TSTP Solution File: SEU492^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU492^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n026.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 03:49:08 EDT 2024
% Result : Theorem 0.15s 0.35s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU492^1 : TPTP v8.2.0. Released v3.6.0.
% 0.11/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.11/0.29 % Computer : n026.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Sun May 19 17:15:22 EDT 2024
% 0.11/0.29 % CPUTime :
% 0.11/0.29 This is a TH0_THM_EQU_NAR problem
% 0.15/0.29 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.31 % (28278)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.15/0.31 % (28274)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.31 % (28277)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.31 % (28279)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.31 % (28277)Instruction limit reached!
% 0.15/0.31 % (28277)------------------------------
% 0.15/0.31 % (28277)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.31 % (28277)Termination reason: Unknown
% 0.15/0.31 % (28277)Termination phase: shuffling
% 0.15/0.31
% 0.15/0.31 % (28277)Memory used [KB]: 1023
% 0.15/0.31 % (28277)Time elapsed: 0.002 s
% 0.15/0.31 % (28277)Instructions burned: 3 (million)
% 0.15/0.31 % (28277)------------------------------
% 0.15/0.31 % (28277)------------------------------
% 0.15/0.31 % (28274)Instruction limit reached!
% 0.15/0.31 % (28274)------------------------------
% 0.15/0.31 % (28274)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.31 % (28274)Termination reason: Unknown
% 0.15/0.31 % (28274)Termination phase: Property scanning
% 0.15/0.31
% 0.15/0.31 % (28274)Memory used [KB]: 1023
% 0.15/0.31 % (28274)Time elapsed: 0.003 s
% 0.15/0.31 % (28274)Instructions burned: 6 (million)
% 0.15/0.31 % (28274)------------------------------
% 0.15/0.31 % (28274)------------------------------
% 0.15/0.31 % (28275)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.15/0.31 % (28280)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.31 % (28279)Instruction limit reached!
% 0.15/0.31 % (28279)------------------------------
% 0.15/0.31 % (28279)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.31 % (28279)Termination reason: Unknown
% 0.15/0.31 % (28279)Termination phase: Saturation
% 0.15/0.31
% 0.15/0.31 % (28279)Memory used [KB]: 5628
% 0.15/0.31 % (28279)Time elapsed: 0.006 s
% 0.15/0.31 % (28279)Instructions burned: 18 (million)
% 0.15/0.31 % (28279)------------------------------
% 0.15/0.31 % (28279)------------------------------
% 0.15/0.31 % (28273)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.31 % (28280)Instruction limit reached!
% 0.15/0.31 % (28280)------------------------------
% 0.15/0.31 % (28280)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.31 % (28280)Termination reason: Unknown
% 0.15/0.31 % (28280)Termination phase: shuffling
% 0.15/0.31
% 0.15/0.31 % (28276)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.31 % (28280)Memory used [KB]: 1023
% 0.15/0.31 % (28280)Time elapsed: 0.003 s
% 0.15/0.31 % (28280)Instructions burned: 4 (million)
% 0.15/0.31 % (28280)------------------------------
% 0.15/0.31 % (28280)------------------------------
% 0.15/0.31 % (28276)Instruction limit reached!
% 0.15/0.31 % (28276)------------------------------
% 0.15/0.31 % (28276)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.31 % (28276)Termination reason: Unknown
% 0.15/0.31 % (28276)Termination phase: shuffling
% 0.15/0.31
% 0.15/0.31 % (28276)Memory used [KB]: 1023
% 0.15/0.31 % (28276)Time elapsed: 0.003 s
% 0.15/0.31 % (28276)Instructions burned: 2 (million)
% 0.15/0.31 % (28276)------------------------------
% 0.15/0.31 % (28276)------------------------------
% 0.15/0.32 % (28281)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.15/0.32 % (28282)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.15/0.32 % (28283)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.32 % (28275)Instruction limit reached!
