TSTP Solution File: SEU691^2 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU691^2 : 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 : n012.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 03:50:47 EDT 2024
% Result : Theorem 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU691^2 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.14 % 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
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun May 19 18:20:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.19/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.37 % (25668)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.19/0.37 % (25669)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)
% 0.19/0.37 % (25670)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)
% 0.19/0.37 % (25671)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.37 % (25673)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)
% 0.19/0.37 % (25674)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.19/0.37 % (25671)Instruction limit reached!
% 0.19/0.37 % (25671)------------------------------
% 0.19/0.37 % (25671)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37 % (25671)Termination reason: Unknown
% 0.19/0.37 % (25671)Termination phase: shuffling
% 0.19/0.37
% 0.19/0.37 % (25671)Memory used [KB]: 1023
% 0.19/0.37 % (25671)Time elapsed: 0.003 s
% 0.19/0.37 % (25671)Instructions burned: 2 (million)
% 0.19/0.37 % (25671)------------------------------
% 0.19/0.37 % (25671)------------------------------
% 0.19/0.37 % (25669)Instruction limit reached!
% 0.19/0.37 % (25669)------------------------------
% 0.19/0.37 % (25669)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37 % (25669)Termination reason: Unknown
% 0.19/0.37 % (25669)Termination phase: Unused predicate definition removal
% 0.19/0.37
% 0.19/0.37 % (25669)Memory used [KB]: 1023
% 0.19/0.37 % (25669)Time elapsed: 0.004 s
% 0.19/0.37 % (25669)Instructions burned: 4 (million)
% 0.19/0.37 % (25669)------------------------------
% 0.19/0.37 % (25669)------------------------------
% 0.19/0.37 % (25672)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)
% 0.19/0.37 % (25672)Instruction limit reached!
% 0.19/0.37 % (25672)------------------------------
% 0.19/0.37 % (25672)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37 % (25672)Termination reason: Unknown
% 0.19/0.37 % (25672)Termination phase: shuffling
% 0.19/0.37
% 0.19/0.37 % (25672)Memory used [KB]: 1023
% 0.19/0.37 % (25672)Time elapsed: 0.004 s
% 0.19/0.37 % (25672)Instructions burned: 2 (million)
% 0.19/0.37 % (25672)------------------------------
% 0.19/0.37 % (25672)------------------------------
% 0.19/0.38 % (25674)Instruction limit reached!
% 0.19/0.38 % (25674)------------------------------
% 0.19/0.38 % (25674)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.38 % (25674)Termination reason: Unknown
% 0.19/0.38 % (25674)Termination phase: Saturation
% 0.19/0.38
% 0.19/0.38 % (25674)Memory used [KB]: 5628
% 0.19/0.38 % (25674)Time elapsed: 0.012 s
% 0.19/0.38 % (25674)Instructions burned: 18 (million)
% 0.19/0.38 % (25674)------------------------------
% 0.19/0.38 % (25674)------------------------------
% 0.19/0.38 % (25675)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)
% 0.19/0.38 % (25670)Instruction limit reached!
% 0.19/0.38 % (25670)------------------------------
% 0.19/0.38 % (25670)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.38 % (25670)Termination reason: Unknown
% 0.19/0.38 % (25670)Termination phase: Saturation
% 0.19/0.38
% 0.19/0.38 % (25670)Memory used [KB]: 5756
% 0.19/0.38 % (25670)Time elapsed: 0.017 s
% 0.19/0.38 % (25670)Instructions burned: 27 (million)
% 0.19/0.38 % (25670)------------------------------
% 0.19/0.38 % (25670)------------------------------
% 0.19/0.38 % (25675)Instruction limit reached!
% 0.19/0.38 % (25675)------------------------------
% 0.19/0.38 % (25675)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.38 % (25675)Termination reason: Unknown
% 0.19/0.38 % (25675)Termination phase: Property scanning
% 0.19/0.38
% 0.19/0.38 % (25675)Memory used [KB]: 1023
% 0.19/0.38 % (25675)Time elapsed: 0.004 s
% 0.19/0.38 % (25675)Instructions burned: 3 (million)
% 0.19/0.38 % (25675)------------------------------
% 0.19/0.38 % (25675)------------------------------
% 0.19/0.38 % (25676)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)
% 0.19/0.38 % (25678)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)
% 0.19/0.39 % (25678)Instruction limit reached!
% 0.19/0.39 % (25678)------------------------------
% 0.19/0.39 % (25678)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.39 % (25678)Termination reason: Unknown
% 0.19/0.39 % (25678)Termination phase: Property scanning
% 0.19/0.39
% 0.19/0.39 % (25678)Memory used [KB]: 1023
% 0.19/0.39 % (25678)Time elapsed: 0.004 s
% 0.19/0.39 % (25678)Instructions burned: 4 (million)
% 0.19/0.39 % (25678)------------------------------
% 0.19/0.39 % (25678)------------------------------
% 0.19/0.39 % (25677)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)
% 0.19/0.39 % (25679)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)
% 0.19/0.40 % (25680)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.40 % (25677)Instruction limit reached!
% 0.19/0.40 % (25677)------------------------------
% 0.19/0.40 % (25677)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.40 % (25677)Termination reason: Unknown
% 0.19/0.40 % (25677)Termination phase: Saturation
% 0.19/0.40
% 0.19/0.40 % (25677)Memory used [KB]: 5628
% 0.19/0.40 % (25677)Time elapsed: 0.010 s
% 0.19/0.40 % (25677)Instructions burned: 15 (million)
% 0.19/0.40 % (25677)------------------------------
% 0.19/0.40 % (25677)------------------------------
% 0.19/0.40 % (25681)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.40 % (25680)Instruction limit reached!
% 0.19/0.40 % (25680)------------------------------
% 0.19/0.40 % (25680)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.40 % (25680)Termination reason: Unknown
% 0.19/0.40 % (25680)Termination phase: Saturation
% 0.19/0.40
% 0.19/0.40 % (25680)Memory used [KB]: 1023
% 0.19/0.40 % (25680)Time elapsed: 0.006 s
% 0.19/0.40 % (25680)Instructions burned: 8 (million)
% 0.19/0.40 % (25680)------------------------------
% 0.19/0.40 % (25680)------------------------------
% 0.19/0.40 % (25676)Instruction limit reached!
% 0.19/0.40 % (25676)------------------------------
% 0.19/0.40 % (25676)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.40 % (25676)Termination reason: Unknown
% 0.19/0.40 % (25676)Termination phase: Saturation
% 0.19/0.40
% 0.19/0.40 % (25676)Memory used [KB]: 5628
% 0.19/0.40 % (25676)Time elapsed: 0.021 s
% 0.19/0.40 % (25676)Instructions burned: 37 (million)
% 0.19/0.40 % (25676)------------------------------
% 0.19/0.40 % (25676)------------------------------
% 0.19/0.40 % (25682)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)
% 0.19/0.40 % (25682)Instruction limit reached!
% 0.19/0.40 % (25682)------------------------------
% 0.19/0.40 % (25682)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.40 % (25682)Termination reason: Unknown
% 0.19/0.40 % (25682)Termination phase: SInE selection
% 0.19/0.40
% 0.19/0.40 % (25682)Memory used [KB]: 1023
% 0.19/0.40 % (25682)Time elapsed: 0.004 s
% 0.19/0.40 % (25682)Instructions burned: 4 (million)
% 0.19/0.40 % (25682)------------------------------
% 0.19/0.40 % (25682)------------------------------
% 0.19/0.41 % (25681)Instruction limit reached!
% 0.19/0.41 % (25681)------------------------------
% 0.19/0.41 % (25681)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.41 % (25681)Termination reason: Unknown
% 0.19/0.41 % (25681)Termination phase: Saturation
% 0.19/0.41
% 0.19/0.41 % (25681)Memory used [KB]: 6012
% 0.19/0.41 % (25681)Time elapsed: 0.012 s
% 0.19/0.41 % (25681)Instructions burned: 16 (million)
% 0.19/0.41 % (25681)------------------------------
% 0.19/0.41 % (25681)------------------------------
% 0.19/0.41 % (25683)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)
% 0.19/0.41 % (25684)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)
% 0.19/0.41 % (25683)Instruction limit reached!
% 0.19/0.41 % (25683)------------------------------
% 0.19/0.41 % (25683)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.41 % (25683)Termination reason: Unknown
% 0.19/0.41 % (25683)Termination phase: Preprocessing 3
% 0.19/0.41
% 0.19/0.41 % (25683)Memory used [KB]: 1023
% 0.19/0.41 % (25683)Time elapsed: 0.004 s
% 0.19/0.41 % (25683)Instructions burned: 4 (million)
% 0.19/0.41 % (25683)------------------------------
% 0.19/0.41 % (25683)------------------------------
% 0.19/0.42 % (25685)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)
% 0.19/0.42 % (25686)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.19/0.42 % (25685)Instruction limit reached!
