @ (kpair @ X1 @ (ap @ sK3 @ sK2 @ sK4 @ X1)) @ sK4)))) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f137])).
% 0.15/0.38 thf(f137,plain,(
% 0.15/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (kpair @ Y0 @ (ap @ sK3 @ sK2 @ sK4 @ Y0)) @ sK4))) @ X1) = $true)) )),
% 0.15/0.38 inference(pi_clausification,[],[f110])).
% 0.15/0.38 thf(f110,plain,(
% 0.15/0.38 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (kpair @ Y0 @ (ap @ sK3 @ sK2 @ sK4 @ Y0)) @ sK4)))) = $true)),
% 0.15/0.38 inference(boolean_simplification,[],[f108])).
% 0.15/0.38 thf(f108,plain,(
% 0.15/0.38 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (kpair @ Y0 @ (ap @ sK3 @ sK2 @ sK4 @ Y0)) @ sK4))))))),
% 0.15/0.38 inference(superposition,[],[f78,f87])).
% 0.15/0.38 thf(f78,plain,(
% 0.15/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((subset @ X3 @ (cartprod @ X1 @ X2)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X3)))) & (in @ Y1 @ (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X3))))))))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ (kpair @ Y0 @ (ap @ X1 @ X2 @ X3 @ Y0)) @ X3))))))) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f77])).
% 0.15/0.38 thf(f77,plain,(
% 0.15/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((subset @ Y0 @ (cartprod @ X1 @ X2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & (in @ Y2 @ (dsetconstr @ X2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (kpair @ Y1 @ (ap @ X1 @ X2 @ Y0 @ Y1)) @ Y0)))))) @ X3))) )),
% 0.15/0.38 inference(pi_clausification,[],[f76])).
% 0.15/0.38 thf(f76,plain,(
% 0.15/0.38 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((subset @ Y0 @ (cartprod @ X1 @ X2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & (in @ Y2 @ (dsetconstr @ X2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (kpair @ Y1 @ (ap @ X1 @ X2 @ Y0 @ Y1)) @ Y0))))))))) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f75])).
% 0.15/0.38 thf(f75,plain,(
% 0.15/0.38 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ Y1 @ (cartprod @ X1 @ Y0)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1)))) & (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (kpair @ Y2 @ (ap @ X1 @ Y0 @ Y1 @ Y2)) @ Y1)))))))) @ X2))) )),
% 0.15/0.38 inference(pi_clausification,[],[f74])).
% 0.15/0.38 thf(f74,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ Y1 @ (cartprod @ X1 @ Y0)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1)))) & (in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (kpair @ Y2 @ (ap @ X1 @ Y0 @ Y1 @ Y2)) @ Y1))))))))) = $true)) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f73])).
% 0.15/0.38 thf(f73,plain,(
% 0.15/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y3 @ (ap @ Y0 @ Y1 @ Y2 @ Y3)) @ Y2)))))))))) @ X1) = $true)) )),
% 0.15/0.38 inference(pi_clausification,[],[f68])).
% 0.15/0.38 thf(f68,plain,(
% 0.15/0.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: (((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & (in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y3 @ (ap @ Y0 @ Y1 @ Y2 @ Y3)) @ Y2))))))))))) = $true)),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f49])).
% 0.15/0.38 thf(f187,plain,(
% 0.15/0.38 ( ! [X1 : $i] : ((((in @ X1 @ sK2) => ((in @ (kpair @ sK5 @ X1) @ sK4) => (sK6 = X1))) = $true)) )),
% 0.15/0.38 inference(boolean_simplification,[],[f186])).
% 0.15/0.38 thf(f186,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK2) => ($true => ((in @ (kpair @ sK5 @ X1) @ sK4) => (sK6 = X1)))))) )),
% 0.15/0.38 inference(forward_demodulation,[],[f185,f123])).
% 0.15/0.38 thf(f123,plain,(
% 0.15/0.38 ((in @ (kpair @ sK5 @ sK6) @ sK4) = $true)),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f100])).
% 0.15/0.38 thf(f185,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK2) => ((in @ (kpair @ sK5 @ sK6) @ sK4) => ((in @ (kpair @ sK5 @ X1) @ sK4) => (sK6 = X1)))))) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f182])).
% 0.15/0.38 thf(f182,plain,(
% 0.15/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ sK6) @ sK4) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => (sK6 = Y0))))) @ X1) = $true)) )),
% 0.15/0.38 inference(pi_clausification,[],[f180])).
% 0.15/0.38 thf(f180,plain,(
% 0.15/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ sK6) @ sK4) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => (sK6 = Y0)))))))),
% 0.15/0.38 inference(boolean_simplification,[],[f178])).
% 0.15/0.38 thf(f178,plain,(
% 0.15/0.38 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ sK6) @ sK4) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => (sK6 = Y0))))))) = $true)),
% 0.15/0.38 inference(superposition,[],[f176,f101])).
