TSTP Solution File: SEU678^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU678^2 : 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 : n014.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 03:50:35 EDT 2024
% Result : Theorem 0.21s 0.49s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU678^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 17:58:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 % (6740)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37 % (6741)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.13/0.37 % (6739)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37 % (6738)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.13/0.38 % (6742)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.38 % (6736)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.38 % (6739)Instruction limit reached!
% 0.13/0.38 % (6739)------------------------------
% 0.13/0.38 % (6739)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (6739)Termination reason: Unknown
% 0.13/0.38 % (6740)Instruction limit reached!
% 0.13/0.38 % (6740)------------------------------
% 0.13/0.38 % (6740)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (6739)Termination phase: shuffling
% 0.13/0.38
% 0.13/0.38 % (6737)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.13/0.38 % (6739)Memory used [KB]: 1023
% 0.13/0.38 % (6739)Time elapsed: 0.004 s
% 0.13/0.38 % (6739)Instructions burned: 2 (million)
% 0.13/0.38 % (6739)------------------------------
% 0.13/0.38 % (6739)------------------------------
% 0.13/0.38 % (6740)Termination reason: Unknown
% 0.13/0.38 % (6740)Termination phase: Property scanning
% 0.13/0.38
% 0.13/0.38 % (6740)Memory used [KB]: 1023
% 0.13/0.38 % (6740)Time elapsed: 0.004 s
% 0.13/0.38 % (6740)Instructions burned: 3 (million)
% 0.13/0.38 % (6740)------------------------------
% 0.13/0.38 % (6740)------------------------------
% 0.13/0.38 % (6737)Instruction limit reached!
% 0.13/0.38 % (6737)------------------------------
% 0.13/0.38 % (6737)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (6737)Termination reason: Unknown
% 0.13/0.38 % (6737)Termination phase: Preprocessing 3
% 0.13/0.38
% 0.13/0.38 % (6737)Memory used [KB]: 1023
% 0.13/0.38 % (6737)Time elapsed: 0.004 s
% 0.13/0.38 % (6737)Instructions burned: 4 (million)
% 0.13/0.38 % (6737)------------------------------
% 0.13/0.38 % (6737)------------------------------
% 0.13/0.38 % (6743)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.13/0.38 % (6743)Instruction limit reached!
% 0.13/0.38 % (6743)------------------------------
% 0.13/0.38 % (6743)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (6743)Termination reason: Unknown
% 0.13/0.38 % (6743)Termination phase: shuffling
% 0.13/0.38
% 0.13/0.38 % (6743)Memory used [KB]: 1023
% 0.13/0.38 % (6743)Time elapsed: 0.003 s
% 0.13/0.38 % (6743)Instructions burned: 3 (million)
% 0.13/0.38 % (6743)------------------------------
% 0.13/0.38 % (6743)------------------------------
% 0.13/0.39 % (6741)Refutation not found, incomplete strategy
% 0.13/0.39 % (6741)------------------------------
% 0.13/0.39 % (6741)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (6741)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.39
% 0.13/0.39
% 0.13/0.39 % (6741)Memory used [KB]: 5628
% 0.13/0.39 % (6741)Time elapsed: 0.012 s
% 0.13/0.39 % (6741)Instructions burned: 14 (million)
% 0.13/0.39 % (6741)------------------------------
% 0.13/0.39 % (6741)------------------------------
% 0.21/0.39 % (6742)Instruction limit reached!
% 0.21/0.39 % (6742)------------------------------
% 0.21/0.39 % (6742)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (6742)Termination reason: Unknown
% 0.21/0.39 % (6742)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (6742)Memory used [KB]: 5756
% 0.21/0.39 % (6742)Time elapsed: 0.015 s
% 0.21/0.39 % (6742)Instructions burned: 19 (million)
% 0.21/0.39 % (6742)------------------------------
% 0.21/0.39 % (6742)------------------------------
% 0.21/0.39 % (6750)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.39 % (6749)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.39 % (6738)Instruction limit reached!
% 0.21/0.39 % (6738)------------------------------
% 0.21/0.39 % (6738)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (6752)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.39 % (6738)Termination reason: Unknown
% 0.21/0.39 % (6738)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (6738)Memory used [KB]: 5756
% 0.21/0.39 % (6738)Time elapsed: 0.020 s
% 0.21/0.39 % (6738)Instructions burned: 27 (million)
% 0.21/0.39 % (6738)------------------------------
% 0.21/0.39 % (6738)------------------------------
% 0.21/0.39 % (6752)Instruction limit reached!
% 0.21/0.39 % (6752)------------------------------
% 0.21/0.39 % (6752)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (6752)Termination reason: Unknown
% 0.21/0.39 % (6752)Termination phase: Property scanning
% 0.21/0.39
% 0.21/0.39 % (6752)Memory used [KB]: 1023
% 0.21/0.39 % (6752)Time elapsed: 0.004 s
% 0.21/0.39 % (6752)Instructions burned: 3 (million)
% 0.21/0.39 % (6752)------------------------------
% 0.21/0.39 % (6752)------------------------------
% 0.21/0.40 % (6753)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.21/0.40 % (6750)Instruction limit reached!
% 0.21/0.40 % (6750)------------------------------
% 0.21/0.40 % (6750)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (6750)Termination reason: Unknown
% 0.21/0.40 % (6750)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (6750)Memory used [KB]: 5628
% 0.21/0.40 % (6750)Time elapsed: 0.012 s
% 0.21/0.40 % (6750)Instructions burned: 15 (million)
% 0.21/0.40 % (6750)------------------------------
% 0.21/0.40 % (6750)------------------------------
% 0.21/0.40 % (6756)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.40 % (6758)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.41 % (6756)Instruction limit reached!
% 0.21/0.41 % (6756)------------------------------
% 0.21/0.41 % (6756)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (6756)Termination reason: Unknown
% 0.21/0.41 % (6756)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (6756)Memory used [KB]: 1023
% 0.21/0.41 % (6756)Time elapsed: 0.007 s
% 0.21/0.41 % (6756)Instructions burned: 7 (million)
% 0.21/0.41 % (6756)------------------------------
% 0.21/0.41 % (6756)------------------------------
% 0.21/0.41 % (6761)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.41 % (6761)Instruction limit reached!
% 0.21/0.41 % (6761)------------------------------
% 0.21/0.41 % (6761)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (6761)Termination reason: Unknown
% 0.21/0.41 % (6761)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (6761)Memory used [KB]: 1023
% 0.21/0.41 % (6761)Time elapsed: 0.004 s
% 0.21/0.41 % (6761)Instructions burned: 4 (million)
% 0.21/0.41 % (6761)------------------------------
% 0.21/0.41 % (6761)------------------------------
% 0.21/0.41 % (6762)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.41 % (6762)Instruction limit reached!
% 0.21/0.41 % (6762)------------------------------
% 0.21/0.41 % (6762)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (6762)Termination reason: Unknown
% 0.21/0.41 % (6762)Termination phase: Clausification
% 0.21/0.41
% 0.21/0.41 % (6762)Memory used [KB]: 1023
% 0.21/0.41 % (6762)Time elapsed: 0.004 s
% 0.21/0.41 % (6762)Instructions burned: 4 (million)
% 0.21/0.41 % (6762)------------------------------
% 0.21/0.41 % (6762)------------------------------
% 0.21/0.41 % (6749)Instruction limit reached!
% 0.21/0.41 % (6749)------------------------------
% 0.21/0.41 % (6749)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (6749)Termination reason: Unknown
% 0.21/0.41 % (6749)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (6749)Memory used [KB]: 5756
% 0.21/0.41 % (6749)Time elapsed: 0.023 s
% 0.21/0.41 % (6749)Instructions burned: 37 (million)
% 0.21/0.41 % (6749)------------------------------
% 0.21/0.41 % (6749)------------------------------
% 0.21/0.41 % (6758)Instruction limit reached!
% 0.21/0.41 % (6758)------------------------------
% 0.21/0.41 % (6758)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (6758)Termination reason: Unknown
% 0.21/0.41 % (6758)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (6758)Memory used [KB]: 6012
% 0.21/0.41 % (6758)Time elapsed: 0.012 s
% 0.21/0.41 % (6758)Instructions burned: 16 (million)
% 0.21/0.41 % (6758)------------------------------
% 0.21/0.41 % (6758)------------------------------
% 0.21/0.42 % (6763)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.42 % (6763)Instruction limit reached!
% 0.21/0.42 % (6763)------------------------------
% 0.21/0.42 % (6763)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (6763)Termination reason: Unknown
% 0.21/0.42 % (6763)Termination phase: Saturation
% 0.21/0.42
% 0.21/0.42 % (6763)Memory used [KB]: 5500
% 0.21/0.42 % (6763)Time elapsed: 0.006 s
% 0.21/0.42 % (6763)Instructions burned: 7 (million)
% 0.21/0.42 % (6763)------------------------------
% 0.21/0.42 % (6763)------------------------------
% 0.21/0.42 % (6764)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.42 % (6764)Instruction limit reached!
% 0.21/0.42 % (6764)------------------------------
% 0.21/0.42 % (6764)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (6764)Termination reason: Unknown
% 0.21/0.42 % (6764)Termination phase: shuffling
% 0.21/0.42
% 0.21/0.42 % (6764)Memory used [KB]: 1023
% 0.21/0.42 % (6764)Time elapsed: 0.003 s
% 0.21/0.42 % (6764)Instructions burned: 3 (million)
% 0.21/0.42 % (6764)------------------------------
% 0.21/0.42 % (6764)------------------------------
% 0.21/0.42 % (6767)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.43 % (6767)Instruction limit reached!