% 0.19/0.42 % (25685)------------------------------
% 0.19/0.42 % (25685)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.42 % (25685)Termination reason: Unknown
% 0.19/0.42 % (25685)Termination phase: Property scanning
% 0.19/0.42
% 0.19/0.42 % (25685)Memory used [KB]: 1023
% 0.19/0.42 % (25685)Time elapsed: 0.004 s
% 0.19/0.42 % (25685)Instructions burned: 4 (million)
% 0.19/0.42 % (25685)------------------------------
% 0.19/0.42 % (25685)------------------------------
% 0.19/0.42 % (25684)Instruction limit reached!
% 0.19/0.42 % (25684)------------------------------
% 0.19/0.42 % (25684)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.42 % (25684)Termination reason: Unknown
% 0.19/0.42 % (25684)Termination phase: Saturation
% 0.19/0.42
% 0.19/0.42 % (25684)Memory used [KB]: 5500
% 0.19/0.42 % (25684)Time elapsed: 0.006 s
% 0.19/0.42 % (25684)Instructions burned: 8 (million)
% 0.19/0.42 % (25684)------------------------------
% 0.19/0.42 % (25684)------------------------------
% 0.19/0.42 % (25686)Instruction limit reached!
% 0.19/0.42 % (25686)------------------------------
% 0.19/0.42 % (25686)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.42 % (25686)Termination reason: Unknown
% 0.19/0.42 % (25686)Termination phase: Property scanning
% 0.19/0.42
% 0.19/0.42 % (25686)Memory used [KB]: 1023
% 0.19/0.42 % (25686)Time elapsed: 0.004 s
% 0.19/0.42 % (25686)Instructions burned: 4 (million)
% 0.19/0.42 % (25686)------------------------------
% 0.19/0.42 % (25686)------------------------------
% 0.19/0.42 % (25687)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)
% 0.19/0.43 % (25688)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.19/0.43 % (25689)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.19/0.43 % (25690)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)
% 0.19/0.43 % (25691)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)
% 0.19/0.44 % (25689)Instruction limit reached!
% 0.19/0.44 % (25689)------------------------------
% 0.19/0.44 % (25689)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.44 % (25689)Termination reason: Unknown
% 0.19/0.44 % (25689)Termination phase: Property scanning
% 0.19/0.44
% 0.19/0.44 % (25689)Memory used [KB]: 1023
% 0.19/0.44 % (25689)Time elapsed: 0.005 s
% 0.19/0.44 % (25689)Instructions burned: 6 (million)
% 0.19/0.44 % (25689)------------------------------
% 0.19/0.44 % (25689)------------------------------
% 0.19/0.44 % (25687)Instruction limit reached!
% 0.19/0.44 % (25687)------------------------------
% 0.19/0.44 % (25687)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.44 % (25687)Termination reason: Unknown
% 0.19/0.44 % (25687)Termination phase: Saturation
% 0.19/0.44
% 0.19/0.44 % (25687)Memory used [KB]: 5628
% 0.19/0.44 % (25687)Time elapsed: 0.017 s
% 0.19/0.44 % (25687)Instructions burned: 18 (million)
% 0.19/0.44 % (25687)------------------------------
% 0.19/0.44 % (25687)------------------------------
% 0.19/0.45 % (25691)Instruction limit reached!
% 0.19/0.45 % (25691)------------------------------
% 0.19/0.45 % (25691)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.45 % (25691)Termination reason: Unknown
% 0.19/0.45 % (25691)Termination phase: Saturation
% 0.19/0.45
% 0.19/0.45 % (25691)Memory used [KB]: 5628
% 0.19/0.45 % (25691)Time elapsed: 0.015 s
% 0.19/0.45 % (25691)Instructions burned: 21 (million)
% 0.19/0.45 % (25691)------------------------------
% 0.19/0.45 % (25691)------------------------------
% 0.19/0.45 % (25692)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.19/0.45 % (25692)Instruction limit reached!
% 0.19/0.45 % (25692)------------------------------
% 0.19/0.45 % (25692)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.45 % (25692)Termination reason: Unknown
% 0.19/0.45 % (25692)Termination phase: Property scanning
% 0.19/0.45
% 0.19/0.45 % (25692)Memory used [KB]: 1023
% 0.19/0.45 % (25692)Time elapsed: 0.005 s
% 0.19/0.45 % (25692)Instructions burned: 7 (million)
% 0.19/0.45 % (25692)------------------------------
% 0.19/0.45 % (25692)------------------------------
% 0.19/0.45 % (25679)First to succeed.
% 0.19/0.46 % (25693)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.19/0.46 % (25694)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.19/0.46 % (25693)Instruction limit reached!
% 0.19/0.46 % (25693)------------------------------
% 0.19/0.46 % (25693)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.46 % (25693)Termination reason: Unknown
% 0.19/0.46 % (25693)Termination phase: Saturation
% 0.19/0.46
% 0.19/0.46 % (25693)Memory used [KB]: 5500
% 0.19/0.46 % (25693)Time elapsed: 0.005 s
% 0.19/0.46 % (25693)Instructions burned: 7 (million)
% 0.19/0.46 % (25693)------------------------------
% 0.19/0.46 % (25693)------------------------------
% 0.19/0.46 % (25679)Refutation found. Thanks to Tanya!
% 0.19/0.46 % SZS status Theorem for theBenchmark
% 0.19/0.46 % SZS output start Proof for theBenchmark
% 0.19/0.46 thf(func_def_0, type, in: $i > $i > $o).
% 0.19/0.46 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.19/0.46 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 0.19/0.46 thf(func_def_4, type, subset: $i > $i > $o).
% 0.19/0.46 thf(func_def_5, type, kpair: $i > $i > $i).
% 0.19/0.46 thf(func_def_6, type, cartprod: $i > $i > $i).
% 0.19/0.46 thf(func_def_7, type, singleton: $i > $o).
% 0.19/0.46 thf(func_def_9, type, ex1: $i > ($i > $o) > $o).
% 0.19/0.46 thf(func_def_10, type, breln: $i > $i > $i > $o).
% 0.19/0.46 thf(func_def_11, type, func: $i > $i > $i > $o).
% 0.19/0.46 thf(func_def_12, type, ap: $i > $i > $i > $i > $i).
% 0.19/0.46 thf(func_def_33, type, ph1: !>[X0: $tType]:(X0)).
% 0.19/0.46 thf(f468,plain,(
% 0.19/0.46 $false),
% 0.19/0.46 inference(avatar_sat_refutation,[],[f211,f344,f467])).
% 0.19/0.46 thf(f467,plain,(
% 0.19/0.46 ~spl0_1),
% 0.19/0.46 inference(avatar_contradiction_clause,[],[f466])).
% 0.19/0.46 thf(f466,plain,(
% 0.19/0.46 $false | ~spl0_1),
% 0.19/0.46 inference(trivial_inequality_removal,[],[f465])).
% 0.19/0.46 thf(f465,plain,(
% 0.19/0.46 ($false = $true) | ~spl0_1),
% 0.19/0.46 inference(forward_demodulation,[],[f458,f394])).
% 0.19/0.46 thf(f394,plain,(
% 0.19/0.46 ((in @ (kpair @ sK8 @ sK9) @ sK5) = $false) | ~spl0_1),
% 0.19/0.46 inference(boolean_simplification,[],[f393])).
% 0.19/0.46 thf(f393,plain,(
% 0.19/0.46 ($false = ($true => (in @ (kpair @ sK8 @ sK9) @ sK5))) | ~spl0_1),
% 0.19/0.46 inference(backward_demodulation,[],[f385,f392])).
% 0.19/0.46 thf(f392,plain,(
% 0.19/0.46 ((in @ (kpair @ sK8 @ sK9) @ sK2) = $true) | ~spl0_1),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f385])).
% 0.19/0.46 thf(f385,plain,(
% 0.19/0.46 ($false = ((in @ (kpair @ sK8 @ sK9) @ sK2) => (in @ (kpair @ sK8 @ sK9) @ sK5))) | ~spl0_1),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f382])).
% 0.19/0.46 thf(f382,plain,(
% 0.19/0.46 (((in @ sK9 @ sK4) => ((in @ (kpair @ sK8 @ sK9) @ sK2) => (in @ (kpair @ sK8 @ sK9) @ sK5))) = $false) | ~spl0_1),
% 0.19/0.46 inference(beta_eta_normalization,[],[f381])).
% 0.19/0.46 thf(f381,plain,(
% 0.19/0.46 ($false = ((^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ sK8 @ Y0) @ sK2) => (in @ (kpair @ sK8 @ Y0) @ sK5)))) @ sK9)) | ~spl0_1),
% 0.19/0.46 inference(sigma_clausification,[],[f359])).
% 0.19/0.46 thf(f359,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ sK8 @ Y0) @ sK2) => (in @ (kpair @ sK8 @ Y0) @ sK5))))) = $false) | ~spl0_1),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f356])).
% 0.19/0.46 thf(f356,plain,(
% 0.19/0.46 (((in @ sK8 @ sK3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ sK8 @ Y0) @ sK2) => (in @ (kpair @ sK8 @ Y0) @ sK5)))))) = $false) | ~spl0_1),
% 0.19/0.46 inference(beta_eta_normalization,[],[f350])).