% 0.15/0.32 % (28275)------------------------------
% 0.15/0.32 % (28275)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (28275)Termination reason: Unknown
% 0.15/0.32 % (28275)Termination phase: Saturation
% 0.15/0.32
% 0.15/0.32 % (28275)Memory used [KB]: 5756
% 0.15/0.32 % (28275)Time elapsed: 0.013 s
% 0.15/0.32 % (28275)Instructions burned: 28 (million)
% 0.15/0.32 % (28275)------------------------------
% 0.15/0.32 % (28275)------------------------------
% 0.15/0.32 % (28283)Instruction limit reached!
% 0.15/0.32 % (28283)------------------------------
% 0.15/0.32 % (28283)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (28283)Termination reason: Unknown
% 0.15/0.32 % (28283)Termination phase: Property scanning
% 0.15/0.32
% 0.15/0.32 % (28283)Memory used [KB]: 1023
% 0.15/0.32 % (28283)Time elapsed: 0.003 s
% 0.15/0.32 % (28283)Instructions burned: 5 (million)
% 0.15/0.32 % (28283)------------------------------
% 0.15/0.32 % (28283)------------------------------
% 0.15/0.32 % (28282)Instruction limit reached!
% 0.15/0.32 % (28282)------------------------------
% 0.15/0.32 % (28282)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (28282)Termination reason: Unknown
% 0.15/0.32 % (28282)Termination phase: Saturation
% 0.15/0.32
% 0.15/0.32 % (28282)Memory used [KB]: 5628
% 0.15/0.32 % (28282)Time elapsed: 0.006 s
% 0.15/0.32 % (28282)Instructions burned: 16 (million)
% 0.15/0.32 % (28282)------------------------------
% 0.15/0.32 % (28282)------------------------------
% 0.15/0.32 % (28284)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.15/0.33 % (28281)Instruction limit reached!
% 0.15/0.33 % (28281)------------------------------
% 0.15/0.33 % (28281)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (28281)Termination reason: Unknown
% 0.15/0.33 % (28281)Termination phase: Saturation
% 0.15/0.33
% 0.15/0.33 % (28281)Memory used [KB]: 5756
% 0.15/0.33 % (28281)Time elapsed: 0.013 s
% 0.15/0.33 % (28281)Instructions burned: 37 (million)
% 0.15/0.33 % (28281)------------------------------
% 0.15/0.33 % (28281)------------------------------
% 0.15/0.33 % (28285)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.33 % (28287)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.33 % (28286)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.15/0.33 % (28287)Instruction limit reached!
% 0.15/0.33 % (28287)------------------------------
% 0.15/0.33 % (28287)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (28287)Termination reason: Unknown
% 0.15/0.33 % (28287)Termination phase: Property scanning
% 0.15/0.33
% 0.15/0.33 % (28287)Memory used [KB]: 1023
% 0.15/0.33 % (28287)Time elapsed: 0.003 s
% 0.15/0.33 % (28287)Instructions burned: 6 (million)
% 0.15/0.33 % (28287)------------------------------
% 0.15/0.33 % (28287)------------------------------
% 0.15/0.33 % (28288)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.33 % (28285)Instruction limit reached!
% 0.15/0.33 % (28285)------------------------------
% 0.15/0.33 % (28285)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (28285)Termination reason: Unknown
% 0.15/0.33 % (28285)Termination phase: Property scanning
% 0.15/0.33
% 0.15/0.33 % (28285)Memory used [KB]: 1023
% 0.15/0.33 % (28285)Time elapsed: 0.006 s
% 0.15/0.33 % (28285)Instructions burned: 8 (million)
% 0.15/0.33 % (28285)------------------------------
% 0.15/0.33 % (28285)------------------------------
% 0.15/0.33 % (28288)Instruction limit reached!
% 0.15/0.33 % (28288)------------------------------
% 0.15/0.33 % (28288)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (28288)Termination reason: Unknown
% 0.15/0.33 % (28288)Termination phase: Property scanning
% 0.15/0.33
% 0.15/0.33 % (28288)Memory used [KB]: 1023
% 0.15/0.33 % (28288)Time elapsed: 0.003 s
% 0.15/0.33 % (28288)Instructions burned: 5 (million)
% 0.15/0.33 % (28288)------------------------------
% 0.15/0.33 % (28288)------------------------------
% 0.15/0.34 % (28289)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.34 % (28286)Instruction limit reached!