% 0.21/0.43 % (6767)------------------------------
% 0.21/0.43 % (6767)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (6767)Termination reason: Unknown
% 0.21/0.43 % (6767)Termination phase: Property scanning
% 0.21/0.43
% 0.21/0.43 % (6767)Memory used [KB]: 1023
% 0.21/0.43 % (6767)Time elapsed: 0.004 s
% 0.21/0.43 % (6767)Instructions burned: 4 (million)
% 0.21/0.43 % (6767)------------------------------
% 0.21/0.43 % (6767)------------------------------
% 0.21/0.43 % (6769)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.43 % (6770)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.43 % (6771)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.43 % (6771)Instruction limit reached!
% 0.21/0.43 % (6771)------------------------------
% 0.21/0.43 % (6771)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (6771)Termination reason: Unknown
% 0.21/0.43 % (6771)Termination phase: Saturation
% 0.21/0.43
% 0.21/0.43 % (6771)Memory used [KB]: 5500
% 0.21/0.43 % (6771)Time elapsed: 0.006 s
% 0.21/0.43 % (6771)Instructions burned: 7 (million)
% 0.21/0.43 % (6771)------------------------------
% 0.21/0.43 % (6771)------------------------------
% 0.21/0.43 % (6774)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.21/0.44 % (6769)Instruction limit reached!
% 0.21/0.44 % (6769)------------------------------
% 0.21/0.44 % (6769)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (6769)Termination reason: Unknown
% 0.21/0.44 % (6769)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (6769)Memory used [KB]: 5756
% 0.21/0.44 % (6769)Time elapsed: 0.036 s
% 0.21/0.44 % (6769)Instructions burned: 18 (million)
% 0.21/0.44 % (6769)------------------------------
% 0.21/0.44 % (6769)------------------------------
% 0.21/0.44 % (6777)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.21/0.44 % (6774)Refutation not found, incomplete strategy
% 0.21/0.44 % (6774)------------------------------
% 0.21/0.44 % (6774)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (6774)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.44
% 0.21/0.44
% 0.21/0.44 % (6774)Memory used [KB]: 5628
% 0.21/0.44 % (6774)Time elapsed: 0.029 s
% 0.21/0.44 % (6774)Instructions burned: 8 (million)
% 0.21/0.44 % (6774)------------------------------
% 0.21/0.44 % (6774)------------------------------
% 0.21/0.44 % (6779)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.21/0.44 % (6779)Instruction limit reached!
% 0.21/0.44 % (6779)------------------------------
% 0.21/0.44 % (6779)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (6779)Termination reason: Unknown
% 0.21/0.44 % (6779)Termination phase: Property scanning
% 0.21/0.44
% 0.21/0.44 % (6779)Memory used [KB]: 1023
% 0.21/0.44 % (6779)Time elapsed: 0.005 s
% 0.21/0.44 % (6779)Instructions burned: 6 (million)
% 0.21/0.44 % (6779)------------------------------
% 0.21/0.44 % (6779)------------------------------
% 0.21/0.45 % (6782)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.45 % (6782)Instruction limit reached!
% 0.21/0.45 % (6782)------------------------------
% 0.21/0.45 % (6782)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (6782)Termination reason: Unknown
% 0.21/0.45 % (6782)Termination phase: Property scanning
% 0.21/0.45
% 0.21/0.45 % (6782)Memory used [KB]: 1023
% 0.21/0.45 % (6782)Time elapsed: 0.005 s
% 0.21/0.45 % (6782)Instructions burned: 6 (million)
% 0.21/0.45 % (6782)------------------------------
% 0.21/0.45 % (6782)------------------------------
% 0.21/0.45 % (6777)Instruction limit reached!
% 0.21/0.45 % (6777)------------------------------
% 0.21/0.45 % (6777)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (6777)Termination reason: Unknown
% 0.21/0.45 % (6777)Termination phase: Saturation
% 0.21/0.45
% 0.21/0.45 % (6777)Memory used [KB]: 5628
% 0.21/0.45 % (6777)Time elapsed: 0.042 s
% 0.21/0.45 % (6777)Instructions burned: 21 (million)
% 0.21/0.45 % (6777)------------------------------
% 0.21/0.45 % (6777)------------------------------
% 0.21/0.45 % (6786)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.21/0.46 % (6788)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.21/0.46 % (6790)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2999ds/19Mi)
% 0.21/0.46 % (6794)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2999ds/879Mi)
% 0.21/0.46 % (6796)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.21/0.47 % (6736)Instruction limit reached!
% 0.21/0.47 % (6736)------------------------------
% 0.21/0.47 % (6736)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (6736)Termination reason: Unknown
% 0.21/0.47 % (6736)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (6736)Memory used [KB]: 6268
% 0.21/0.47 % (6736)Time elapsed: 0.096 s
% 0.21/0.47 % (6736)Instructions burned: 184 (million)
% 0.21/0.47 % (6736)------------------------------
% 0.21/0.47 % (6736)------------------------------
% 0.21/0.47 % (6790)Instruction limit reached!
% 0.21/0.47 % (6790)------------------------------
% 0.21/0.47 % (6790)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (6790)Termination reason: Unknown
% 0.21/0.47 % (6790)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (6790)Memory used [KB]: 5628
% 0.21/0.47 % (6790)Time elapsed: 0.013 s
% 0.21/0.47 % (6790)Instructions burned: 19 (million)
% 0.21/0.47 % (6790)------------------------------
% 0.21/0.47 % (6790)------------------------------
% 0.21/0.47 % (6796)Instruction limit reached!
% 0.21/0.47 % (6796)------------------------------
% 0.21/0.47 % (6796)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (6796)Termination reason: Unknown
% 0.21/0.47 % (6796)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (6796)Memory used [KB]: 5756
% 0.21/0.47 % (6796)Time elapsed: 0.009 s
% 0.21/0.47 % (6796)Instructions burned: 18 (million)
% 0.21/0.47 % (6796)------------------------------
% 0.21/0.47 % (6796)------------------------------
% 0.21/0.48 % (6807)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 0.21/0.48 % (6803)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.21/0.48 % (6805)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.21/0.48 % (6803)Instruction limit reached!
% 0.21/0.48 % (6803)------------------------------
% 0.21/0.48 % (6803)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48 % (6803)Termination reason: Unknown
% 0.21/0.48 % (6803)Termination phase: shuffling
% 0.21/0.48
% 0.21/0.48 % (6803)Memory used [KB]: 1023
% 0.21/0.48 % (6803)Time elapsed: 0.003 s
% 0.21/0.48 % (6803)Instructions burned: 4 (million)
% 0.21/0.48 % (6803)------------------------------
% 0.21/0.48 % (6803)------------------------------
% 0.21/0.48 % (6786)First to succeed.
% 0.21/0.49 % (6805)Refutation not found, incomplete strategy
% 0.21/0.49 % (6805)------------------------------
% 0.21/0.49 % (6805)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49 % (6805)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.49
% 0.21/0.49
% 0.21/0.49 % (6805)Memory used [KB]: 5628
% 0.21/0.49 % (6805)Time elapsed: 0.008 s
% 0.21/0.49 % (6805)Instructions burned: 11 (million)
% 0.21/0.49 % (6805)------------------------------
% 0.21/0.49 % (6805)------------------------------
% 0.21/0.49 % (6794)Also succeeded, but the first one will report.
% 0.21/0.49 % (6786)Refutation found. Thanks to Tanya!
% 0.21/0.49 % SZS status Theorem for theBenchmark
% 0.21/0.49 % SZS output start Proof for theBenchmark
% 0.21/0.49 thf(func_def_0, type, in: $i > $i > $o).
% 0.21/0.49 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.21/0.49 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 0.21/0.49 thf(func_def_4, type, subset: $i > $i > $o).
% 0.21/0.49 thf(func_def_5, type, kpair: $i > $i > $i).
% 0.21/0.49 thf(func_def_6, type, cartprod: $i > $i > $i).
% 0.21/0.49 thf(func_def_7, type, singleton: $i > $o).
% 0.21/0.49 thf(func_def_9, type, ex1: $i > ($i > $o) > $o).
% 0.21/0.49 thf(func_def_11, type, breln: $i > $i > $i > $o).
% 0.21/0.49 thf(func_def_12, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.21/0.49 thf(func_def_16, type, func: $i > $i > $i > $o).
% 0.21/0.49 thf(func_def_32, type, sK1: $i > $i).
% 0.21/0.49 thf(func_def_36, type, sK5: $i > $i > ($i > $o) > $i).
% 0.21/0.49 thf(func_def_37, type, sK6: $i > ($i > $o) > $i).
% 0.21/0.49 thf(func_def_38, type, sK7: $i > ($i > $o) > $i).
% 0.21/0.49 thf(func_def_39, type, ph8: !>[X0: $tType]:(X0)).
% 0.21/0.49 thf(f397,plain,(
% 0.21/0.49 $false),
% 0.21/0.49 inference(avatar_sat_refutation,[],[f143,f153,f234,f235,f236,f240,f247,f248,f335,f341,f376,f393])).
% 0.21/0.49 thf(f393,plain,(
% 0.21/0.49 ~spl3_10 | ~spl3_11),
% 0.21/0.49 inference(avatar_contradiction_clause,[],[f392])).
% 0.21/0.49 thf(f392,plain,(
% 0.21/0.49 $false | (~spl3_10 | ~spl3_11)),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f380])).
% 0.21/0.49 thf(f380,plain,(
% 0.21/0.49 ($true = $false) | ((sK1 @ sK4) != (sK1 @ sK4)) | (~spl3_10 | ~spl3_11)),
% 0.21/0.49 inference(superposition,[],[f329,f290])).
% 0.21/0.49 thf(f290,plain,(
% 0.21/0.49 ($true = (in @ (sK1 @ sK4) @ sK0)) | ~spl3_10),
% 0.21/0.49 inference(avatar_component_clause,[],[f288])).
% 0.21/0.49 thf(f288,plain,(
% 0.21/0.49 spl3_10 <=> ($true = (in @ (sK1 @ sK4) @ sK0))),
% 0.21/0.49 introduced(avatar_definition,[new_symbols(naming,[spl3_10])])).