% 0.19/0.46 thf(f350,plain,(
% 0.19/0.46 (((^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK2) => (in @ (kpair @ Y0 @ Y1) @ sK5))))))) @ sK8) = $false) | ~spl0_1),
% 0.19/0.46 inference(sigma_clausification,[],[f207])).
% 0.19/0.46 thf(f207,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK2) => (in @ (kpair @ Y0 @ Y1) @ sK5)))))))) = $false) | ~spl0_1),
% 0.19/0.46 inference(avatar_component_clause,[],[f206])).
% 0.19/0.46 thf(f206,plain,(
% 0.19/0.46 spl0_1 <=> ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK2) => (in @ (kpair @ Y0 @ Y1) @ sK5)))))))) = $false)),
% 0.19/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.19/0.46 thf(f458,plain,(
% 0.19/0.46 ((in @ (kpair @ sK8 @ sK9) @ sK5) = $true) | ~spl0_1),
% 0.19/0.46 inference(backward_demodulation,[],[f398,f449])).
% 0.19/0.46 thf(f449,plain,(
% 0.19/0.46 (sK9 = (ap @ sK3 @ sK4 @ sK2 @ sK8)) | ~spl0_1),
% 0.19/0.46 inference(equality_proxy_clausification,[],[f442])).
% 0.19/0.46 thf(f442,plain,(
% 0.19/0.46 (((ap @ sK3 @ sK4 @ sK2 @ sK8) = sK9) = $true) | ~spl0_1),
% 0.19/0.46 inference(boolean_simplification,[],[f441])).
% 0.19/0.46 thf(f441,plain,(
% 0.19/0.46 (($true => ((ap @ sK3 @ sK4 @ sK2 @ sK8) = sK9)) = $true) | ~spl0_1),
% 0.19/0.46 inference(forward_demodulation,[],[f434,f392])).
% 0.19/0.46 thf(f434,plain,(
% 0.19/0.46 (((in @ (kpair @ sK8 @ sK9) @ sK2) => ((ap @ sK3 @ sK4 @ sK2 @ sK8) = sK9)) = $true) | ~spl0_1),
% 0.19/0.46 inference(boolean_simplification,[],[f432])).
% 0.19/0.46 thf(f432,plain,(
% 0.19/0.46 ($true = ($true => ((in @ (kpair @ sK8 @ sK9) @ sK2) => ((ap @ sK3 @ sK4 @ sK2 @ sK8) = sK9)))) | ~spl0_1),
% 0.19/0.46 inference(superposition,[],[f426,f386])).
% 0.19/0.46 thf(f386,plain,(
% 0.19/0.46 ((in @ sK9 @ sK4) = $true) | ~spl0_1),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f382])).
% 0.19/0.46 thf(f426,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((in @ X1 @ sK4) => ((in @ (kpair @ sK8 @ X1) @ sK2) => ((ap @ sK3 @ sK4 @ sK2 @ sK8) = X1))) = $true)) ) | ~spl0_1),
% 0.19/0.46 inference(beta_eta_normalization,[],[f424])).
% 0.19/0.46 thf(f424,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ sK8 @ Y0) @ sK2) => ((ap @ sK3 @ sK4 @ sK2 @ sK8) = Y0)))) @ X1) = $true)) ) | ~spl0_1),
% 0.19/0.46 inference(pi_clausification,[],[f376])).
% 0.19/0.46 thf(f376,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ sK8 @ Y0) @ sK2) => ((ap @ sK3 @ sK4 @ sK2 @ sK8) = Y0))))) = $true) | ~spl0_1),
% 0.19/0.46 inference(boolean_simplification,[],[f368])).
% 0.19/0.46 thf(f368,plain,(
% 0.19/0.46 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ sK8 @ Y0) @ sK2) => ((ap @ sK3 @ sK4 @ sK2 @ sK8) = Y0)))))) = $true) | ~spl0_1),
% 0.19/0.46 inference(superposition,[],[f156,f360])).
% 0.19/0.46 thf(f360,plain,(
% 0.19/0.46 ((in @ sK8 @ sK3) = $true) | ~spl0_1),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f356])).
% 0.19/0.46 thf(f156,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ X1 @ Y0) @ sK2) => ((ap @ sK3 @ sK4 @ sK2 @ X1) = Y0)))))))) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f154])).
% 0.19/0.46 thf(f154,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK2) => ((ap @ sK3 @ sK4 @ sK2 @ Y0) = Y1))))))) @ X1) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f98])).
% 0.19/0.46 thf(f98,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK2) => ((ap @ sK3 @ sK4 @ sK2 @ Y0) = Y1)))))))) = $true)),
% 0.19/0.46 inference(boolean_simplification,[],[f96])).
% 0.19/0.46 thf(f96,plain,(
% 0.19/0.46 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK2) => ((ap @ sK3 @ sK4 @ sK2 @ Y0) = Y1))))))))) = $true)),
% 0.19/0.46 inference(superposition,[],[f67,f89])).
% 0.19/0.46 thf(f89,plain,(
% 0.19/0.46 (((subset @ sK2 @ (cartprod @ sK3 @ sK4)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK4 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK4 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2))))))))))) = $true)),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f87])).
% 0.19/0.46 thf(f87,plain,(
% 0.19/0.46 ((((subset @ sK2 @ (cartprod @ sK3 @ sK4)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK4 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK4 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2))))))))))) => (!! @ $i @ (^[Y0 : $i]: (((subset @ Y0 @ (cartprod @ sK3 @ sK4)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ sK4 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK4 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0))))))))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => ((ap @ sK3 @ sK4 @ sK2 @ Y1) = (ap @ sK3 @ sK4 @ Y0 @ Y1))))) => (sK2 = Y0)))))) = $false)),
% 0.19/0.46 inference(beta_eta_normalization,[],[f86])).
% 0.19/0.46 thf(f86,plain,(
% 0.19/0.46 (((^[Y0 : $i]: (((subset @ sK2 @ (cartprod @ sK3 @ Y0)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ sK2)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ sK2))))))))))) => (!! @ $i @ (^[Y1 : $i]: (((subset @ Y1 @ (cartprod @ sK3 @ Y0)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK3) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1))))))))))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK3) => ((ap @ sK3 @ Y0 @ sK2 @ Y2) = (ap @ sK3 @ Y0 @ Y1 @ Y2))))) => (sK2 = Y1))))))) @ sK4) = $false)),
% 0.19/0.46 inference(sigma_clausification,[],[f85])).
% 0.19/0.46 thf(f85,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: (((subset @ sK2 @ (cartprod @ sK3 @ Y0)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ sK2)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ sK2))))))))))) => (!! @ $i @ (^[Y1 : $i]: (((subset @ Y1 @ (cartprod @ sK3 @ Y0)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK3) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ Y1))))))))))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK3) => ((ap @ sK3 @ Y0 @ sK2 @ Y2) = (ap @ sK3 @ Y0 @ Y1 @ Y2))))) => (sK2 = Y1)))))))) = $false)),
% 0.19/0.46 inference(beta_eta_normalization,[],[f84])).
% 0.19/0.46 thf(f84,plain,(
% 0.19/0.46 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ sK2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ sK2)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ sK2))))))))))) => (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ap @ Y0 @ Y1 @ sK2 @ Y3) = (ap @ Y0 @ Y1 @ Y2 @ Y3))))) => (sK2 = Y2))))))))) @ sK3) = $false)),
% 0.19/0.46 inference(sigma_clausification,[],[f83])).
% 0.19/0.46 thf(f83,plain,(
% 0.19/0.46 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ sK2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ sK2)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ sK2))))))))))) => (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((ap @ Y0 @ Y1 @ sK2 @ Y3) = (ap @ Y0 @ Y1 @ Y2 @ Y3))))) => (sK2 = Y2)))))))))))),
% 0.19/0.46 inference(beta_eta_normalization,[],[f82])).
% 0.19/0.46 thf(f82,plain,(
% 0.19/0.46 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: (((subset @ Y3 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (dsetconstr @ Y2 @ (^[Y6 : $i]: (in @ (kpair @ Y4 @ Y6) @ Y3)))) & ((setadjoin @ Y5 @ emptyset) = (dsetconstr @ Y2 @ (^[Y6 : $i]: (in @ (kpair @ Y4 @ Y6) @ Y3))))))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y0 @ Y4) = (ap @ Y1 @ Y2 @ Y3 @ Y4))))) => (Y0 = Y3))))))))))) @ sK2) = $false)),
% 0.19/0.46 inference(sigma_clausification,[],[f69])).
% 0.19/0.46 thf(f69,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: (((subset @ Y3 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (dsetconstr @ Y2 @ (^[Y6 : $i]: (in @ (kpair @ Y4 @ Y6) @ Y3)))) & ((setadjoin @ Y5 @ emptyset) = (dsetconstr @ Y2 @ (^[Y6 : $i]: (in @ (kpair @ Y4 @ Y6) @ Y3))))))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y0 @ Y4) = (ap @ Y1 @ Y2 @ Y3 @ Y4))))) => (Y0 = Y3)))))))))))) = $false)),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f49])).