% 0.15/0.34 % (28286)------------------------------
% 0.15/0.34 % (28286)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34 % (28286)Termination reason: Unknown
% 0.15/0.34 % (28286)Termination phase: Saturation
% 0.15/0.34
% 0.15/0.34 % (28286)Memory used [KB]: 5756
% 0.15/0.34 % (28286)Time elapsed: 0.008 s
% 0.15/0.34 % (28286)Instructions burned: 16 (million)
% 0.15/0.34 % (28286)------------------------------
% 0.15/0.34 % (28286)------------------------------
% 0.15/0.34 % (28290)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.34 % (28289)Instruction limit reached!
% 0.15/0.34 % (28289)------------------------------
% 0.15/0.34 % (28289)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34 % (28289)Termination reason: Unknown
% 0.15/0.34 % (28289)Termination phase: Saturation
% 0.15/0.34
% 0.15/0.34 % (28289)Memory used [KB]: 1151
% 0.15/0.34 % (28289)Time elapsed: 0.004 s
% 0.15/0.34 % (28289)Instructions burned: 10 (million)
% 0.15/0.34 % (28289)------------------------------
% 0.15/0.34 % (28289)------------------------------
% 0.15/0.34 % (28290)Instruction limit reached!
% 0.15/0.34 % (28290)------------------------------
% 0.15/0.34 % (28290)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34 % (28290)Termination reason: Unknown
% 0.15/0.34 % (28290)Termination phase: Property scanning
% 0.15/0.34
% 0.15/0.34 % (28290)Memory used [KB]: 1023
% 0.15/0.34 % (28290)Time elapsed: 0.003 s
% 0.15/0.34 % (28290)Instructions burned: 6 (million)
% 0.15/0.34 % (28290)------------------------------
% 0.15/0.34 % (28290)------------------------------
% 0.15/0.34 % (28292)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.34 % (28284)First to succeed.
% 0.15/0.35 % (28284)Refutation found. Thanks to Tanya!
% 0.15/0.35 % SZS status Theorem for theBenchmark
% 0.15/0.35 % SZS output start Proof for theBenchmark
% 0.15/0.35 thf(func_def_0, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_2, type, inv: ($i > $i > $o) > $i > $i > $o).
% 0.15/0.35 thf(func_def_3, type, idem: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_4, type, infl: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_5, type, mono: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_6, type, refl: ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_7, type, irrefl: ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_8, type, rc: ($i > $i > $o) > $i > $i > $o).
% 0.15/0.35 thf(func_def_9, type, symm: ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_10, type, antisymm: ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_11, type, asymm: ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_12, type, sc: ($i > $i > $o) > $i > $i > $o).
% 0.15/0.35 thf(func_def_13, type, trans: ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_14, type, tc: ($i > $i > $o) > $i > $i > $o).
% 0.15/0.35 thf(func_def_15, type, trc: ($i > $i > $o) > $i > $i > $o).
% 0.15/0.35 thf(func_def_16, type, trsc: ($i > $i > $o) > $i > $i > $o).
% 0.15/0.35 thf(func_def_17, type, po: ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_18, type, so: ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_19, type, total: ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_20, type, term: ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_21, type, ind: ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_22, type, innf: ($i > $i > $o) > $i > $o).
% 0.15/0.35 thf(func_def_23, type, nfof: ($i > $i > $o) > $i > $i > $o).
% 0.15/0.35 thf(func_def_24, type, norm: ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_25, type, join: ($i > $i > $o) > $i > $i > $o).
% 0.15/0.35 thf(func_def_26, type, lconfl: ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_27, type, sconfl: ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_28, type, confl: ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_29, type, cr: ($i > $i > $o) > $o).
% 0.15/0.35 thf(func_def_45, type, ph1: !>[X0: $tType]:(X0)).
% 0.15/0.35 thf(func_def_46, type, sK2: $i > $i > $o).