% 0.21/0.49 thf(f329,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((in @ X0 @ sK0) = $false) | ((sK1 @ sK4) != X0)) ) | ~spl3_11),
% 0.21/0.49 inference(avatar_component_clause,[],[f328])).
% 0.21/0.49 thf(f328,plain,(
% 0.21/0.49 spl3_11 <=> ! [X0] : (((sK1 @ sK4) != X0) | ((in @ X0 @ sK0) = $false))),
% 0.21/0.49 introduced(avatar_definition,[new_symbols(naming,[spl3_11])])).
% 0.21/0.49 thf(f376,plain,(
% 0.21/0.49 ~spl3_1 | spl3_10),
% 0.21/0.49 inference(avatar_split_clause,[],[f361,f288,f136])).
% 0.21/0.49 thf(f136,plain,(
% 0.21/0.49 spl3_1 <=> ($true = (in @ sK4 @ sK2))),
% 0.21/0.49 introduced(avatar_definition,[new_symbols(naming,[spl3_1])])).
% 0.21/0.49 thf(f361,plain,(
% 0.21/0.49 ($true != (in @ sK4 @ sK2)) | spl3_10),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f359])).
% 0.21/0.49 thf(f359,plain,(
% 0.21/0.49 ($true != $true) | ($true != (in @ sK4 @ sK2)) | spl3_10),
% 0.21/0.49 inference(superposition,[],[f289,f46])).
% 0.21/0.49 thf(f46,plain,(
% 0.21/0.49 ( ! [X3 : $i] : (($true = (in @ (sK1 @ X3) @ sK0)) | ($true != (in @ X3 @ sK2))) )),
% 0.21/0.49 inference(cnf_transformation,[],[f33])).
% 0.21/0.49 thf(f33,plain,(
% 0.21/0.49 (($true != (func @ sK2 @ sK0 @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((sK1 @ Y0) = Y1))))))) & ! [X3] : (($true = (in @ (sK1 @ X3) @ sK0)) | ($true != (in @ X3 @ sK2)))) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrI = $true) & (ex1I = $true)),
% 0.21/0.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f31,f32])).
% 0.21/0.49 thf(f32,plain,(
% 0.21/0.49 ? [X0,X1 : $i > $i,X2] : (($true != (func @ X2 @ X0 @ (dpsetconstr @ X2 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X1 @ Y0) = Y1))))))) & ! [X3] : (($true = (in @ (X1 @ X3) @ X0)) | ((in @ X3 @ X2) != $true))) => (($true != (func @ sK2 @ sK0 @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((sK1 @ Y0) = Y1))))))) & ! [X3] : (($true = (in @ (sK1 @ X3) @ sK0)) | ($true != (in @ X3 @ sK2))))),
% 0.21/0.49 introduced(choice_axiom,[])).
% 0.21/0.49 thf(f31,plain,(
% 0.21/0.49 ? [X0,X1 : $i > $i,X2] : (($true != (func @ X2 @ X0 @ (dpsetconstr @ X2 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X1 @ Y0) = Y1))))))) & ! [X3] : (($true = (in @ (X1 @ X3) @ X0)) | ((in @ X3 @ X2) != $true))) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrI = $true) & (ex1I = $true)),
% 0.21/0.49 inference(flattening,[],[f30])).
% 0.21/0.49 thf(f30,plain,(
% 0.21/0.49 (((? [X0,X1 : $i > $i,X2] : (($true != (func @ X2 @ X0 @ (dpsetconstr @ X2 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X1 @ Y0) = Y1))))))) & ! [X3] : (($true = (in @ (X1 @ X3) @ X0)) | ((in @ X3 @ X2) != $true))) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrI = $true)) & (ex1I = $true)),
% 0.21/0.49 inference(ennf_transformation,[],[f19])).
% 0.21/0.49 thf(f19,plain,(
% 0.21/0.49 ~((ex1I = $true) => ((dpsetconstrI = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ! [X0,X1 : $i > $i,X2] : (! [X3] : (((in @ X3 @ X2) = $true) => ($true = (in @ (X1 @ X3) @ X0))) => ($true = (func @ X2 @ X0 @ (dpsetconstr @ X2 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((X1 @ Y0) = Y1))))))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f18])).
% 0.21/0.49 thf(f18,plain,(
% 0.21/0.49 ~(ex1I => (dpsetconstrI => (setOfPairsIsBReln => (dpsetconstrERa => ! [X0,X1 : $i > $i,X2] : (! [X3] : ((in @ X3 @ X2) => (in @ (X1 @ X3) @ X0)) => (func @ X2 @ X0 @ (dpsetconstr @ X2 @ X0 @ (^[X4 : $i, X5 : $i] : (((X1 @ X4) = X5))))))))))),
% 0.21/0.49 inference(rectify,[],[f10])).
% 0.21/0.49 thf(f10,negated_conjecture,(
% 0.21/0.49 ~(ex1I => (dpsetconstrI => (setOfPairsIsBReln => (dpsetconstrERa => ! [X4,X9 : $i > $i,X0] : (! [X1] : ((in @ X1 @ X0) => (in @ (X9 @ X1) @ X4)) => (func @ X0 @ X4 @ (dpsetconstr @ X0 @ X4 @ (^[X1 : $i, X3 : $i] : (((X9 @ X1) = X3))))))))))),
% 0.21/0.49 inference(negated_conjecture,[],[f9])).
% 0.21/0.49 thf(f9,conjecture,(
% 0.21/0.49 ex1I => (dpsetconstrI => (setOfPairsIsBReln => (dpsetconstrERa => ! [X4,X9 : $i > $i,X0] : (! [X1] : ((in @ X1 @ X0) => (in @ (X9 @ X1) @ X4)) => (func @ X0 @ X4 @ (dpsetconstr @ X0 @ X4 @ (^[X1 : $i, X3 : $i] : (((X9 @ X1) = X3)))))))))),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamProp)).
% 0.21/0.49 thf(f289,plain,(
% 0.21/0.49 ($true != (in @ (sK1 @ sK4) @ sK0)) | spl3_10),
% 0.21/0.49 inference(avatar_component_clause,[],[f288])).
% 0.21/0.49 thf(f341,plain,(
% 0.21/0.49 ~spl3_1 | ~spl3_12),
% 0.21/0.49 inference(avatar_contradiction_clause,[],[f340])).
% 0.21/0.49 thf(f340,plain,(
% 0.21/0.49 $false | (~spl3_1 | ~spl3_12)),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f339])).
% 0.21/0.49 thf(f339,plain,(
% 0.21/0.49 ($true = $false) | (~spl3_1 | ~spl3_12)),
% 0.21/0.49 inference(backward_demodulation,[],[f138,f333])).
% 0.21/0.49 thf(f333,plain,(
% 0.21/0.49 ((in @ sK4 @ sK2) = $false) | ~spl3_12),
% 0.21/0.49 inference(avatar_component_clause,[],[f331])).
% 0.21/0.49 thf(f331,plain,(
% 0.21/0.49 spl3_12 <=> ((in @ sK4 @ sK2) = $false)),
% 0.21/0.49 introduced(avatar_definition,[new_symbols(naming,[spl3_12])])).
% 0.21/0.49 thf(f138,plain,(
% 0.21/0.49 ($true = (in @ sK4 @ sK2)) | ~spl3_1),
% 0.21/0.49 inference(avatar_component_clause,[],[f136])).
% 0.21/0.49 thf(f335,plain,(
% 0.21/0.49 spl3_12 | spl3_11 | ~spl3_1 | ~spl3_3 | ~spl3_5 | ~spl3_7),
% 0.21/0.49 inference(avatar_split_clause,[],[f321,f231,f223,f215,f136,f328,f331])).
% 0.21/0.49 thf(f215,plain,(
% 0.21/0.49 spl3_3 <=> ! [X0] : (((in @ X0 @ sK0) = $false) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ($true = (in @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ sK0)))),
% 0.21/0.49 introduced(avatar_definition,[new_symbols(naming,[spl3_3])])).
% 0.21/0.49 thf(f223,plain,(
% 0.21/0.49 spl3_5 <=> ! [X0] : (((in @ (kpair @ sK4 @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))))) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0))))) = $true) | ((in @ X0 @ sK0) = $false) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))))),
% 0.21/0.49 introduced(avatar_definition,[new_symbols(naming,[spl3_5])])).
% 0.21/0.49 thf(f231,plain,(
% 0.21/0.49 spl3_7 <=> ! [X0] : (((sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != X0) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ((in @ X0 @ sK0) = $false))),
% 0.21/0.49 introduced(avatar_definition,[new_symbols(naming,[spl3_7])])).
% 0.21/0.49 thf(f321,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((sK1 @ sK4) != X0) | ((in @ X0 @ sK0) = $false) | ((in @ sK4 @ sK2) = $false)) ) | (~spl3_1 | ~spl3_3 | ~spl3_5 | ~spl3_7)),
% 0.21/0.49 inference(duplicate_literal_removal,[],[f320])).
% 0.21/0.49 thf(f320,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((sK1 @ sK4) != X0) | ((in @ X0 @ sK0) = $false) | ((in @ sK4 @ sK2) = $false) | ((sK1 @ sK4) != X0)) ) | (~spl3_1 | ~spl3_3 | ~spl3_5 | ~spl3_7)),
% 0.21/0.49 inference(equality_proxy_clausification,[],[f319])).
% 0.21/0.49 thf(f319,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((in @ sK4 @ sK2) = $false) | (((sK1 @ sK4) = X0) = $false) | ((in @ X0 @ sK0) = $false) | ((sK1 @ sK4) != X0)) ) | (~spl3_1 | ~spl3_3 | ~spl3_5 | ~spl3_7)),
% 0.21/0.49 inference(beta_eta_normalization,[],[f318])).