% 0.19/0.46 thf(f49,plain,(
% 0.19/0.46 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ (cartprod @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((subset @ Y3 @ (cartprod @ Y1 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = Y3))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: (((subset @ Y3 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (dsetconstr @ Y2 @ (^[Y6 : $i]: (in @ (kpair @ Y4 @ Y6) @ Y3)))) & ((setadjoin @ Y5 @ emptyset) = (dsetconstr @ Y2 @ (^[Y6 : $i]: (in @ (kpair @ Y4 @ Y6) @ Y3))))))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y0 @ Y4) = (ap @ Y1 @ Y2 @ Y3 @ Y4))))) => (Y0 = Y3))))))))))))) = $false)),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f48])).
% 0.19/0.46 thf(f48,plain,(
% 0.19/0.46 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => ((ap @ Y1 @ Y2 @ Y0 @ Y3) = Y4))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ (cartprod @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((subset @ Y3 @ (cartprod @ Y1 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = Y3))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: (((subset @ Y3 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (dsetconstr @ Y2 @ (^[Y6 : $i]: (in @ (kpair @ Y4 @ Y6) @ Y3)))) & ((setadjoin @ Y5 @ emptyset) = (dsetconstr @ Y2 @ (^[Y6 : $i]: (in @ (kpair @ Y4 @ Y6) @ Y3))))))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y0 @ Y4) = (ap @ Y1 @ Y2 @ Y3 @ Y4))))) => (Y0 = Y3)))))))))))))) = $false)),
% 0.19/0.46 inference(boolean_simplification,[],[f47])).
% 0.19/0.46 thf(f47,plain,(
% 0.19/0.46 ($false = ($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => ((ap @ Y1 @ Y2 @ Y0 @ Y3) = Y4))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ (cartprod @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((subset @ Y3 @ (cartprod @ Y1 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = Y3))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: (((subset @ Y3 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (dsetconstr @ Y2 @ (^[Y6 : $i]: (in @ (kpair @ Y4 @ Y6) @ Y3)))) & ((setadjoin @ Y5 @ emptyset) = (dsetconstr @ Y2 @ (^[Y6 : $i]: (in @ (kpair @ Y4 @ Y6) @ Y3))))))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y0 @ Y4) = (ap @ Y1 @ Y2 @ Y3 @ Y4))))) => (Y0 = Y3))))))))))))))))),
% 0.19/0.46 inference(backward_demodulation,[],[f42,f46])).
% 0.19/0.46 thf(f46,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y2 @ Y0 @ Y3)) @ Y0))))))))))) = $true)),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f42])).
% 0.19/0.46 thf(f42,plain,(
% 0.19/0.46 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y2 @ Y0 @ Y3)) @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => ((ap @ Y1 @ Y2 @ Y0 @ Y3) = Y4))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ (cartprod @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((subset @ Y3 @ (cartprod @ Y1 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = Y3))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: (((subset @ Y3 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (dsetconstr @ Y2 @ (^[Y6 : $i]: (in @ (kpair @ Y4 @ Y6) @ Y3)))) & ((setadjoin @ Y5 @ emptyset) = (dsetconstr @ Y2 @ (^[Y6 : $i]: (in @ (kpair @ Y4 @ Y6) @ Y3))))))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y0 @ Y4) = (ap @ Y1 @ Y2 @ Y3 @ Y4))))) => (Y0 = Y3))))))))))))))) = $false)),
% 0.19/0.46 inference(not_proxy_clausification,[],[f41])).
% 0.19/0.46 thf(f41,plain,(
% 0.19/0.46 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y2 @ Y0 @ Y3)) @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => ((ap @ Y1 @ Y2 @ Y0 @ Y3) = Y4))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ (cartprod @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((subset @ Y3 @ (cartprod @ Y1 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = Y3))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: (((subset @ Y3 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (dsetconstr @ Y2 @ (^[Y6 : $i]: (in @ (kpair @ Y4 @ Y6) @ Y3)))) & ((setadjoin @ Y5 @ emptyset) = (dsetconstr @ Y2 @ (^[Y6 : $i]: (in @ (kpair @ Y4 @ Y6) @ Y3))))))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y0 @ Y4) = (ap @ Y1 @ Y2 @ Y3 @ Y4))))) => (Y0 = Y3)))))))))))))))) = $true)),
% 0.19/0.46 inference(beta_eta_normalization,[],[f40])).
% 0.19/0.46 thf(f40,plain,(
% 0.19/0.46 ((~ ((!! @ $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]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y2 @ Y0 @ Y3)) @ Y0))))))))))) => ((!! @ $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]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => ((ap @ Y1 @ Y2 @ Y0 @ Y3) = Y4))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = 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]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (subset @ Y9 @ (cartprod @ Y7 @ Y8))))))) @ Y4 @ Y5 @ Y6) & (!! @ $i @ (^[Y7 : $i]: ((in @ Y7 @ Y4) => ((^[Y8 : $i]: ((^[Y9 : $i > $o]: ((^[Y10 : $i]: (?? @ $i @ (^[Y11 : $i]: ((in @ Y11 @ Y10) & ((setadjoin @ Y11 @ emptyset) = Y10))))) @ (dsetconstr @ Y8 @ (^[Y10 : $i]: (Y9 @ Y10))))))) @ Y5 @ (^[Y8 : $i]: (in @ (kpair @ Y7 @ Y8) @ Y6)))))))))))) @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((ap @ Y1 @ Y2 @ Y0 @ Y4) = (ap @ Y1 @ Y2 @ Y3 @ Y4))))) => (Y0 = Y3)))))))))))))))) = $true)),
% 0.19/0.46 inference(definition_unfolding,[],[f27,f37,f38,f39,f36,f36])).
% 0.19/0.46 thf(f36,plain,(
% 0.19/0.46 (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]: ((in @ Y7 @ Y6) & ((setadjoin @ Y7 @ emptyset) = Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 0.19/0.46 inference(definition_unfolding,[],[f28,f32,f35])).
% 0.19/0.46 thf(f35,plain,(
% 0.19/0.46 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & ((setadjoin @ Y3 @ emptyset) = Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.19/0.46 inference(definition_unfolding,[],[f29,f30])).
% 0.19/0.46 thf(f30,plain,(
% 0.19/0.46 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 0.19/0.46 inference(cnf_transformation,[],[f22])).
% 0.19/0.46 thf(f22,plain,(
% 0.19/0.46 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 0.19/0.46 inference(fool_elimination,[],[f21])).
% 0.19/0.46 thf(f21,plain,(
% 0.19/0.46 (singleton = (^[X0 : $i] : (? [X1] : (((setadjoin @ X1 @ emptyset) = X0) & (in @ X1 @ X0)))))),
% 0.19/0.46 inference(rectify,[],[f1])).
% 0.19/0.46 thf(f1,axiom,(
% 0.19/0.46 (singleton = (^[X0 : $i] : (? [X1] : (((setadjoin @ X1 @ emptyset) = X0) & (in @ X1 @ X0)))))),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)).
% 0.19/0.46 thf(f29,plain,(
% 0.19/0.46 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.19/0.46 inference(cnf_transformation,[],[f18])).
% 0.19/0.46 thf(f18,plain,(
% 0.19/0.46 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.19/0.46 inference(fool_elimination,[],[f17])).
% 0.19/0.46 thf(f17,plain,(
% 0.19/0.46 (ex1 = (^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))),
% 0.19/0.46 inference(rectify,[],[f2])).
% 0.19/0.46 thf(f2,axiom,(
% 0.19/0.46 (ex1 = (^[X0 : $i, X2 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X1 : $i] : (X2 @ X1))))))),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1)).
% 0.19/0.46 thf(f32,plain,(
% 0.19/0.46 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.19/0.46 inference(cnf_transformation,[],[f24])).
% 0.19/0.46 thf(f24,plain,(
% 0.19/0.46 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.19/0.46 inference(fool_elimination,[],[f23])).
% 0.19/0.46 thf(f23,plain,(
% 0.19/0.46 ((^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))) = breln)),
% 0.19/0.46 inference(rectify,[],[f3])).
% 0.19/0.46 thf(f3,axiom,(
% 0.19/0.46 ((^[X0 : $i, X3 : $i, X4 : $i] : (subset @ X4 @ (cartprod @ X0 @ X3))) = breln)),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln)).
% 0.19/0.46 thf(f28,plain,(
% 0.19/0.46 (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)))))))))))))),
% 0.19/0.46 inference(cnf_transformation,[],[f16])).
% 0.19/0.46 thf(f16,plain,(
% 0.19/0.46 (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)))))))))))))),
% 0.19/0.46 inference(fool_elimination,[],[f15])).