% 0.15/0.35 thf(f289,plain,(
% 0.15/0.35 $false),
% 0.15/0.35 inference(avatar_sat_refutation,[],[f152,f159,f163,f172,f202,f208,f219,f288])).
% 0.15/0.35 thf(f288,plain,(
% 0.15/0.35 ~spl0_2 | ~spl0_4),
% 0.15/0.35 inference(avatar_contradiction_clause,[],[f287])).
% 0.15/0.35 thf(f287,plain,(
% 0.15/0.35 $false | (~spl0_2 | ~spl0_4)),
% 0.15/0.35 inference(trivial_inequality_removal,[],[f286])).
% 0.15/0.35 thf(f286,plain,(
% 0.15/0.35 ($true = $false) | (~spl0_2 | ~spl0_4)),
% 0.15/0.35 inference(boolean_simplification,[],[f285])).
% 0.15/0.35 thf(f285,plain,(
% 0.15/0.35 ($true = (~ $true)) | (~spl0_2 | ~spl0_4)),
% 0.15/0.35 inference(forward_demodulation,[],[f278,f238])).
% 0.15/0.35 thf(f238,plain,(
% 0.15/0.35 ($true = (sK2 @ sK5 @ sK4)) | (~spl0_2 | ~spl0_4)),
% 0.15/0.35 inference(binary_proxy_clausification,[],[f236])).
% 0.15/0.35 thf(f236,plain,(
% 0.15/0.35 (((sK2 @ sK5 @ sK4) => (~ (sK2 @ sK4 @ sK5))) = $false) | (~spl0_2 | ~spl0_4)),
% 0.15/0.35 inference(beta_eta_normalization,[],[f235])).
% 0.15/0.35 thf(f235,plain,(
% 0.15/0.35 (((^[Y0 : $i]: ((sK2 @ Y0 @ sK4) => (~ (sK2 @ sK4 @ Y0)))) @ sK5) = $false) | (~spl0_2 | ~spl0_4)),
% 0.15/0.35 inference(sigma_clausification,[],[f231])).
% 0.15/0.35 thf(f231,plain,(
% 0.15/0.35 ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0 @ sK4) => (~ (sK2 @ sK4 @ Y0))))) = $false) | (~spl0_2 | ~spl0_4)),
% 0.15/0.35 inference(beta_eta_normalization,[],[f230])).
% 0.15/0.35 thf(f230,plain,(
% 0.15/0.35 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1)))))) @ sK4)) | (~spl0_2 | ~spl0_4)),
% 0.15/0.35 inference(sigma_clausification,[],[f227])).
% 0.15/0.35 thf(f227,plain,(
% 0.15/0.35 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1))))))) = $false) | (~spl0_2 | ~spl0_4)),
% 0.15/0.35 inference(boolean_simplification,[],[f226])).
% 0.15/0.35 thf(f226,plain,(
% 0.15/0.35 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1))))))) & $true)) | (~spl0_2 | ~spl0_4)),
% 0.15/0.35 inference(backward_demodulation,[],[f151,f225])).
% 0.15/0.35 thf(f225,plain,(
% 0.15/0.35 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))))) | ~spl0_4),
% 0.15/0.35 inference(boolean_simplification,[],[f224])).
% 0.15/0.35 thf(f224,plain,(
% 0.15/0.35 ($true = ($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0)))))))))) | ~spl0_4),
% 0.15/0.35 inference(backward_demodulation,[],[f158,f223])).
% 0.15/0.35 thf(f223,plain,(
% 0.15/0.35 ($true = (!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0 @ Y0))))) | ~spl0_4),
% 0.15/0.35 inference(binary_proxy_clausification,[],[f158])).
% 0.15/0.35 thf(f158,plain,(
% 0.15/0.35 ($true = ((!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0)))))))))) | ~spl0_4),
% 0.15/0.35 inference(avatar_component_clause,[],[f157])).
% 0.15/0.35 thf(f157,plain,(
% 0.15/0.35 spl0_4 <=> ($true = ((!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))))))),
% 0.15/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.15/0.35 thf(f151,plain,(
% 0.15/0.35 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))))) = $false) | ~spl0_2),
% 0.15/0.35 inference(avatar_component_clause,[],[f150])).