% 0.21/0.49 thf(f318,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (($false = ((^[Y0 : $i]: (= @ (sK1 @ Y0))) @ sK4 @ X0)) | ((sK1 @ sK4) != X0) | ((in @ sK4 @ sK2) = $false) | ((in @ X0 @ sK0) = $false)) ) | (~spl3_1 | ~spl3_3 | ~spl3_5 | ~spl3_7)),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f317])).
% 0.21/0.49 thf(f317,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((in @ X0 @ sK0) = $false) | ($true = $false) | ((in @ sK4 @ sK2) = $false) | ((sK1 @ sK4) != X0) | ($false = ((^[Y0 : $i]: (= @ (sK1 @ Y0))) @ sK4 @ X0))) ) | (~spl3_1 | ~spl3_3 | ~spl3_5 | ~spl3_7)),
% 0.21/0.49 inference(duplicate_literal_removal,[],[f307])).
% 0.21/0.49 thf(f307,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (($true = $false) | ((in @ sK4 @ sK2) = $false) | ($false = ((^[Y0 : $i]: (= @ (sK1 @ Y0))) @ sK4 @ X0)) | ((in @ X0 @ sK0) = $false) | ((sK1 @ sK4) != X0) | ((in @ X0 @ sK0) = $false)) ) | (~spl3_1 | ~spl3_3 | ~spl3_5 | ~spl3_7)),
% 0.21/0.49 inference(superposition,[],[f132,f278])).
% 0.21/0.49 thf(f278,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ((sK1 @ sK4) != X0) | ((in @ X0 @ sK0) = $false)) ) | (~spl3_1 | ~spl3_3 | ~spl3_5 | ~spl3_7)),
% 0.21/0.49 inference(duplicate_literal_removal,[],[f275])).
% 0.21/0.49 thf(f275,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ((sK1 @ sK4) != X0) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ((in @ X0 @ sK0) = $false) | ((in @ X0 @ sK0) = $false)) ) | (~spl3_1 | ~spl3_3 | ~spl3_5 | ~spl3_7)),
% 0.21/0.49 inference(superposition,[],[f232,f271])).
% 0.21/0.49 thf(f271,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) = (sK1 @ sK4)) | ((in @ X0 @ sK0) = $false) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0))))))) ) | (~spl3_1 | ~spl3_3 | ~spl3_5)),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f270])).
% 0.21/0.49 thf(f270,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (($true = $false) | ((sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) = (sK1 @ sK4)) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ((in @ X0 @ sK0) = $false)) ) | (~spl3_1 | ~spl3_3 | ~spl3_5)),
% 0.21/0.49 inference(duplicate_literal_removal,[],[f262])).
% 0.21/0.49 thf(f262,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((in @ X0 @ sK0) = $false) | ($true = $false) | ((sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) = (sK1 @ sK4)) | ((in @ X0 @ sK0) = $false) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0))))))) ) | (~spl3_1 | ~spl3_3 | ~spl3_5)),
% 0.21/0.49 inference(superposition,[],[f260,f216])).
% 0.21/0.49 thf(f216,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (($true = (in @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ sK0)) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ((in @ X0 @ sK0) = $false)) ) | ~spl3_3),
% 0.21/0.49 inference(avatar_component_clause,[],[f215])).
% 0.21/0.49 thf(f260,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((in @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ sK0) = $false) | ((in @ X0 @ sK0) = $false) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ((sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) = (sK1 @ sK4))) ) | (~spl3_1 | ~spl3_5)),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f259])).
% 0.21/0.49 thf(f259,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) = (sK1 @ sK4)) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ((in @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ sK0) = $false) | ($true = $false) | ((in @ X0 @ sK0) = $false)) ) | (~spl3_1 | ~spl3_5)),
% 0.21/0.49 inference(forward_demodulation,[],[f258,f138])).
% 0.21/0.49 thf(f258,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) = (sK1 @ sK4)) | ((in @ X0 @ sK0) = $false) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ((in @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ sK0) = $false) | ((in @ sK4 @ sK2) = $false)) ) | ~spl3_5),
% 0.21/0.49 inference(equality_proxy_clausification,[],[f257])).
% 0.21/0.49 thf(f257,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((in @ X0 @ sK0) = $false) | ((in @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ sK0) = $false) | ((in @ sK4 @ sK2) = $false) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ($true = ((sK1 @ sK4) = (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))))))) ) | ~spl3_5),
% 0.21/0.49 inference(beta_eta_normalization,[],[f256])).
% 0.21/0.49 thf(f256,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((in @ sK4 @ sK2) = $false) | ((in @ X0 @ sK0) = $false) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ((in @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ sK0) = $false) | ($true = ((^[Y0 : $i]: (= @ (sK1 @ Y0))) @ sK4 @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))))))) ) | ~spl3_5),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f252])).
% 0.21/0.49 thf(f252,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (($true = ((^[Y0 : $i]: (= @ (sK1 @ Y0))) @ sK4 @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))))) | ((in @ sK4 @ sK2) = $false) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ($true = $false) | ((in @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ sK0) = $false) | ((in @ X0 @ sK0) = $false)) ) | ~spl3_5),
% 0.21/0.49 inference(superposition,[],[f87,f224])).
% 0.21/0.49 thf(f224,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((in @ (kpair @ sK4 @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))))) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0))))) = $true) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ((in @ X0 @ sK0) = $false)) ) | ~spl3_5),
% 0.21/0.49 inference(avatar_component_clause,[],[f223])).
% 0.21/0.49 thf(f87,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i,X5 : $i] : (($false = (in @ (kpair @ X3 @ X5) @ (dpsetconstr @ X4 @ X2 @ X1))) | ($true = (X1 @ X3 @ X5)) | ($false = (in @ X5 @ X2)) | ((in @ X3 @ X4) = $false)) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f86])).
% 0.21/0.49 thf(f86,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $false) | ($false = (in @ X5 @ X2)) | ($true = ((in @ (kpair @ X3 @ X5) @ (dpsetconstr @ X4 @ X2 @ X1)) => (X1 @ X3 @ X5)))) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f85])).
% 0.21/0.49 thf(f85,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i,X5 : $i] : ((((in @ X5 @ X2) => ((in @ (kpair @ X3 @ X5) @ (dpsetconstr @ X4 @ X2 @ X1)) => (X1 @ X3 @ X5))) = $true) | ((in @ X3 @ X4) = $false)) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f84])).
% 0.21/0.49 thf(f84,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $false) | ($true = ((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ X3 @ Y0) @ (dpsetconstr @ X4 @ X2 @ X1)) => (X1 @ X3 @ Y0)))) @ X5))) )),
% 0.21/0.49 inference(pi_clausification,[],[f83])).
% 0.21/0.49 thf(f83,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i] : (((in @ X3 @ X4) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ X3 @ Y0) @ (dpsetconstr @ X4 @ X2 @ X1)) => (X1 @ X3 @ Y0))))))) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f82])).
% 0.21/0.49 thf(f82,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i] : (($true = ((in @ X3 @ X4) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ X3 @ Y0) @ (dpsetconstr @ X4 @ X2 @ X1)) => (X1 @ X3 @ Y0)))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f81])).
% 0.21/0.49 thf(f81,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i] : (($true = ((^[Y0 : $i]: ((in @ X3 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ X3 @ Y1) @ (dpsetconstr @ Y0 @ X2 @ X1)) => (X1 @ X3 @ Y1))))))) @ X4))) )),
% 0.21/0.49 inference(pi_clausification,[],[f80])).
% 0.21/0.49 thf(f80,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X3 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ X3 @ Y1) @ (dpsetconstr @ Y0 @ X2 @ X1)) => (X1 @ X3 @ Y1)))))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f79])).
% 0.21/0.49 thf(f79,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ Y1 @ X2 @ X1)) => (X1 @ Y0 @ Y2))))))))) @ X3))) )),
% 0.21/0.49 inference(pi_clausification,[],[f78])).
% 0.21/0.49 thf(f78,plain,(
% 0.21/0.49 ( ! [X2 : $i,X1 : $i > $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ Y1 @ X2 @ X1)) => (X1 @ Y0 @ Y2)))))))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f77])).
% 0.21/0.49 thf(f77,plain,(
% 0.21/0.49 ( ! [X2 : $i,X1 : $i > $i > $o] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ Y2 @ Y0 @ X1)) => (X1 @ Y1 @ Y3))))))))))) @ X2))) )),
% 0.21/0.49 inference(pi_clausification,[],[f76])).
% 0.21/0.49 thf(f76,plain,(
% 0.21/0.49 ( ! [X1 : $i > $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ Y2 @ Y0 @ X1)) => (X1 @ Y1 @ Y3)))))))))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f75])).
% 0.21/0.49 thf(f75,plain,(
% 0.21/0.49 ( ! [X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ Y0)) => (Y0 @ Y2 @ Y4))))))))))))) @ X1))) )),
% 0.21/0.49 inference(pi_clausification,[],[f74])).
% 0.21/0.49 thf(f74,plain,(
% 0.21/0.49 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ Y0)) => (Y0 @ Y2 @ Y4)))))))))))))))),
% 0.21/0.49 inference(beta_eta_normalization,[],[f53])).
% 0.21/0.49 thf(f53,plain,(
% 0.21/0.49 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6)))))) => (Y0 @ Y2 @ Y4)))))))))))))))),
% 0.21/0.49 inference(definition_unfolding,[],[f45,f38])).
% 0.21/0.49 thf(f38,plain,(
% 0.21/0.49 (dpsetconstrERa = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6)))))) => (Y0 @ Y2 @ Y4)))))))))))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f29])).
% 0.21/0.49 thf(f29,plain,(
% 0.21/0.49 (dpsetconstrERa = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6)))))) => (Y0 @ Y2 @ Y4)))))))))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f28])).