% 0.19/0.46 thf(f15,plain,(
% 0.19/0.46 ((^[X0 : $i, X1 : $i, X2 : $i] : (! [X3] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))) & (breln @ X0 @ X1 @ X2))) = func)),
% 0.19/0.46 inference(rectify,[],[f4])).
% 0.19/0.46 thf(f4,axiom,(
% 0.19/0.46 ((^[X0 : $i, X3 : $i, X5 : $i] : (! [X1] : ((in @ X1 @ X0) => (ex1 @ X3 @ (^[X6 : $i] : (in @ (kpair @ X1 @ X6) @ X5)))) & (breln @ X0 @ X3 @ X5))) = func)),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',func)).
% 0.19/0.46 thf(f39,plain,(
% 0.19/0.46 (eqbreln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (subset @ Y6 @ (cartprod @ Y4 @ Y5))))))) @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = Y3))))))))))))))),
% 0.19/0.46 inference(definition_unfolding,[],[f33,f32,f32])).
% 0.19/0.46 thf(f33,plain,(
% 0.19/0.46 (eqbreln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((breln @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = Y3))))))))))))))),
% 0.19/0.46 inference(cnf_transformation,[],[f14])).
% 0.19/0.46 thf(f14,plain,(
% 0.19/0.46 (eqbreln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((breln @ Y1 @ Y2 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = Y3))))))))))))))),
% 0.19/0.46 inference(fool_elimination,[],[f13])).
% 0.19/0.46 thf(f13,plain,(
% 0.19/0.46 (! [X0,X1,X2] : ((breln @ X1 @ X0 @ X2) => ! [X3] : ((breln @ X1 @ X0 @ X3) => (! [X4] : ((in @ X4 @ X1) => ! [X5] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (! [X6] : ((in @ X6 @ X1) => ! [X7] : ((in @ X7 @ X0) => ((in @ (kpair @ X6 @ X7) @ X3) => (in @ (kpair @ X6 @ X7) @ X2)))) => (X2 = X3))))) = eqbreln)),
% 0.19/0.46 inference(rectify,[],[f7])).
% 0.19/0.46 thf(f7,axiom,(
% 0.19/0.46 (! [X3,X0,X5] : ((breln @ X0 @ X3 @ X5) => ! [X8] : ((breln @ X0 @ X3 @ X8) => (! [X1] : ((in @ X1 @ X0) => ! [X6] : ((in @ X6 @ X3) => ((in @ (kpair @ X1 @ X6) @ X5) => (in @ (kpair @ X1 @ X6) @ X8)))) => (! [X1] : ((in @ X1 @ X0) => ! [X6] : ((in @ X6 @ X3) => ((in @ (kpair @ X1 @ X6) @ X8) => (in @ (kpair @ X1 @ X6) @ X5)))) => (X5 = X8))))) = eqbreln)),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqbreln)).
% 0.19/0.46 thf(f38,plain,(
% 0.19/0.46 (funcGraphProp2 = (!! @ $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]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => ((ap @ Y1 @ Y2 @ Y0 @ Y3) = Y4))))))))))))))))),
% 0.19/0.46 inference(definition_unfolding,[],[f34,f36])).
% 0.19/0.46 thf(f34,plain,(
% 0.19/0.46 (funcGraphProp2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => ((ap @ Y1 @ Y2 @ Y0 @ Y3) = Y4))))))))))))))))),
% 0.19/0.46 inference(cnf_transformation,[],[f12])).
% 0.19/0.46 thf(f12,plain,(
% 0.19/0.46 (funcGraphProp2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => ((ap @ Y1 @ Y2 @ Y0 @ Y3) = Y4))))))))))))))))),
% 0.19/0.46 inference(fool_elimination,[],[f11])).
% 0.19/0.46 thf(f11,plain,(
% 0.19/0.46 (funcGraphProp2 = ! [X0,X1,X2] : ((func @ X1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X1) => ! [X4] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X2) => ((ap @ X1 @ X0 @ X2 @ X3) = X4))))))),
% 0.19/0.46 inference(rectify,[],[f6])).
% 0.19/0.46 thf(f6,axiom,(
% 0.19/0.46 (funcGraphProp2 = ! [X3,X0,X7] : ((func @ X0 @ X3 @ X7) => ! [X1] : ((in @ X1 @ X0) => ! [X6] : ((in @ X6 @ X3) => ((in @ (kpair @ X1 @ X6) @ X7) => ((ap @ X0 @ X3 @ X7 @ X1) = X6))))))),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp2)).
% 0.19/0.46 thf(f37,plain,(
% 0.19/0.46 (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]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y2 @ Y0 @ Y3)) @ Y0))))))))))))),
% 0.19/0.46 inference(definition_unfolding,[],[f31,f36])).
% 0.19/0.46 thf(f31,plain,(
% 0.19/0.46 (funcGraphProp1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y2 @ Y0 @ Y3)) @ Y0))))))))))))),
% 0.19/0.46 inference(cnf_transformation,[],[f20])).
% 0.19/0.46 thf(f20,plain,(
% 0.19/0.46 (funcGraphProp1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y2 @ Y0 @ Y3)) @ Y0))))))))))))),
% 0.19/0.46 inference(fool_elimination,[],[f19])).
% 0.19/0.46 thf(f19,plain,(
% 0.19/0.46 (funcGraphProp1 = ! [X0,X1,X2] : ((func @ X1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X1) => (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2))))),
% 0.19/0.46 inference(rectify,[],[f5])).
% 0.19/0.46 thf(f5,axiom,(
% 0.19/0.46 (funcGraphProp1 = ! [X3,X0,X7] : ((func @ X0 @ X3 @ X7) => ! [X1] : ((in @ X1 @ X0) => (in @ (kpair @ X1 @ (ap @ X0 @ X3 @ X7 @ X1)) @ X7))))),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp1)).
% 0.19/0.46 thf(f27,plain,(
% 0.19/0.46 ((~ (funcGraphProp1 => (funcGraphProp2 => (eqbreln => (!! @ $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 @ Y0 @ Y4) = (ap @ Y1 @ Y2 @ Y3 @ Y4))))) => (Y0 = Y3)))))))))))))))) = $true)),
% 0.19/0.46 inference(cnf_transformation,[],[f26])).
% 0.19/0.46 thf(f26,plain,(
% 0.19/0.46 ((~ (funcGraphProp1 => (funcGraphProp2 => (eqbreln => (!! @ $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 @ Y0 @ Y4) = (ap @ Y1 @ Y2 @ Y3 @ Y4))))) => (Y0 = Y3)))))))))))))))) = $true)),
% 0.19/0.46 inference(fool_elimination,[],[f25])).
% 0.19/0.46 thf(f25,plain,(
% 0.19/0.46 ~(funcGraphProp1 => (funcGraphProp2 => (eqbreln => ! [X0,X1,X2] : ((func @ X1 @ X0 @ X2) => ! [X3] : ((func @ X1 @ X0 @ X3) => (! [X4] : ((in @ X4 @ X1) => ((ap @ X1 @ X0 @ X2 @ X4) = (ap @ X1 @ X0 @ X3 @ X4))) => (X2 = X3)))))))),
% 0.19/0.46 inference(rectify,[],[f9])).
% 0.19/0.46 thf(f9,negated_conjecture,(
% 0.19/0.46 ~(funcGraphProp1 => (funcGraphProp2 => (eqbreln => ! [X3,X0,X7] : ((func @ X0 @ X3 @ X7) => ! [X9] : ((func @ X0 @ X3 @ X9) => (! [X1] : ((in @ X1 @ X0) => ((ap @ X0 @ X3 @ X7 @ X1) = (ap @ X0 @ X3 @ X9 @ X1))) => (X7 = X9)))))))),
% 0.19/0.46 inference(negated_conjecture,[],[f8])).
% 0.19/0.46 thf(f8,conjecture,(
% 0.19/0.46 funcGraphProp1 => (funcGraphProp2 => (eqbreln => ! [X3,X0,X7] : ((func @ X0 @ X3 @ X7) => ! [X9] : ((func @ X0 @ X3 @ X9) => (! [X1] : ((in @ X1 @ X0) => ((ap @ X0 @ X3 @ X7 @ X1) = (ap @ X0 @ X3 @ X9 @ X1))) => (X7 = X9))))))),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcext)).
% 0.19/0.46 thf(f67,plain,(
% 0.19/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((subset @ X1 @ (cartprod @ X2 @ X3)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X3 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X3 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1))))))))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => ((in @ (kpair @ Y0 @ Y1) @ X1) => ((ap @ X2 @ X3 @ X1 @ Y0) = Y1))))))))))) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f66])).
% 0.19/0.46 thf(f66,plain,(
% 0.19/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((subset @ X1 @ (cartprod @ X2 @ Y0)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X1)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X1))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ (kpair @ Y1 @ Y2) @ X1) => ((ap @ X2 @ Y0 @ X1 @ Y1) = Y2)))))))))) @ X3) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f65])).