% 0.15/0.35 thf(f150,plain,(
% 0.15/0.35 spl0_2 <=> (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))))) = $false)),
% 0.15/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.15/0.35 thf(f278,plain,(
% 0.15/0.35 ((~ (sK2 @ sK5 @ sK4)) = $true) | (~spl0_2 | ~spl0_4)),
% 0.15/0.35 inference(boolean_simplification,[],[f275])).
% 0.15/0.35 thf(f275,plain,(
% 0.15/0.35 ($true = ((sK2 @ sK5 @ sK4) => $false)) | (~spl0_2 | ~spl0_4)),
% 0.15/0.35 inference(superposition,[],[f262,f232])).
% 0.15/0.35 thf(f232,plain,(
% 0.15/0.35 ( ! [X1 : $i] : (((sK2 @ X1 @ X1) = $false)) ) | ~spl0_4),
% 0.15/0.35 inference(not_proxy_clausification,[],[f229])).
% 0.15/0.35 thf(f229,plain,(
% 0.15/0.35 ( ! [X1 : $i] : (($true = (~ (sK2 @ X1 @ X1)))) ) | ~spl0_4),
% 0.15/0.35 inference(beta_eta_normalization,[],[f228])).
% 0.15/0.35 thf(f228,plain,(
% 0.15/0.35 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (~ (sK2 @ Y0 @ Y0))) @ X1))) ) | ~spl0_4),
% 0.15/0.35 inference(pi_clausification,[],[f223])).
% 0.15/0.35 thf(f262,plain,(
% 0.15/0.35 ( ! [X0 : $i] : (($true = ((sK2 @ X0 @ sK4) => (sK2 @ X0 @ sK5)))) ) | (~spl0_2 | ~spl0_4)),
% 0.15/0.35 inference(boolean_simplification,[],[f261])).
% 0.15/0.35 thf(f261,plain,(
% 0.15/0.35 ( ! [X0 : $i] : (($true = (($true & (sK2 @ X0 @ sK4)) => (sK2 @ X0 @ sK5)))) ) | (~spl0_2 | ~spl0_4)),
% 0.15/0.35 inference(superposition,[],[f251,f245])).
% 0.15/0.35 thf(f245,plain,(
% 0.15/0.35 ($true = (sK2 @ sK4 @ sK5)) | (~spl0_2 | ~spl0_4)),
% 0.15/0.35 inference(not_proxy_clausification,[],[f237])).
% 0.15/0.35 thf(f237,plain,(
% 0.15/0.35 ((~ (sK2 @ sK4 @ sK5)) = $false) | (~spl0_2 | ~spl0_4)),
% 0.15/0.35 inference(binary_proxy_clausification,[],[f236])).
% 0.15/0.35 thf(f251,plain,(
% 0.15/0.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((sK2 @ X2 @ X1) & (sK2 @ X3 @ X2)) => (sK2 @ X3 @ X1)))) ) | ~spl0_4),
% 0.15/0.35 inference(beta_eta_normalization,[],[f250])).
% 0.15/0.35 thf(f250,plain,(
% 0.15/0.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((sK2 @ X2 @ X1) & (sK2 @ Y0 @ X2)) => (sK2 @ Y0 @ X1))) @ X3))) ) | ~spl0_4),
% 0.15/0.35 inference(pi_clausification,[],[f249])).
% 0.15/0.35 thf(f249,plain,(
% 0.15/0.35 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((sK2 @ X2 @ X1) & (sK2 @ Y0 @ X2)) => (sK2 @ Y0 @ X1)))) = $true)) ) | ~spl0_4),
% 0.15/0.35 inference(beta_eta_normalization,[],[f248])).
% 0.15/0.35 thf(f248,plain,(
% 0.15/0.35 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0 @ X1) & (sK2 @ Y1 @ Y0)) => (sK2 @ Y1 @ X1))))) @ X2))) ) | ~spl0_4),
% 0.15/0.35 inference(pi_clausification,[],[f244])).