% 0.21/0.49 thf(f28,plain,(
% 0.21/0.49 (dpsetconstrERa = ! [X0,X1,X2,X3 : $i > $i > $o] : ((in @ X1 @ X0) => ! [X4] : ((in @ X4 @ X2) => ((in @ (kpair @ X1 @ X4) @ (dpsetconstr @ X0 @ X2 @ (^[X5 : $i, X6 : $i] : (X3 @ X5 @ X6)))) => (X3 @ X1 @ X4)))))),
% 0.21/0.49 inference(rectify,[],[f7])).
% 0.21/0.49 thf(f7,axiom,(
% 0.21/0.49 (dpsetconstrERa = ! [X0,X1,X4,X2 : $i > $i > $o] : ((in @ X1 @ X0) => ! [X3] : ((in @ X3 @ X4) => ((in @ (kpair @ X1 @ X3) @ (dpsetconstr @ X0 @ X4 @ (^[X6 : $i, X7 : $i] : (X2 @ X6 @ X7)))) => (X2 @ X1 @ X3)))))),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrERa)).
% 0.21/0.49 thf(f45,plain,(
% 0.21/0.49 (dpsetconstrERa = $true)),
% 0.21/0.49 inference(cnf_transformation,[],[f33])).
% 0.21/0.49 thf(f232,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != X0) | ((in @ X0 @ sK0) = $false) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0))))))) ) | ~spl3_7),
% 0.21/0.49 inference(avatar_component_clause,[],[f231])).
% 0.21/0.49 thf(f132,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i,X4 : $i,X5 : $i] : (($true = (in @ (kpair @ X2 @ X5) @ (dpsetconstr @ X1 @ X4 @ X3))) | ($false = (in @ X5 @ X4)) | ((in @ X2 @ X1) = $false) | ((X3 @ X2 @ X5) = $false)) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f131])).
% 0.21/0.49 thf(f131,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i,X4 : $i,X5 : $i] : (((in @ X2 @ X1) = $false) | ($true = ((X3 @ X2 @ X5) => (in @ (kpair @ X2 @ X5) @ (dpsetconstr @ X1 @ X4 @ X3)))) | ($false = (in @ X5 @ X4))) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f130])).
% 0.21/0.49 thf(f130,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i,X4 : $i,X5 : $i] : (((in @ X2 @ X1) = $false) | ($true = ((in @ X5 @ X4) => ((X3 @ X2 @ X5) => (in @ (kpair @ X2 @ X5) @ (dpsetconstr @ X1 @ X4 @ X3)))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f129])).
% 0.21/0.49 thf(f129,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i,X4 : $i,X5 : $i] : (((in @ X2 @ X1) = $false) | ($true = ((^[Y0 : $i]: ((in @ Y0 @ X4) => ((X3 @ X2 @ Y0) => (in @ (kpair @ X2 @ Y0) @ (dpsetconstr @ X1 @ X4 @ X3))))) @ X5))) )),
% 0.21/0.49 inference(pi_clausification,[],[f128])).
% 0.21/0.49 thf(f128,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i,X4 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X4) => ((X3 @ X2 @ Y0) => (in @ (kpair @ X2 @ Y0) @ (dpsetconstr @ X1 @ X4 @ X3))))))) | ((in @ X2 @ X1) = $false)) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f127])).
% 0.21/0.49 thf(f127,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i,X4 : $i] : (($true = ((in @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X4) => ((X3 @ X2 @ Y0) => (in @ (kpair @ X2 @ Y0) @ (dpsetconstr @ X1 @ X4 @ X3))))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f126])).
% 0.21/0.49 thf(f126,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i,X4 : $i] : (($true = ((^[Y0 : $i]: ((in @ X2 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X3 @ X2 @ Y1) => (in @ (kpair @ X2 @ Y1) @ (dpsetconstr @ X1 @ Y0 @ X3)))))))) @ X4))) )),
% 0.21/0.49 inference(pi_clausification,[],[f125])).
% 0.21/0.49 thf(f125,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X3 @ X2 @ Y1) => (in @ (kpair @ X2 @ Y1) @ (dpsetconstr @ X1 @ Y0 @ X3))))))))) = $true)) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f124])).
% 0.21/0.49 thf(f124,plain,(
% 0.21/0.49 ( ! [X2 : $i,X3 : $i > $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X2 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ X2 @ Y2) => (in @ (kpair @ X2 @ Y2) @ (dpsetconstr @ X1 @ Y1 @ Y0)))))))))) @ X3))) )),
% 0.21/0.49 inference(pi_clausification,[],[f123])).
% 0.21/0.49 thf(f123,plain,(
% 0.21/0.49 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X2 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ X2 @ Y2) => (in @ (kpair @ X2 @ Y2) @ (dpsetconstr @ X1 @ Y1 @ Y0))))))))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f122])).
% 0.21/0.49 thf(f122,plain,(
% 0.21/0.49 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y0 @ Y3) => (in @ (kpair @ Y0 @ Y3) @ (dpsetconstr @ X1 @ Y2 @ Y1)))))))))))) @ X2))) )),
% 0.21/0.49 inference(pi_clausification,[],[f121])).
% 0.21/0.49 thf(f121,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y0 @ Y3) => (in @ (kpair @ Y0 @ Y3) @ (dpsetconstr @ X1 @ Y2 @ Y1))))))))))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f120])).
% 0.21/0.49 thf(f120,plain,(
% 0.21/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ Y2)))))))))))))) @ X1) = $true)) )),
% 0.21/0.49 inference(pi_clausification,[],[f119])).
% 0.21/0.49 thf(f119,plain,(
% 0.21/0.49 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ Y2))))))))))))))))),
% 0.21/0.49 inference(beta_eta_normalization,[],[f55])).
% 0.21/0.49 thf(f55,plain,(
% 0.21/0.49 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6))))))))))))))))))))),
% 0.21/0.49 inference(definition_unfolding,[],[f43,f36])).
% 0.21/0.49 thf(f36,plain,(
% 0.21/0.49 (dpsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6))))))))))))))))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f13])).
% 0.21/0.49 thf(f13,plain,(
% 0.21/0.49 (dpsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6))))))))))))))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f12])).
% 0.21/0.49 thf(f12,plain,(
% 0.21/0.49 (dpsetconstrI = ! [X0,X1 : $i > $i > $o,X2,X3] : ((in @ X2 @ X3) => ! [X4] : ((in @ X4 @ X0) => ((X1 @ X2 @ X4) => (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X0 @ (^[X5 : $i, X6 : $i] : (X1 @ X5 @ X6))))))))),
% 0.21/0.49 inference(rectify,[],[f5])).
% 0.21/0.49 thf(f5,axiom,(
% 0.21/0.49 (dpsetconstrI = ! [X4,X2 : $i > $i > $o,X1,X0] : ((in @ X1 @ X0) => ! [X3] : ((in @ X3 @ X4) => ((X2 @ X1 @ X3) => (in @ (kpair @ X1 @ X3) @ (dpsetconstr @ X0 @ X4 @ (^[X6 : $i, X7 : $i] : (X2 @ X6 @ X7))))))))),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI)).
% 0.21/0.49 thf(f43,plain,(
% 0.21/0.49 (dpsetconstrI = $true)),
% 0.21/0.49 inference(cnf_transformation,[],[f33])).
% 0.21/0.49 thf(f248,plain,(
% 0.21/0.49 spl3_7 | spl3_6),
% 0.21/0.49 inference(avatar_split_clause,[],[f244,f226,f231])).
% 0.21/0.49 thf(f226,plain,(
% 0.21/0.49 spl3_6 <=> ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) = (setadjoin @ (sK7 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ emptyset))),
% 0.21/0.49 introduced(avatar_definition,[new_symbols(naming,[spl3_6])])).
% 0.21/0.49 thf(f244,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((in @ X0 @ sK0) = $false) | ((sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != X0) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0))))))) ) | spl3_6),
% 0.21/0.49 inference(beta_eta_normalization,[],[f243])).
% 0.21/0.49 thf(f243,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((in @ X0 @ sK0) = $false) | ((sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != X0) | (((^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))) @ X0) = $false)) ) | spl3_6),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f242])).
% 0.21/0.49 thf(f242,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != X0) | ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))))) | (((^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))) @ X0) = $false) | ((in @ X0 @ sK0) = $false)) ) | spl3_6),
% 0.21/0.49 inference(superposition,[],[f228,f117])).
% 0.21/0.49 thf(f117,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((dsetconstr @ X1 @ X2) = (setadjoin @ (sK7 @ X1 @ X2) @ emptyset)) | ((in @ X3 @ X1) = $false) | ((sK5 @ X3 @ X1 @ X2) != X3) | ((X2 @ X3) = $false)) )),
% 0.21/0.49 inference(equality_proxy_clausification,[],[f116])).
% 0.21/0.49 thf(f116,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((X2 @ X3) = $false) | ((sK5 @ X3 @ X1 @ X2) != X3) | ($true = ((setadjoin @ (sK7 @ X1 @ X2) @ emptyset) = (dsetconstr @ X1 @ X2))) | ((in @ X3 @ X1) = $false)) )),
% 0.21/0.49 inference(equality_proxy_clausification,[],[f115])).
% 0.21/0.49 thf(f115,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = (X3 = (sK5 @ X3 @ X1 @ X2))) | ((X2 @ X3) = $false) | ((in @ X3 @ X1) = $false) | ($true = ((setadjoin @ (sK7 @ X1 @ X2) @ emptyset) = (dsetconstr @ X1 @ X2)))) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f109])).
% 0.21/0.49 thf(f109,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((X2 @ X3) = $false) | ((in @ X3 @ X1) = $false) | ($true = (((setadjoin @ (sK7 @ X1 @ X2) @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ (sK7 @ X1 @ X2) @ (dsetconstr @ X1 @ X2)))) | ($false = (X3 = (sK5 @ X3 @ X1 @ X2)))) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f108])).