% 0.19/0.46 thf(f65,plain,(
% 0.19/0.46 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((subset @ X1 @ (cartprod @ X2 @ Y0)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X1)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X1))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ (kpair @ Y1 @ Y2) @ X1) => ((ap @ X2 @ Y0 @ X1 @ Y1) = Y2))))))))))))) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f64])).
% 0.19/0.46 thf(f64,plain,(
% 0.19/0.46 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ X1 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ X1)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ X1))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ (kpair @ Y2 @ Y3) @ X1) => ((ap @ Y0 @ Y1 @ X1 @ Y2) = Y3)))))))))))) @ X2) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f63])).
% 0.19/0.46 thf(f63,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ X1 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ X1)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ X1))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ (kpair @ Y2 @ Y3) @ X1) => ((ap @ Y0 @ Y1 @ X1 @ Y2) = Y3))))))))))))) = $true)) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f62])).
% 0.19/0.46 thf(f62,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => ((ap @ Y1 @ Y2 @ Y0 @ Y3) = Y4)))))))))))))) @ X1) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f50])).
% 0.19/0.46 thf(f50,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => ((ap @ Y1 @ Y2 @ Y0 @ Y3) = Y4))))))))))))))) = $true)),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f48])).
% 0.19/0.46 thf(f398,plain,(
% 0.19/0.46 ($true = (in @ (kpair @ sK8 @ (ap @ sK3 @ sK4 @ sK2 @ sK8)) @ sK5)) | ~spl0_1),
% 0.19/0.46 inference(backward_demodulation,[],[f373,f395])).
% 0.19/0.46 thf(f395,plain,(
% 0.19/0.46 ((ap @ sK3 @ sK4 @ sK5 @ sK8) = (ap @ sK3 @ sK4 @ sK2 @ sK8)) | ~spl0_1),
% 0.19/0.46 inference(equality_proxy_clausification,[],[f374])).
% 0.19/0.46 thf(f374,plain,(
% 0.19/0.46 (((ap @ sK3 @ sK4 @ sK2 @ sK8) = (ap @ sK3 @ sK4 @ sK5 @ sK8)) = $true) | ~spl0_1),
% 0.19/0.46 inference(boolean_simplification,[],[f367])).
% 0.19/0.46 thf(f367,plain,(
% 0.19/0.46 (($true => ((ap @ sK3 @ sK4 @ sK2 @ sK8) = (ap @ sK3 @ sK4 @ sK5 @ sK8))) = $true) | ~spl0_1),
% 0.19/0.46 inference(superposition,[],[f152,f360])).
% 0.19/0.46 thf(f152,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((in @ X1 @ sK3) => ((ap @ sK3 @ sK4 @ sK2 @ X1) = (ap @ sK3 @ sK4 @ sK5 @ X1))) = $true)) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f151])).
% 0.19/0.46 thf(f151,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK3) => ((ap @ sK3 @ sK4 @ sK2 @ Y0) = (ap @ sK3 @ sK4 @ sK5 @ Y0)))) @ X1) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f119])).
% 0.19/0.46 thf(f119,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((ap @ sK3 @ sK4 @ sK2 @ Y0) = (ap @ sK3 @ sK4 @ sK5 @ Y0))))) = $true)),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f102])).
% 0.19/0.46 thf(f102,plain,(
% 0.19/0.46 ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((ap @ sK3 @ sK4 @ sK2 @ Y0) = (ap @ sK3 @ sK4 @ sK5 @ Y0))))) => (sK2 = sK5)))),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f93])).
% 0.19/0.46 thf(f93,plain,(
% 0.19/0.46 ((((subset @ sK5 @ (cartprod @ sK3 @ sK4)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK4 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK5)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK4 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK5))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((ap @ sK3 @ sK4 @ sK2 @ Y0) = (ap @ sK3 @ sK4 @ sK5 @ Y0))))) => (sK2 = sK5))) = $false)),
% 0.19/0.46 inference(beta_eta_normalization,[],[f92])).
% 0.19/0.46 thf(f92,plain,(
% 0.19/0.46 ($false = ((^[Y0 : $i]: (((subset @ Y0 @ (cartprod @ sK3 @ sK4)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ sK4 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK4 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0))))))))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => ((ap @ sK3 @ sK4 @ sK2 @ Y1) = (ap @ sK3 @ sK4 @ Y0 @ Y1))))) => (sK2 = Y0)))) @ sK5))),
% 0.19/0.46 inference(sigma_clausification,[],[f91])).
% 0.19/0.46 thf(f91,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: (((subset @ Y0 @ (cartprod @ sK3 @ sK4)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ sK4 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK4 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0))))))))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => ((ap @ sK3 @ sK4 @ sK2 @ Y1) = (ap @ sK3 @ sK4 @ Y0 @ Y1))))) => (sK2 = Y0))))) = $false)),
% 0.19/0.46 inference(boolean_simplification,[],[f90])).
% 0.19/0.46 thf(f90,plain,(
% 0.19/0.46 ($false = ($true => (!! @ $i @ (^[Y0 : $i]: (((subset @ Y0 @ (cartprod @ sK3 @ sK4)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ sK4 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK4 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0))))))))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => ((ap @ sK3 @ sK4 @ sK2 @ Y1) = (ap @ sK3 @ sK4 @ Y0 @ Y1))))) => (sK2 = Y0)))))))),
% 0.19/0.46 inference(backward_demodulation,[],[f87,f89])).
% 0.19/0.46 thf(f373,plain,(
% 0.19/0.46 ((in @ (kpair @ sK8 @ (ap @ sK3 @ sK4 @ sK5 @ sK8)) @ sK5) = $true) | ~spl0_1),
% 0.19/0.46 inference(boolean_simplification,[],[f366])).
% 0.19/0.46 thf(f366,plain,(
% 0.19/0.46 (($true => (in @ (kpair @ sK8 @ (ap @ sK3 @ sK4 @ sK5 @ sK8)) @ sK5)) = $true) | ~spl0_1),
% 0.19/0.46 inference(superposition,[],[f148,f360])).
% 0.19/0.46 thf(f148,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((in @ X1 @ sK3) => (in @ (kpair @ X1 @ (ap @ sK3 @ sK4 @ sK5 @ X1)) @ sK5)) = $true)) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f146])).
% 0.19/0.46 thf(f146,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (kpair @ Y0 @ (ap @ sK3 @ sK4 @ sK5 @ Y0)) @ sK5))) @ X1) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f132])).
% 0.19/0.46 thf(f132,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (kpair @ Y0 @ (ap @ sK3 @ sK4 @ sK5 @ Y0)) @ sK5)))) = $true)),
% 0.19/0.46 inference(boolean_simplification,[],[f130])).
% 0.19/0.46 thf(f130,plain,(
% 0.19/0.46 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (kpair @ Y0 @ (ap @ sK3 @ sK4 @ sK5 @ Y0)) @ sK5))))))),
% 0.19/0.46 inference(superposition,[],[f60,f103])).
% 0.19/0.46 thf(f103,plain,(
% 0.19/0.46 (((subset @ sK5 @ (cartprod @ sK3 @ sK4)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK4 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK5)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK4 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK5))))))))))) = $true)),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f93])).
% 0.19/0.46 thf(f60,plain,(
% 0.19/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((subset @ X1 @ (cartprod @ X2 @ X3)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X3 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X3 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1))))))))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ (kpair @ Y0 @ (ap @ X2 @ X3 @ X1 @ Y0)) @ X1))))) = $true)) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f59])).
% 0.19/0.46 thf(f59,plain,(
% 0.19/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((subset @ X1 @ (cartprod @ X2 @ Y0)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X1)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X1))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (in @ (kpair @ Y1 @ (ap @ X2 @ Y0 @ X1 @ Y1)) @ X1)))))) @ X3) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f58])).
% 0.19/0.46 thf(f58,plain,(
% 0.19/0.46 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((subset @ X1 @ (cartprod @ X2 @ Y0)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X1)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X1))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (in @ (kpair @ Y1 @ (ap @ X2 @ Y0 @ X1 @ Y1)) @ X1))))))) = $true)) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f57])).
% 0.19/0.46 thf(f57,plain,(
% 0.19/0.46 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ X1 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ X1)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ X1))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (kpair @ Y2 @ (ap @ Y0 @ Y1 @ X1 @ Y2)) @ X1)))))))) @ X2) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f56])).
% 0.19/0.46 thf(f56,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ X1 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ X1)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ X1))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (kpair @ Y2 @ (ap @ Y0 @ Y1 @ X1 @ Y2)) @ X1))))))))) = $true)) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f55])).
% 0.19/0.46 thf(f55,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y3 @ (ap @ Y1 @ Y2 @ Y0 @ Y3)) @ Y0)))))))))) @ X1) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f46])).
% 0.19/0.46 thf(f344,plain,(
% 0.19/0.46 ~spl0_2),
% 0.19/0.46 inference(avatar_contradiction_clause,[],[f343])).
% 0.19/0.46 thf(f343,plain,(
% 0.19/0.46 $false | ~spl0_2),
% 0.19/0.46 inference(trivial_inequality_removal,[],[f342])).