% 0.15/0.38 thf(f101,plain,(
% 0.15/0.38 ($true = (in @ sK6 @ sK2))),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f99])).
% 0.15/0.38 thf(f176,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => ((in @ (kpair @ sK5 @ X1) @ sK4) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => (X1 = Y0))))))))) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f175])).
% 0.15/0.38 thf(f175,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => ((in @ (kpair @ sK5 @ Y1) @ sK4) => (Y0 = Y1)))))))) @ X1))) )),
% 0.15/0.38 inference(pi_clausification,[],[f166])).
% 0.15/0.38 thf(f166,plain,(
% 0.15/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => ((in @ (kpair @ sK5 @ Y1) @ sK4) => (Y0 = Y1))))))))))),
% 0.15/0.38 inference(boolean_simplification,[],[f165])).
% 0.15/0.38 thf(f165,plain,(
% 0.15/0.38 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => ((in @ (kpair @ sK5 @ Y0) @ sK4) => ((in @ (kpair @ sK5 @ Y1) @ sK4) => (Y0 = Y1)))))))))) = $true)),
% 0.15/0.38 inference(beta_eta_normalization,[],[f162])).
% 0.15/0.38 thf(f162,plain,(
% 0.15/0.38 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK2) => (((^[Y2 : $i]: (in @ (kpair @ sK5 @ Y2) @ sK4)) @ Y0) => (((^[Y2 : $i]: (in @ (kpair @ sK5 @ Y2) @ sK4)) @ Y1) => (Y0 = Y1)))))))))))),
% 0.15/0.38 inference(superposition,[],[f58,f159])).
% 0.15/0.38 thf(f159,plain,(
% 0.15/0.38 ($true = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ sK4)))) & (in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ sK4))))))))),
% 0.15/0.38 inference(boolean_simplification,[],[f158])).
% 0.15/0.38 thf(f158,plain,(
% 0.15/0.38 ($true = ($true => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ sK4)))) & (in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ sK5 @ Y1) @ sK4)))))))))),
% 0.15/0.38 inference(superposition,[],[f150,f95])).
% 0.15/0.38 thf(f150,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK3) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK4)))) & (in @ Y0 @ (dsetconstr @ sK2 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK4)))))))))) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f145])).
% 0.15/0.38 thf(f145,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK4)))) & (in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK4))))))))) @ X1))) )),
% 0.15/0.38 inference(pi_clausification,[],[f106])).
% 0.15/0.38 thf(f106,plain,(
% 0.15/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK4)))) & (in @ Y1 @ (dsetconstr @ sK2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK4)))))))))))),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f87])).
% 0.15/0.38 thf(f58,plain,(
% 0.15/0.38 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ Y0 @ (dsetconstr @ X1 @ X2))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((X2 @ Y0) => ((X2 @ Y1) => (Y0 = Y1)))))))))))) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f57])).
% 0.15/0.38 thf(f57,plain,(
% 0.15/0.38 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X1 @ Y0)) & (in @ Y1 @ (dsetconstr @ X1 @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y0 @ Y1) => ((Y0 @ Y2) => (Y1 = Y2))))))))))) @ X2))) )),
% 0.15/0.38 inference(pi_clausification,[],[f56])).
% 0.15/0.38 thf(f56,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X1 @ Y0)) & (in @ Y1 @ (dsetconstr @ X1 @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y0 @ Y1) => ((Y0 @ Y2) => (Y1 = Y2)))))))))))) = $true)) )),
% 0.15/0.38 inference(beta_eta_normalization,[],[f55])).
% 0.15/0.38 thf(f55,plain,(
% 0.15/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)) & (in @ Y2 @ (dsetconstr @ Y0 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))))))) @ X1))) )),
% 0.15/0.38 inference(pi_clausification,[],[f50])).
% 0.15/0.38 thf(f50,plain,(
% 0.15/0.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1)) & (in @ Y2 @ (dsetconstr @ Y0 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3)))))))))))))) = $true)),
% 0.15/0.38 inference(binary_proxy_clausification,[],[f48])).
% 0.15/0.38 % SZS output end Proof for theBenchmark
% 0.15/0.38 % (5492)------------------------------
% 0.15/0.38 % (5492)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (5492)Termination reason: Refutation
% 0.15/0.38
% 0.15/0.38 % (5492)Memory used [KB]: 6140
% 0.15/0.38 % (5492)Time elapsed: 0.042 s
% 0.15/0.38 % (5492)Instructions burned: 77 (million)
% 0.15/0.38 % (5492)------------------------------
% 0.15/0.38 % (5492)------------------------------
% 0.15/0.38 % (5480)Success in time 0.073 s
% 0.15/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------