% 0.21/0.49 thf(f108,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((in @ X3 @ X1) = $false) | ((X2 @ X3) = $false) | (((X2 @ (sK5 @ X3 @ X1 @ X2)) => (X3 = (sK5 @ X3 @ X1 @ X2))) = $false) | ($true = (((setadjoin @ (sK7 @ X1 @ X2) @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ (sK7 @ X1 @ X2) @ (dsetconstr @ X1 @ X2))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f107])).
% 0.21/0.49 thf(f107,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((in @ X3 @ X1) = $false) | ((X2 @ X3) = $false) | (((X2 @ (sK5 @ X3 @ X1 @ X2)) => (X3 = (sK5 @ X3 @ X1 @ X2))) = $false) | ($true = ((^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ Y0 @ (dsetconstr @ X1 @ X2)))) @ (sK7 @ X1 @ X2)))) )),
% 0.21/0.49 inference(sigma_clausification,[],[f100])).
% 0.21/0.49 thf(f100,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ Y0 @ (dsetconstr @ X1 @ X2)))))) | (((X2 @ (sK5 @ X3 @ X1 @ X2)) => (X3 = (sK5 @ X3 @ X1 @ X2))) = $false) | ((X2 @ X3) = $false) | ((in @ X3 @ X1) = $false)) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f99])).
% 0.21/0.49 thf(f99,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((in @ X3 @ X1) = $false) | ((X2 @ X3) = $false) | ($false = ((in @ (sK5 @ X3 @ X1 @ X2) @ X1) => ((X2 @ (sK5 @ X3 @ X1 @ X2)) => (X3 = (sK5 @ X3 @ X1 @ X2))))) | ($true = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ Y0 @ (dsetconstr @ X1 @ X2))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f98])).
% 0.21/0.49 thf(f98,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ Y0 @ (dsetconstr @ X1 @ X2)))))) | ((in @ X3 @ X1) = $false) | ((X2 @ X3) = $false) | (((^[Y0 : $i]: ((in @ Y0 @ X1) => ((X2 @ Y0) => (X3 = Y0)))) @ (sK5 @ X3 @ X1 @ X2)) = $false)) )),
% 0.21/0.49 inference(sigma_clausification,[],[f97])).
% 0.21/0.49 thf(f97,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((X2 @ X3) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((X2 @ Y0) => (X3 = Y0)))))) | ($true = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ Y0 @ (dsetconstr @ X1 @ X2)))))) | ((in @ X3 @ X1) = $false)) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f96])).
% 0.21/0.49 thf(f96,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((X2 @ X3) = $false) | ((in @ X3 @ X1) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((X2 @ Y0) => (X3 = Y0))))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ Y0 @ (dsetconstr @ X1 @ X2)))))))) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f95])).
% 0.21/0.49 thf(f95,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((in @ X3 @ X1) = $false) | ($true = ((X2 @ X3) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((X2 @ Y0) => (X3 = Y0))))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ Y0 @ (dsetconstr @ X1 @ X2))))))))) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f94])).
% 0.21/0.49 thf(f94,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ X1) => ((X2 @ X3) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((X2 @ Y0) => (X3 = Y0))))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ Y0 @ (dsetconstr @ X1 @ X2)))))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f93])).
% 0.21/0.49 thf(f93,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X1) => ((X2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((X2 @ Y1) => (Y0 = Y1))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ Y1 @ (dsetconstr @ X1 @ X2))))))))) @ X3))) )),
% 0.21/0.49 inference(pi_clausification,[],[f92])).
% 0.21/0.49 thf(f92,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((X2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((X2 @ Y1) => (Y0 = Y1))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ Y1 @ (dsetconstr @ X1 @ X2)))))))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f91])).
% 0.21/0.49 thf(f91,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y0 @ Y2) => (Y1 = Y2))))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X1 @ Y0)) & (in @ Y2 @ (dsetconstr @ X1 @ Y0))))))))))) @ X2))) )),
% 0.21/0.49 inference(pi_clausification,[],[f90])).
% 0.21/0.49 thf(f90,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y0 @ Y2) => (Y1 = Y2))))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X1 @ Y0)) & (in @ Y2 @ (dsetconstr @ X1 @ Y0)))))))))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f89])).
% 0.21/0.49 thf(f89,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y1)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y1))))))))))))) @ X1))) )),
% 0.21/0.49 inference(pi_clausification,[],[f88])).
% 0.21/0.49 thf(f88,plain,(
% 0.21/0.49 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y1)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y1)))))))))))))))),
% 0.21/0.49 inference(beta_eta_normalization,[],[f56])).
% 0.21/0.49 thf(f56,plain,(
% 0.21/0.49 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y3) => (Y2 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (((setadjoin @ Y6 @ emptyset) = Y5) & (in @ Y6 @ Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 0.21/0.49 inference(definition_unfolding,[],[f42,f51])).
% 0.21/0.49 thf(f51,plain,(
% 0.21/0.49 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y3) => (Y2 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (((setadjoin @ Y6 @ emptyset) = Y5) & (in @ Y6 @ Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 0.21/0.49 inference(definition_unfolding,[],[f41,f49])).
% 0.21/0.49 thf(f49,plain,(
% 0.21/0.49 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.21/0.49 inference(definition_unfolding,[],[f40,f34])).
% 0.21/0.49 thf(f34,plain,(
% 0.21/0.49 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f15])).
% 0.21/0.49 thf(f15,plain,(
% 0.21/0.49 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 0.21/0.49 inference(fool_elimination,[],[f14])).
% 0.21/0.49 thf(f14,plain,(
% 0.21/0.49 ((^[X0 : $i] : (? [X1] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 0.21/0.49 inference(rectify,[],[f1])).
% 0.21/0.49 thf(f1,axiom,(
% 0.21/0.49 ((^[X0 : $i] : (? [X1] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)).
% 0.21/0.49 thf(f40,plain,(
% 0.21/0.49 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f27])).
% 0.21/0.49 thf(f27,plain,(
% 0.21/0.49 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f26])).
% 0.21/0.49 thf(f26,plain,(
% 0.21/0.49 (ex1 = (^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))),
% 0.21/0.49 inference(rectify,[],[f2])).
% 0.21/0.49 thf(f2,axiom,(
% 0.21/0.49 (ex1 = (^[X0 : $i, X2 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X1 : $i] : (X2 @ X1))))))),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1)).
% 0.21/0.49 thf(f41,plain,(
% 0.21/0.49 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y3) => (Y2 = Y3))))) => (ex1 @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f21])).
% 0.21/0.49 thf(f21,plain,(
% 0.21/0.49 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y3) => (Y2 = Y3))))) => (ex1 @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f20])).
% 0.21/0.49 thf(f20,plain,(
% 0.21/0.49 (ex1I = ! [X0,X1 : $i > $o,X2] : ((in @ X0 @ X2) => ((X1 @ X0) => (! [X3] : ((in @ X3 @ X2) => ((X1 @ X3) => (X0 = X3))) => (ex1 @ X2 @ (^[X4 : $i] : (X1 @ X4)))))))),
% 0.21/0.49 inference(rectify,[],[f3])).
% 0.21/0.49 thf(f3,axiom,(
% 0.21/0.49 (ex1I = ! [X1,X2 : $i > $o,X0] : ((in @ X1 @ X0) => ((X2 @ X1) => (! [X3] : ((in @ X3 @ X0) => ((X2 @ X3) => (X1 = X3))) => (ex1 @ X0 @ (^[X3 : $i] : (X2 @ X3)))))))),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I)).
% 0.21/0.49 thf(f42,plain,(
% 0.21/0.49 (ex1I = $true)),
% 0.21/0.49 inference(cnf_transformation,[],[f33])).
% 0.21/0.49 thf(f228,plain,(
% 0.21/0.49 ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != (setadjoin @ (sK7 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ emptyset)) | spl3_6),
% 0.21/0.49 inference(avatar_component_clause,[],[f226])).
% 0.21/0.49 thf(f247,plain,(
% 0.21/0.49 spl3_5 | spl3_6),
% 0.21/0.49 inference(avatar_split_clause,[],[f246,f226,f223])).
% 0.21/0.49 thf(f246,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((in @ X0 @ sK0) = $false) | ((in @ (kpair @ sK4 @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))))) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0))))) = $true) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0))))))) ) | spl3_6),
% 0.21/0.49 inference(beta_eta_normalization,[],[f245])).
% 0.21/0.49 thf(f245,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (($true = ((^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))) @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))))) | ((in @ X0 @ sK0) = $false) | (((^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))) @ X0) = $false)) ) | spl3_6),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f241])).
% 0.21/0.49 thf(f241,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (($true = ((^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))) @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))))) | ((in @ X0 @ sK0) = $false) | (((^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))) @ X0) = $false) | ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))))) ) | spl3_6),
% 0.21/0.49 inference(superposition,[],[f228,f113])).
% 0.21/0.49 thf(f113,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((dsetconstr @ X1 @ X2) = (setadjoin @ (sK7 @ X1 @ X2) @ emptyset)) | ((in @ X3 @ X1) = $false) | ((X2 @ X3) = $false) | ($true = (X2 @ (sK5 @ X3 @ X1 @ X2)))) )),
% 0.21/0.49 inference(equality_proxy_clausification,[],[f112])).
% 0.21/0.49 thf(f112,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (X2 @ (sK5 @ X3 @ X1 @ X2))) | ($true = ((setadjoin @ (sK7 @ X1 @ X2) @ emptyset) = (dsetconstr @ X1 @ X2))) | ((in @ X3 @ X1) = $false) | ((X2 @ X3) = $false)) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f110])).
% 0.21/0.49 thf(f110,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (((setadjoin @ (sK7 @ X1 @ X2) @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ (sK7 @ X1 @ X2) @ (dsetconstr @ X1 @ X2)))) | ((in @ X3 @ X1) = $false) | ((X2 @ X3) = $false) | ($true = (X2 @ (sK5 @ X3 @ X1 @ X2)))) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f108])).