% 0.15/0.35 thf(f244,plain,(
% 0.15/0.35 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0 @ X1) & (sK2 @ Y1 @ Y0)) => (sK2 @ Y1 @ X1)))))) = $true)) ) | ~spl0_4),
% 0.15/0.35 inference(beta_eta_normalization,[],[f243])).
% 0.15/0.35 thf(f243,plain,(
% 0.15/0.35 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))) @ X1))) ) | ~spl0_4),
% 0.15/0.35 inference(pi_clausification,[],[f225])).
% 0.15/0.35 thf(f219,plain,(
% 0.15/0.35 ~spl0_6),
% 0.15/0.35 inference(avatar_contradiction_clause,[],[f218])).
% 0.15/0.35 thf(f218,plain,(
% 0.15/0.35 $false | ~spl0_6),
% 0.15/0.35 inference(trivial_inequality_removal,[],[f217])).
% 0.15/0.35 thf(f217,plain,(
% 0.15/0.35 ($false != $false) | ~spl0_6),
% 0.15/0.35 inference(boolean_simplification,[],[f216])).
% 0.15/0.35 thf(f216,plain,(
% 0.15/0.35 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1))))))) & $false) != $false) | ~spl0_6),
% 0.15/0.35 inference(boolean_simplification,[],[f215])).
% 0.15/0.35 thf(f215,plain,(
% 0.15/0.35 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1))))))) & $false) != ((!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0 @ Y0)))) & $false)) | ~spl0_6),
% 0.15/0.35 inference(forward_demodulation,[],[f143,f171])).
% 0.15/0.35 thf(f171,plain,(
% 0.15/0.35 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0)))))))) = $false) | ~spl0_6),
% 0.15/0.35 inference(avatar_component_clause,[],[f170])).
% 0.15/0.35 thf(f170,plain,(
% 0.15/0.35 spl0_6 <=> ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0)))))))) = $false)),
% 0.15/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.15/0.35 thf(f143,plain,(
% 0.15/0.35 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))))) != ((!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))))))),
% 0.15/0.35 inference(beta_eta_normalization,[],[f142])).
% 0.15/0.35 thf(f142,plain,(
% 0.15/0.35 (((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1)))))))))) @ sK2) != ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1)))))))))) @ sK2))),
% 0.15/0.35 inference(negative_extensionality,[],[f141])).
% 0.15/0.35 thf(f141,plain,(
% 0.15/0.35 ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1)))))))))) != (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1)))))))))))),
% 0.15/0.35 inference(equality_proxy_clausification,[],[f138])).
% 0.15/0.35 thf(f138,plain,(
% 0.15/0.35 (((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1)))))))))) = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))))) = $false)),
% 0.15/0.35 inference(not_proxy_clausification,[],[f137])).
% 0.15/0.35 thf(f137,plain,(
% 0.15/0.35 ($true = (~ ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1)))))))))) = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1)))))))))))))),
% 0.15/0.35 inference(beta_eta_normalization,[],[f136])).
% 0.15/0.35 thf(f136,plain,(
% 0.15/0.35 ((~ ((^[Y0 : $i > $i > $o]: (((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) => (~ (Y1 @ Y2 @ Y3)))))))) @ Y0) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) @ Y0))) = (^[Y0 : $i > $i > $o]: (((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (~ (Y1 @ Y2 @ Y2))))) @ Y0) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) @ Y0))))) = $true)),
% 0.15/0.35 inference(definition_unfolding,[],[f108,f127,f103,f93])).
% 0.15/0.35 thf(f93,plain,(
% 0.15/0.35 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.15/0.35 inference(cnf_transformation,[],[f77])).
% 0.15/0.35 thf(f77,plain,(
% 0.15/0.35 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.15/0.35 inference(fool_elimination,[],[f76])).
% 0.15/0.35 thf(f76,plain,(
% 0.15/0.35 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)))) = trans)),
% 0.15/0.35 inference(rectify,[],[f13])).