% 0.19/0.46 thf(f342,plain,(
% 0.19/0.46 ($false = $true) | ~spl0_2),
% 0.19/0.46 inference(forward_demodulation,[],[f333,f271])).
% 0.19/0.46 thf(f271,plain,(
% 0.19/0.46 ((in @ (kpair @ sK6 @ sK7) @ sK2) = $false) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f270])).
% 0.19/0.46 thf(f270,plain,(
% 0.19/0.46 (($true => (in @ (kpair @ sK6 @ sK7) @ sK2)) = $false) | ~spl0_2),
% 0.19/0.46 inference(backward_demodulation,[],[f267,f269])).
% 0.19/0.46 thf(f269,plain,(
% 0.19/0.46 ((in @ (kpair @ sK6 @ sK7) @ sK5) = $true) | ~spl0_2),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f267])).
% 0.19/0.46 thf(f267,plain,(
% 0.19/0.46 ($false = ((in @ (kpair @ sK6 @ sK7) @ sK5) => (in @ (kpair @ sK6 @ sK7) @ sK2))) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f266])).
% 0.19/0.46 thf(f266,plain,(
% 0.19/0.46 (($true => ((in @ (kpair @ sK6 @ sK7) @ sK5) => (in @ (kpair @ sK6 @ sK7) @ sK2))) = $false) | ~spl0_2),
% 0.19/0.46 inference(backward_demodulation,[],[f261,f265])).
% 0.19/0.46 thf(f265,plain,(
% 0.19/0.46 ($true = (in @ sK7 @ sK4)) | ~spl0_2),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f261])).
% 0.19/0.46 thf(f261,plain,(
% 0.19/0.46 (((in @ sK7 @ sK4) => ((in @ (kpair @ sK6 @ sK7) @ sK5) => (in @ (kpair @ sK6 @ sK7) @ sK2))) = $false) | ~spl0_2),
% 0.19/0.46 inference(beta_eta_normalization,[],[f260])).
% 0.19/0.46 thf(f260,plain,(
% 0.19/0.46 (((^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ sK6 @ Y0) @ sK5) => (in @ (kpair @ sK6 @ Y0) @ sK2)))) @ sK7) = $false) | ~spl0_2),
% 0.19/0.46 inference(sigma_clausification,[],[f240])).
% 0.19/0.46 thf(f240,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ sK6 @ Y0) @ sK5) => (in @ (kpair @ sK6 @ Y0) @ sK2))))) = $false) | ~spl0_2),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f239])).
% 0.19/0.46 thf(f239,plain,(
% 0.19/0.46 (((in @ sK6 @ sK3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ sK6 @ Y0) @ sK5) => (in @ (kpair @ sK6 @ Y0) @ sK2)))))) = $false) | ~spl0_2),
% 0.19/0.46 inference(beta_eta_normalization,[],[f231])).
% 0.19/0.46 thf(f231,plain,(
% 0.19/0.46 (((^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK5) => (in @ (kpair @ Y0 @ Y1) @ sK2))))))) @ sK6) = $false) | ~spl0_2),
% 0.19/0.46 inference(sigma_clausification,[],[f218])).
% 0.19/0.46 thf(f218,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK5) => (in @ (kpair @ Y0 @ Y1) @ sK2)))))))) = $false) | ~spl0_2),
% 0.19/0.46 inference(not_proxy_clausification,[],[f210])).
% 0.19/0.46 thf(f210,plain,(
% 0.19/0.46 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK5) => (in @ (kpair @ Y0 @ Y1) @ sK2))))))))) = $true) | ~spl0_2),
% 0.19/0.46 inference(avatar_component_clause,[],[f209])).
% 0.19/0.46 thf(f209,plain,(
% 0.19/0.46 spl0_2 <=> ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK5) => (in @ (kpair @ Y0 @ Y1) @ sK2))))))))) = $true)),
% 0.19/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.19/0.46 thf(f333,plain,(
% 0.19/0.46 ((in @ (kpair @ sK6 @ sK7) @ sK2) = $true) | ~spl0_2),
% 0.19/0.46 inference(backward_demodulation,[],[f253,f326])).
% 0.19/0.46 thf(f326,plain,(
% 0.19/0.46 ((ap @ sK3 @ sK4 @ sK2 @ sK6) = sK7) | ~spl0_2),
% 0.19/0.46 inference(equality_proxy_clausification,[],[f323])).
% 0.19/0.46 thf(f323,plain,(
% 0.19/0.46 (((ap @ sK3 @ sK4 @ sK2 @ sK6) = sK7) = $true) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f322])).
% 0.19/0.46 thf(f322,plain,(
% 0.19/0.46 (($true => ((ap @ sK3 @ sK4 @ sK2 @ sK6) = sK7)) = $true) | ~spl0_2),
% 0.19/0.46 inference(forward_demodulation,[],[f321,f269])).
% 0.19/0.46 thf(f321,plain,(
% 0.19/0.46 (((in @ (kpair @ sK6 @ sK7) @ sK5) => ((ap @ sK3 @ sK4 @ sK2 @ sK6) = sK7)) = $true) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f316])).
% 0.19/0.46 thf(f316,plain,(
% 0.19/0.46 (($true => ((in @ (kpair @ sK6 @ sK7) @ sK5) => ((ap @ sK3 @ sK4 @ sK2 @ sK6) = sK7))) = $true) | ~spl0_2),
% 0.19/0.46 inference(superposition,[],[f312,f265])).
% 0.19/0.46 thf(f312,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((in @ X1 @ sK4) => ((in @ (kpair @ sK6 @ X1) @ sK5) => ((ap @ sK3 @ sK4 @ sK2 @ sK6) = X1))) = $true)) ) | ~spl0_2),
% 0.19/0.46 inference(forward_demodulation,[],[f310,f274])).
% 0.19/0.46 thf(f274,plain,(
% 0.19/0.46 ((ap @ sK3 @ sK4 @ sK2 @ sK6) = (ap @ sK3 @ sK4 @ sK5 @ sK6)) | ~spl0_2),
% 0.19/0.46 inference(equality_proxy_clausification,[],[f259])).
% 0.19/0.46 thf(f259,plain,(
% 0.19/0.46 ($true = ((ap @ sK3 @ sK4 @ sK2 @ sK6) = (ap @ sK3 @ sK4 @ sK5 @ sK6))) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f248])).
% 0.19/0.46 thf(f248,plain,(
% 0.19/0.46 ($true = ($true => ((ap @ sK3 @ sK4 @ sK2 @ sK6) = (ap @ sK3 @ sK4 @ sK5 @ sK6)))) | ~spl0_2),
% 0.19/0.46 inference(superposition,[],[f152,f241])).
% 0.19/0.46 thf(f241,plain,(
% 0.19/0.46 ($true = (in @ sK6 @ sK3)) | ~spl0_2),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f239])).
% 0.19/0.46 thf(f310,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK4) => ((in @ (kpair @ sK6 @ X1) @ sK5) => ((ap @ sK3 @ sK4 @ sK5 @ sK6) = X1))))) ) | ~spl0_2),
% 0.19/0.46 inference(beta_eta_normalization,[],[f308])).
% 0.19/0.46 thf(f308,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ sK6 @ Y0) @ sK5) => ((ap @ sK3 @ sK4 @ sK5 @ sK6) = Y0)))) @ X1) = $true)) ) | ~spl0_2),
% 0.19/0.46 inference(pi_clausification,[],[f257])).
% 0.19/0.46 thf(f257,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ sK6 @ Y0) @ sK5) => ((ap @ sK3 @ sK4 @ sK5 @ sK6) = Y0))))) = $true) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f250])).
% 0.19/0.46 thf(f250,plain,(
% 0.19/0.46 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ sK6 @ Y0) @ sK5) => ((ap @ sK3 @ sK4 @ sK5 @ sK6) = Y0)))))) = $true) | ~spl0_2),
% 0.19/0.46 inference(superposition,[],[f162,f241])).
% 0.19/0.46 thf(f162,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((in @ X1 @ sK3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ X1 @ Y0) @ sK5) => ((ap @ sK3 @ sK4 @ sK5 @ X1) = Y0)))))) = $true)) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f159])).
% 0.19/0.46 thf(f159,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK5) => ((ap @ sK3 @ sK4 @ sK5 @ Y0) = Y1))))))) @ X1) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f131])).
% 0.19/0.46 thf(f131,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK5) => ((ap @ sK3 @ sK4 @ sK5 @ Y0) = Y1)))))))) = $true)),
% 0.19/0.46 inference(boolean_simplification,[],[f129])).
% 0.19/0.46 thf(f129,plain,(
% 0.19/0.46 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK5) => ((ap @ sK3 @ sK4 @ sK5 @ Y0) = Y1))))))))))),
% 0.19/0.46 inference(superposition,[],[f67,f103])).
% 0.19/0.46 thf(f253,plain,(
% 0.19/0.46 ((in @ (kpair @ sK6 @ (ap @ sK3 @ sK4 @ sK2 @ sK6)) @ sK2) = $true) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f246])).