% 0.21/0.49 thf(f240,plain,(
% 0.21/0.49 spl3_3 | spl3_4),
% 0.21/0.49 inference(avatar_split_clause,[],[f239,f218,f215])).
% 0.21/0.49 thf(f218,plain,(
% 0.21/0.49 spl3_4 <=> ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) = (setadjoin @ (sK6 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ emptyset))),
% 0.21/0.49 introduced(avatar_definition,[new_symbols(naming,[spl3_4])])).
% 0.21/0.49 thf(f239,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ($true = (in @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ sK0)) | ((in @ X0 @ sK0) = $false)) ) | spl3_4),
% 0.21/0.49 inference(beta_eta_normalization,[],[f238])).
% 0.21/0.49 thf(f238,plain,(
% 0.21/0.49 ( ! [X0 : $i] : ((((^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))) @ X0) = $false) | ($true = (in @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ sK0)) | ((in @ X0 @ sK0) = $false)) ) | spl3_4),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f237])).
% 0.21/0.49 thf(f237,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (($true = (in @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ sK0)) | ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))))) | ((in @ X0 @ sK0) = $false) | (((^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))) @ X0) = $false)) ) | spl3_4),
% 0.21/0.49 inference(superposition,[],[f220,f106])).
% 0.21/0.49 thf(f106,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((dsetconstr @ X1 @ X2) = (setadjoin @ (sK6 @ X1 @ X2) @ emptyset)) | ($true = (in @ (sK5 @ X3 @ X1 @ X2) @ X1)) | ((in @ X3 @ X1) = $false) | ((X2 @ X3) = $false)) )),
% 0.21/0.49 inference(equality_proxy_clausification,[],[f105])).
% 0.21/0.49 thf(f105,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((in @ X3 @ X1) = $false) | ((X2 @ X3) = $false) | ($true = ((setadjoin @ (sK6 @ X1 @ X2) @ emptyset) = (dsetconstr @ X1 @ X2))) | ($true = (in @ (sK5 @ X3 @ X1 @ X2) @ X1))) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f103])).
% 0.21/0.49 thf(f103,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((X2 @ X3) = $false) | ((in @ X3 @ X1) = $false) | ($true = (in @ (sK5 @ X3 @ X1 @ X2) @ X1)) | ($true = (((setadjoin @ (sK6 @ X1 @ X2) @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ (sK6 @ X1 @ X2) @ (dsetconstr @ X1 @ X2))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f102])).
% 0.21/0.49 thf(f102,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (in @ (sK5 @ X3 @ X1 @ X2) @ X1)) | ((X2 @ X3) = $false) | ($true = ((^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ Y0 @ (dsetconstr @ X1 @ X2)))) @ (sK6 @ X1 @ X2))) | ((in @ X3 @ X1) = $false)) )),
% 0.21/0.49 inference(sigma_clausification,[],[f101])).
% 0.21/0.49 thf(f101,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((X2 @ X3) = $false) | ($true = (in @ (sK5 @ X3 @ X1 @ X2) @ X1)) | ((in @ X3 @ X1) = $false) | ($true = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ Y0 @ (dsetconstr @ X1 @ X2))))))) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f99])).
% 0.21/0.49 thf(f220,plain,(
% 0.21/0.49 ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != (setadjoin @ (sK6 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ emptyset)) | spl3_4),
% 0.21/0.49 inference(avatar_component_clause,[],[f218])).
% 0.21/0.49 thf(f236,plain,(
% 0.21/0.49 spl3_5 | ~spl3_6),
% 0.21/0.49 inference(avatar_split_clause,[],[f201,f226,f223])).
% 0.21/0.49 thf(f201,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != (setadjoin @ (sK7 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ emptyset)) | ((in @ X0 @ sK0) = $false) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ((in @ (kpair @ sK4 @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))))) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0))))) = $true)) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f200])).
% 0.21/0.49 thf(f200,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((in @ X0 @ sK0) = $false) | (((^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))) @ X0) = $false) | ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != (setadjoin @ (sK7 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ emptyset)) | ($true = ((^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))) @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))))))) )),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f196])).
% 0.21/0.49 thf(f196,plain,(
% 0.21/0.49 ( ! [X0 : $i] : ((((^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))) @ X0) = $false) | ((in @ X0 @ sK0) = $false) | ($true = $false) | ($true = ((^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))) @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))))) | ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != (setadjoin @ (sK7 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ emptyset))) )),
% 0.21/0.49 inference(superposition,[],[f111,f134])).
% 0.21/0.49 thf(f134,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (((in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))))) = $false) | ((setadjoin @ X1 @ emptyset) != (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))))) )),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f133])).
% 0.21/0.49 thf(f133,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (((setadjoin @ X1 @ emptyset) != (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))))) | ($true = $false) | ((in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))))) = $false)) )),
% 0.21/0.49 inference(forward_demodulation,[],[f66,f73])).
% 0.21/0.49 thf(f73,plain,(
% 0.21/0.49 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (($true = (subset @ (dpsetconstr @ X1 @ X3 @ X2) @ (cartprod @ X1 @ X3)))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f72])).
% 0.21/0.49 thf(f72,plain,(
% 0.21/0.49 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (subset @ (dpsetconstr @ X1 @ Y0 @ X2) @ (cartprod @ X1 @ Y0))) @ X3))) )),
% 0.21/0.49 inference(pi_clausification,[],[f71])).
% 0.21/0.49 thf(f71,plain,(
% 0.21/0.49 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (subset @ (dpsetconstr @ X1 @ Y0 @ X2) @ (cartprod @ X1 @ Y0)))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f70])).
% 0.21/0.49 thf(f70,plain,(
% 0.21/0.49 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dpsetconstr @ X1 @ Y1 @ Y0) @ (cartprod @ X1 @ Y1))))) @ X2))) )),
% 0.21/0.49 inference(pi_clausification,[],[f69])).
% 0.21/0.49 thf(f69,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dpsetconstr @ X1 @ Y1 @ Y0) @ (cartprod @ X1 @ Y1)))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f68])).
% 0.21/0.49 thf(f68,plain,(
% 0.21/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y0 @ Y2 @ Y1) @ (cartprod @ Y0 @ Y2))))))) @ X1) = $true)) )),
% 0.21/0.49 inference(pi_clausification,[],[f67])).
% 0.21/0.49 thf(f67,plain,(
% 0.21/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y0 @ Y2 @ Y1) @ (cartprod @ Y0 @ Y2)))))))) = $true)),
% 0.21/0.49 inference(beta_eta_normalization,[],[f54])).
% 0.21/0.49 thf(f54,plain,(
% 0.21/0.49 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4)))))))))))))),
% 0.21/0.49 inference(definition_unfolding,[],[f44,f48])).
% 0.21/0.49 thf(f48,plain,(
% 0.21/0.49 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4)))))))))))))),
% 0.21/0.49 inference(definition_unfolding,[],[f37,f39])).
% 0.21/0.49 thf(f39,plain,(
% 0.21/0.49 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f17])).
% 0.21/0.49 thf(f17,plain,(
% 0.21/0.49 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f16])).
% 0.21/0.49 thf(f16,plain,(
% 0.21/0.49 ((^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))) = breln)),
% 0.21/0.49 inference(rectify,[],[f4])).
% 0.21/0.49 thf(f4,axiom,(
% 0.21/0.49 ((^[X0 : $i, X4 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X0 @ X4))) = breln)),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln)).
% 0.21/0.49 thf(f37,plain,(
% 0.21/0.49 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (breln @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4)))))))))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f23])).
% 0.21/0.49 thf(f23,plain,(
% 0.21/0.49 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (breln @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4)))))))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f22])).
% 0.21/0.49 thf(f22,plain,(
% 0.21/0.49 (! [X0,X1 : $i > $i > $o,X2] : (breln @ X2 @ X0 @ (dpsetconstr @ X2 @ X0 @ (^[X3 : $i, X4 : $i] : (X1 @ X3 @ X4)))) = setOfPairsIsBReln)),
% 0.21/0.49 inference(rectify,[],[f6])).
% 0.21/0.49 thf(f6,axiom,(
% 0.21/0.49 (! [X4,X2 : $i > $i > $o,X0] : (breln @ X0 @ X4 @ (dpsetconstr @ X0 @ X4 @ (^[X1 : $i, X3 : $i] : (X2 @ X1 @ X3)))) = setOfPairsIsBReln)),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln)).
% 0.21/0.49 thf(f44,plain,(
% 0.21/0.49 (setOfPairsIsBReln = $true)),
% 0.21/0.49 inference(cnf_transformation,[],[f33])).
% 0.21/0.49 thf(f66,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($false = (subset @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))) @ (cartprod @ sK2 @ sK0))) | ((in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))))) = $false) | ((setadjoin @ X1 @ emptyset) != (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))))) )),
% 0.21/0.49 inference(equality_proxy_clausification,[],[f65])).
% 0.21/0.49 thf(f65,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (((in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))))) = $false) | ($false = (subset @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))) @ (cartprod @ sK2 @ sK0))) | (((setadjoin @ X1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))))) = $false)) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f64])).
% 0.21/0.49 thf(f64,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($false = (subset @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))) @ (cartprod @ sK2 @ sK0))) | ($false = (((setadjoin @ X1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))))) & (in @ X1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f63])).
% 0.21/0.49 thf(f63,plain,(
% 0.21/0.49 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK4 @ Y1) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y2 : $i]: (= @ (sK1 @ Y2)))))))) & (in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK4 @ Y1) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y2 : $i]: (= @ (sK1 @ Y2)))))))))) @ X1)) | ($false = (subset @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))) @ (cartprod @ sK2 @ sK0)))) )),
% 0.21/0.49 inference(pi_clausification,[],[f61])).
% 0.21/0.49 thf(f61,plain,(
% 0.21/0.49 ($false = (subset @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))) @ (cartprod @ sK2 @ sK0))) | ($false = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK4 @ Y1) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y2 : $i]: (= @ (sK1 @ Y2)))))))) & (in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK4 @ Y1) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y2 : $i]: (= @ (sK1 @ Y2))))))))))))),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f60])).