% 0.15/0.35 thf(f13,axiom,(
% 0.15/0.35 ((^[X0 : $i > $i > $o] : (! [X2,X3,X5] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X5)) => (X0 @ X2 @ X5)))) = trans)),
% 0.15/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive)).
% 0.15/0.35 thf(f103,plain,(
% 0.15/0.35 (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))),
% 0.15/0.35 inference(cnf_transformation,[],[f79])).
% 0.15/0.35 thf(f79,plain,(
% 0.15/0.35 (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))),
% 0.15/0.35 inference(fool_elimination,[],[f78])).
% 0.15/0.35 thf(f78,plain,(
% 0.15/0.35 ((^[X0 : $i > $i > $o] : (! [X1] : ~(X0 @ X1 @ X1))) = irrefl)),
% 0.15/0.35 inference(rectify,[],[f7])).
% 0.15/0.35 thf(f7,axiom,(
% 0.15/0.35 ((^[X0 : $i > $i > $o] : (! [X2] : ~(X0 @ X2 @ X2))) = irrefl)),
% 0.15/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexive)).
% 0.15/0.35 thf(f127,plain,(
% 0.15/0.35 (so = (^[Y0 : $i > $i > $o]: (((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) => (~ (Y1 @ Y2 @ Y3)))))))) @ Y0) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) @ Y0))))),
% 0.15/0.35 inference(definition_unfolding,[],[f118,f95,f93])).
% 0.15/0.35 thf(f95,plain,(
% 0.15/0.35 (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (~ (Y0 @ Y1 @ Y2)))))))))),
% 0.15/0.35 inference(cnf_transformation,[],[f84])).
% 0.15/0.35 thf(f84,plain,(
% 0.15/0.35 (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (~ (Y0 @ Y1 @ Y2)))))))))),
% 0.15/0.35 inference(fool_elimination,[],[f83])).
% 0.15/0.35 thf(f83,plain,(
% 0.15/0.35 (asymm = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X1 @ X2) => ~(X0 @ X2 @ X1)))))),
% 0.15/0.35 inference(rectify,[],[f11])).
% 0.15/0.35 thf(f11,axiom,(
% 0.15/0.35 (asymm = (^[X0 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X2 @ X3) => ~(X0 @ X3 @ X2)))))),
% 0.15/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',asymmetric)).
% 0.15/0.35 thf(f118,plain,(
% 0.15/0.35 (so = (^[Y0 : $i > $i > $o]: ((asymm @ Y0) & (trans @ Y0))))),
% 0.15/0.35 inference(cnf_transformation,[],[f34])).
% 0.15/0.35 thf(f34,plain,(
% 0.15/0.35 (so = (^[Y0 : $i > $i > $o]: ((asymm @ Y0) & (trans @ Y0))))),
% 0.15/0.35 inference(fool_elimination,[],[f33])).
% 0.15/0.35 thf(f33,plain,(
% 0.15/0.35 (so = (^[X0 : $i > $i > $o] : ((trans @ X0) & (asymm @ X0))))),
% 0.15/0.35 inference(rectify,[],[f18])).
% 0.15/0.35 thf(f18,axiom,(
% 0.15/0.35 (so = (^[X0 : $i > $i > $o] : ((trans @ X0) & (asymm @ X0))))),
% 0.15/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',strict_order)).
% 0.15/0.35 thf(f108,plain,(
% 0.15/0.35 ($true = (~ (so = (^[Y0 : $i > $i > $o]: ((irrefl @ Y0) & (trans @ Y0))))))),
% 0.15/0.35 inference(cnf_transformation,[],[f53])).
% 0.15/0.35 thf(f53,plain,(
% 0.15/0.35 ($true = (~ (so = (^[Y0 : $i > $i > $o]: ((irrefl @ Y0) & (trans @ Y0))))))),
% 0.15/0.35 inference(fool_elimination,[],[f52])).
% 0.15/0.35 thf(f52,plain,(
% 0.15/0.35 ~(so = (^[X0 : $i > $i > $o] : ((trans @ X0) & (irrefl @ X0))))),
% 0.15/0.35 inference(rectify,[],[f31])).