% 0.19/0.46 thf(f246,plain,(
% 0.19/0.46 (($true => (in @ (kpair @ sK6 @ (ap @ sK3 @ sK4 @ sK2 @ sK6)) @ sK2)) = $true) | ~spl0_2),
% 0.19/0.46 inference(superposition,[],[f126,f241])).
% 0.19/0.46 thf(f126,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((in @ X1 @ sK3) => (in @ (kpair @ X1 @ (ap @ sK3 @ sK4 @ sK2 @ X1)) @ sK2)) = $true)) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f123])).
% 0.19/0.46 thf(f123,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (kpair @ Y0 @ (ap @ sK3 @ sK4 @ sK2 @ Y0)) @ sK2))) @ X1) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f99])).
% 0.19/0.46 thf(f99,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (kpair @ Y0 @ (ap @ sK3 @ sK4 @ sK2 @ Y0)) @ sK2)))) = $true)),
% 0.19/0.46 inference(boolean_simplification,[],[f97])).
% 0.19/0.46 thf(f97,plain,(
% 0.19/0.46 (($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (kpair @ Y0 @ (ap @ sK3 @ sK4 @ sK2 @ Y0)) @ sK2))))) = $true)),
% 0.19/0.46 inference(superposition,[],[f60,f89])).
% 0.19/0.46 thf(f211,plain,(
% 0.19/0.46 spl0_1 | spl0_2),
% 0.19/0.46 inference(avatar_split_clause,[],[f204,f209,f206])).
% 0.19/0.46 thf(f204,plain,(
% 0.19/0.46 ((~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK5) => (in @ (kpair @ Y0 @ Y1) @ sK2))))))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK2) => (in @ (kpair @ Y0 @ Y1) @ sK5)))))))) = $false)),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f201])).
% 0.19/0.46 thf(f201,plain,(
% 0.19/0.46 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK2) => (in @ (kpair @ Y0 @ Y1) @ sK5)))))))) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK5) => (in @ (kpair @ Y0 @ Y1) @ sK2)))))))))) = $true)),
% 0.19/0.46 inference(boolean_simplification,[],[f200])).
% 0.19/0.46 thf(f200,plain,(
% 0.19/0.46 (($true => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK2) => (in @ (kpair @ Y0 @ Y1) @ sK5)))))))) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK5) => (in @ (kpair @ Y0 @ Y1) @ sK2))))))))))) = $true)),
% 0.19/0.46 inference(forward_demodulation,[],[f199,f134])).
% 0.19/0.46 thf(f134,plain,(
% 0.19/0.46 ($true = (subset @ sK5 @ (cartprod @ sK3 @ sK4)))),
% 0.19/0.46 inference(boolean_simplification,[],[f133])).
% 0.19/0.46 thf(f133,plain,(
% 0.19/0.46 (((subset @ sK5 @ (cartprod @ sK3 @ sK4)) & $true) = $true)),
% 0.19/0.46 inference(backward_demodulation,[],[f103,f127])).
% 0.19/0.46 thf(f127,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK4 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK5)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK4 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK5)))))))))) = $true)),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f103])).
% 0.19/0.46 thf(f199,plain,(
% 0.19/0.46 (((subset @ sK5 @ (cartprod @ sK3 @ sK4)) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK2) => (in @ (kpair @ Y0 @ Y1) @ sK5)))))))) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK5) => (in @ (kpair @ Y0 @ Y1) @ sK2))))))))))) = $true)),
% 0.19/0.46 inference(boolean_simplification,[],[f191])).
% 0.19/0.46 thf(f191,plain,(
% 0.19/0.46 (((subset @ sK5 @ (cartprod @ sK3 @ sK4)) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK2) => (in @ (kpair @ Y0 @ Y1) @ sK5)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK5) => (in @ (kpair @ Y0 @ Y1) @ sK2)))))))) => $false))) = $true)),
% 0.19/0.46 inference(superposition,[],[f189,f121])).
% 0.19/0.46 thf(f121,plain,(
% 0.19/0.46 ((sK2 = sK5) = $false)),
% 0.19/0.46 inference(boolean_simplification,[],[f120])).
% 0.19/0.46 thf(f120,plain,(
% 0.19/0.46 (($true => (sK2 = sK5)) = $false)),
% 0.19/0.46 inference(backward_demodulation,[],[f102,f119])).
% 0.19/0.46 thf(f189,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (($true = ((subset @ X1 @ (cartprod @ sK3 @ sK4)) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ sK2) => (in @ (kpair @ Y0 @ Y1) @ X1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (in @ (kpair @ Y0 @ Y1) @ sK2)))))))) => (sK2 = X1)))))) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f186])).
% 0.19/0.46 thf(f186,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK3 @ sK4)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK4) => ((in @ (kpair @ Y1 @ Y2) @ sK2) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK4) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => (in @ (kpair @ Y1 @ Y2) @ sK2)))))))) => (sK2 = Y0))))) @ X1) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f111])).
% 0.19/0.46 thf(f111,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK3 @ sK4)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK4) => ((in @ (kpair @ Y1 @ Y2) @ sK2) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK4) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => (in @ (kpair @ Y1 @ Y2) @ sK2)))))))) => (sK2 = Y0)))))) = $true)),
% 0.19/0.46 inference(boolean_simplification,[],[f108])).
% 0.19/0.46 thf(f108,plain,(
% 0.19/0.46 (($true => (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ sK3 @ sK4)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK4) => ((in @ (kpair @ Y1 @ Y2) @ sK2) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK4) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => (in @ (kpair @ Y1 @ Y2) @ sK2)))))))) => (sK2 = Y0))))))) = $true)),
% 0.19/0.46 inference(superposition,[],[f80,f101])).
% 0.19/0.46 thf(f101,plain,(
% 0.19/0.46 ((subset @ sK2 @ (cartprod @ sK3 @ sK4)) = $true)),
% 0.19/0.46 inference(boolean_simplification,[],[f100])).
% 0.19/0.46 thf(f100,plain,(
% 0.19/0.46 (((subset @ sK2 @ (cartprod @ sK3 @ sK4)) & $true) = $true)),
% 0.19/0.46 inference(backward_demodulation,[],[f89,f94])).
% 0.19/0.46 thf(f94,plain,(
% 0.19/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ sK4 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK4 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK2)))))))))))),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f89])).
% 0.19/0.46 thf(f80,plain,(
% 0.19/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X1 @ (cartprod @ X2 @ X3)) => (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X2 @ X3)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X3) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X3) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => (in @ (kpair @ Y1 @ Y2) @ X1)))))))) => (X1 = Y0))))))))) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f79])).
% 0.19/0.46 thf(f79,plain,(
% 0.19/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((subset @ X1 @ (cartprod @ X2 @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ X2 @ Y0)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ X1) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ Y1) => (in @ (kpair @ Y2 @ Y3) @ X1)))))))) => (X1 = Y1)))))))) @ X3) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f78])).
% 0.19/0.46 thf(f78,plain,(
% 0.19/0.46 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ (cartprod @ X2 @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ X2 @ Y0)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ X1) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ Y1) => (in @ (kpair @ Y2 @ Y3) @ X1)))))))) => (X1 = Y1))))))))) = $true)) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f77])).
% 0.19/0.46 thf(f77,plain,(
% 0.19/0.46 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ (cartprod @ Y0 @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ X1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => (in @ (kpair @ Y3 @ Y4) @ X1)))))))) => (X1 = Y2)))))))))) @ X2))) )),
% 0.19/0.46 inference(pi_clausification,[],[f76])).
% 0.19/0.46 thf(f76,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ (cartprod @ Y0 @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ X1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => (in @ (kpair @ Y3 @ Y4) @ X1)))))))) => (X1 = Y2))))))))))) = $true)) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f75])).
% 0.19/0.46 thf(f75,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ (cartprod @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((subset @ Y3 @ (cartprod @ Y1 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = Y3)))))))))))) @ X1) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f70])).
% 0.19/0.46 thf(f70,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ (cartprod @ Y1 @ Y2)) => (!! @ $i @ (^[Y3 : $i]: ((subset @ Y3 @ (cartprod @ Y1 @ Y2)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) => ((in @ (kpair @ Y4 @ Y5) @ Y3) => (in @ (kpair @ Y4 @ Y5) @ Y0)))))))) => (Y0 = Y3))))))))))))) = $true)),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f49])).
% 0.19/0.46 % SZS output end Proof for theBenchmark
% 0.19/0.46 % (25679)------------------------------
% 0.19/0.46 % (25679)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.46 % (25679)Termination reason: Refutation
% 0.19/0.46
% 0.19/0.46 % (25679)Memory used [KB]: 6396
% 0.19/0.46 % (25679)Time elapsed: 0.074 s
% 0.19/0.46 % (25679)Instructions burned: 176 (million)
% 0.19/0.46 % (25679)------------------------------
% 0.19/0.46 % (25679)------------------------------
% 0.19/0.46 % (25667)Success in time 0.111 s
% 0.19/0.46 % Vampire---4.8 exiting
%------------------------------------------------------------------------------