% 0.21/0.49 thf(f60,plain,(
% 0.21/0.49 ($false = ((in @ sK4 @ sK2) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK4 @ Y1) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y2 : $i]: (= @ (sK1 @ Y2)))))))) & (in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (in @ (kpair @ sK4 @ Y1) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y2 : $i]: (= @ (sK1 @ Y2))))))))))))) | ($false = (subset @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))) @ (cartprod @ sK2 @ sK0)))),
% 0.21/0.49 inference(beta_eta_normalization,[],[f59])).
% 0.21/0.49 thf(f59,plain,(
% 0.21/0.49 ($false = (subset @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))) @ (cartprod @ sK2 @ sK0))) | ($false = ((^[Y0 : $i]: ((in @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y3 : $i]: (= @ (sK1 @ Y3)))))))) & (in @ Y1 @ (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y3 : $i]: (= @ (sK1 @ Y3))))))))))))) @ sK4))),
% 0.21/0.49 inference(sigma_clausification,[],[f58])).
% 0.21/0.49 thf(f58,plain,(
% 0.21/0.49 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y3 : $i]: (= @ (sK1 @ Y3)))))))) & (in @ Y1 @ (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y3 : $i]: (= @ (sK1 @ Y3)))))))))))))) = $false) | ($false = (subset @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))) @ (cartprod @ sK2 @ sK0)))),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f57])).
% 0.21/0.49 thf(f57,plain,(
% 0.21/0.49 ($true != ((subset @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))) @ (cartprod @ sK2 @ sK0)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y3 : $i]: (= @ (sK1 @ Y3)))))))) & (in @ Y1 @ (dsetconstr @ sK0 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y3 : $i]: (= @ (sK1 @ Y3))))))))))))))))),
% 0.21/0.49 inference(beta_eta_normalization,[],[f52])).
% 0.21/0.49 thf(f52,plain,(
% 0.21/0.49 ($true != ((^[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)))))))))))) @ sK2 @ sK0 @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((sK1 @ Y0) = Y1)))))))),
% 0.21/0.49 inference(definition_unfolding,[],[f47,f50])).
% 0.21/0.49 thf(f50,plain,(
% 0.21/0.49 (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)))))))))))))),
% 0.21/0.49 inference(definition_unfolding,[],[f35,f39,f49])).
% 0.21/0.49 thf(f35,plain,(
% 0.21/0.49 (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)))))))))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f25])).
% 0.21/0.49 thf(f25,plain,(
% 0.21/0.49 (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)))))))))))))),
% 0.21/0.49 inference(fool_elimination,[],[f24])).
% 0.21/0.49 thf(f24,plain,(
% 0.21/0.49 (func = (^[X0 : $i, X1 : $i, X2 : $i] : (! [X3] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))) & (breln @ X0 @ X1 @ X2))))),
% 0.21/0.49 inference(rectify,[],[f8])).
% 0.21/0.49 thf(f8,axiom,(
% 0.21/0.49 (func = (^[X0 : $i, X4 : $i, X8 : $i] : (! [X1] : ((in @ X1 @ X0) => (ex1 @ X4 @ (^[X3 : $i] : (in @ (kpair @ X1 @ X3) @ X8)))) & (breln @ X0 @ X4 @ X8))))),
% 0.21/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',func)).
% 0.21/0.49 thf(f47,plain,(
% 0.21/0.49 ($true != (func @ sK2 @ sK0 @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((sK1 @ Y0) = Y1)))))))),
% 0.21/0.49 inference(cnf_transformation,[],[f33])).
% 0.21/0.49 thf(f111,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (in @ (sK7 @ X1 @ X2) @ (dsetconstr @ X1 @ X2))) | ((in @ X3 @ X1) = $false) | ((X2 @ X3) = $false) | ($true = (X2 @ (sK5 @ X3 @ X1 @ X2)))) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f110])).
% 0.21/0.49 thf(f235,plain,(
% 0.21/0.49 ~spl3_4 | spl3_3),
% 0.21/0.49 inference(avatar_split_clause,[],[f203,f215,f218])).
% 0.21/0.49 thf(f203,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((in @ X0 @ sK0) = $false) | ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != (setadjoin @ (sK6 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ emptyset)) | ($true = (in @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ sK0)) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0))))))) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f202])).
% 0.21/0.49 thf(f202,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != (setadjoin @ (sK6 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ emptyset)) | ((in @ X0 @ sK0) = $false) | (((^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))) @ X0) = $false) | ($true = (in @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ sK0))) )),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f198])).
% 0.21/0.49 thf(f198,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (($true = $false) | ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != (setadjoin @ (sK6 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ emptyset)) | (((^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))) @ X0) = $false) | ($true = (in @ (sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ sK0)) | ((in @ X0 @ sK0) = $false)) )),
% 0.21/0.49 inference(superposition,[],[f104,f134])).
% 0.21/0.49 thf(f104,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (in @ (sK6 @ X1 @ X2) @ (dsetconstr @ X1 @ X2))) | ((in @ X3 @ X1) = $false) | ((X2 @ X3) = $false) | ($true = (in @ (sK5 @ X3 @ X1 @ X2) @ X1))) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f103])).
% 0.21/0.49 thf(f234,plain,(
% 0.21/0.49 spl3_7 | ~spl3_6),
% 0.21/0.49 inference(avatar_split_clause,[],[f205,f226,f231])).
% 0.21/0.49 thf(f205,plain,(
% 0.21/0.49 ( ! [X0 : $i] : (((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != (setadjoin @ (sK7 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ emptyset)) | ($false = (in @ (kpair @ sK4 @ X0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))))) | ((in @ X0 @ sK0) = $false) | ((sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != X0)) )),
% 0.21/0.49 inference(beta_eta_normalization,[],[f204])).
% 0.21/0.49 thf(f204,plain,(
% 0.21/0.49 ( ! [X0 : $i] : ((((^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))) @ X0) = $false) | ((sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != X0) | ((in @ X0 @ sK0) = $false) | ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != (setadjoin @ (sK7 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ emptyset))) )),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f193])).
% 0.21/0.49 thf(f193,plain,(
% 0.21/0.49 ( ! [X0 : $i] : ((((^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1)))))) @ X0) = $false) | ((sK5 @ X0 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != X0) | ($true = $false) | ((in @ X0 @ sK0) = $false) | ((dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) != (setadjoin @ (sK7 @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK4 @ Y0) @ (dpsetconstr @ sK2 @ sK0 @ (^[Y1 : $i]: (= @ (sK1 @ Y1))))))) @ emptyset))) )),
% 0.21/0.49 inference(superposition,[],[f134,f118])).
% 0.21/0.49 thf(f118,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (in @ (sK7 @ X1 @ X2) @ (dsetconstr @ X1 @ X2))) | ((in @ X3 @ X1) = $false) | ((sK5 @ X3 @ X1 @ X2) != X3) | ((X2 @ X3) = $false)) )),
% 0.21/0.49 inference(equality_proxy_clausification,[],[f114])).
% 0.21/0.49 thf(f114,plain,(
% 0.21/0.49 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((in @ X3 @ X1) = $false) | ($true = (in @ (sK7 @ X1 @ X2) @ (dsetconstr @ X1 @ X2))) | ($false = (X3 = (sK5 @ X3 @ X1 @ X2))) | ((X2 @ X3) = $false)) )),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f109])).
% 0.21/0.49 thf(f153,plain,(
% 0.21/0.49 ~spl3_2),
% 0.21/0.49 inference(avatar_contradiction_clause,[],[f152])).
% 0.21/0.49 thf(f152,plain,(
% 0.21/0.49 $false | ~spl3_2),
% 0.21/0.49 inference(trivial_inequality_removal,[],[f148])).
% 0.21/0.49 thf(f148,plain,(
% 0.21/0.49 ($true = $false) | ~spl3_2),
% 0.21/0.49 inference(superposition,[],[f73,f142])).
% 0.21/0.49 thf(f142,plain,(
% 0.21/0.49 ($false = (subset @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))) @ (cartprod @ sK2 @ sK0))) | ~spl3_2),
% 0.21/0.49 inference(avatar_component_clause,[],[f140])).
% 0.21/0.49 thf(f140,plain,(
% 0.21/0.49 spl3_2 <=> ($false = (subset @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))) @ (cartprod @ sK2 @ sK0)))),
% 0.21/0.49 introduced(avatar_definition,[new_symbols(naming,[spl3_2])])).
% 0.21/0.49 thf(f143,plain,(
% 0.21/0.49 spl3_1 | spl3_2),
% 0.21/0.49 inference(avatar_split_clause,[],[f62,f140,f136])).
% 0.21/0.49 thf(f62,plain,(
% 0.21/0.49 ($true = (in @ sK4 @ sK2)) | ($false = (subset @ (dpsetconstr @ sK2 @ sK0 @ (^[Y0 : $i]: (= @ (sK1 @ Y0)))) @ (cartprod @ sK2 @ sK0)))),
% 0.21/0.49 inference(binary_proxy_clausification,[],[f60])).
% 0.21/0.49 % SZS output end Proof for theBenchmark
% 0.21/0.49 % (6786)------------------------------
% 0.21/0.49 % (6786)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49 % (6786)Termination reason: Refutation
% 0.21/0.49
% 0.21/0.49 % (6786)Memory used [KB]: 6012
% 0.21/0.49 % (6786)Time elapsed: 0.041 s
% 0.21/0.49 % (6786)Instructions burned: 58 (million)
% 0.21/0.49 % (6786)------------------------------
% 0.21/0.49 % (6786)------------------------------
% 0.21/0.49 % (6735)Success in time 0.128 s
% 0.21/0.49 % Vampire---4.8 exiting
%------------------------------------------------------------------------------