% 0.15/0.35 thf(f31,negated_conjecture,(
% 0.15/0.35 ~(so = (^[X0 : $i > $i > $o] : ((trans @ X0) & (irrefl @ X0))))),
% 0.15/0.35 inference(negated_conjecture,[],[f30])).
% 0.15/0.35 thf(f30,conjecture,(
% 0.15/0.35 (so = (^[X0 : $i > $i > $o] : ((trans @ X0) & (irrefl @ X0))))),
% 0.15/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',alternative_definition_of_strict_order)).
% 0.15/0.35 thf(f208,plain,(
% 0.15/0.35 ~spl0_4 | ~spl0_5),
% 0.15/0.35 inference(avatar_contradiction_clause,[],[f207])).
% 0.15/0.35 thf(f207,plain,(
% 0.15/0.35 $false | (~spl0_4 | ~spl0_5)),
% 0.15/0.35 inference(trivial_inequality_removal,[],[f206])).
% 0.15/0.35 thf(f206,plain,(
% 0.15/0.35 ($true = $false) | (~spl0_4 | ~spl0_5)),
% 0.15/0.35 inference(boolean_simplification,[],[f205])).
% 0.15/0.35 thf(f205,plain,(
% 0.15/0.35 ($true = ($false & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0)))))))))) | (~spl0_4 | ~spl0_5)),
% 0.15/0.35 inference(forward_demodulation,[],[f158,f168])).
% 0.15/0.35 thf(f168,plain,(
% 0.15/0.35 ((!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0 @ Y0)))) = $false) | ~spl0_5),
% 0.15/0.35 inference(avatar_component_clause,[],[f167])).
% 0.15/0.35 thf(f167,plain,(
% 0.15/0.35 spl0_5 <=> ((!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0 @ Y0)))) = $false)),
% 0.15/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.15/0.35 thf(f202,plain,(
% 0.15/0.35 ~spl0_3 | ~spl0_5),
% 0.15/0.35 inference(avatar_contradiction_clause,[],[f201])).
% 0.15/0.35 thf(f201,plain,(
% 0.15/0.35 $false | (~spl0_3 | ~spl0_5)),
% 0.15/0.35 inference(trivial_inequality_removal,[],[f200])).
% 0.15/0.35 thf(f200,plain,(
% 0.15/0.35 ($true = $false) | (~spl0_3 | ~spl0_5)),
% 0.15/0.35 inference(boolean_simplification,[],[f199])).
% 0.15/0.35 thf(f199,plain,(
% 0.15/0.35 ($true = (~ $true)) | (~spl0_3 | ~spl0_5)),
% 0.15/0.35 inference(boolean_simplification,[],[f193])).
% 0.15/0.35 thf(f193,plain,(
% 0.15/0.35 ($true = ($true => (~ $true))) | (~spl0_3 | ~spl0_5)),
% 0.15/0.35 inference(superposition,[],[f189,f177])).
% 0.15/0.35 thf(f177,plain,(
% 0.15/0.35 ($true = (sK2 @ sK3 @ sK3)) | ~spl0_5),
% 0.15/0.35 inference(not_proxy_clausification,[],[f176])).
% 0.15/0.35 thf(f176,plain,(
% 0.15/0.35 ((~ (sK2 @ sK3 @ sK3)) = $false) | ~spl0_5),
% 0.15/0.35 inference(beta_eta_normalization,[],[f175])).
% 0.15/0.35 thf(f175,plain,(
% 0.15/0.35 (((^[Y0 : $i]: (~ (sK2 @ Y0 @ Y0))) @ sK3) = $false) | ~spl0_5),
% 0.15/0.35 inference(sigma_clausification,[],[f168])).
% 0.15/0.35 thf(f189,plain,(
% 0.15/0.35 ( ! [X2 : $i,X1 : $i] : (($true = ((sK2 @ X2 @ X1) => (~ (sK2 @ X1 @ X2))))) ) | ~spl0_3),
% 0.15/0.35 inference(beta_eta_normalization,[],[f188])).
% 0.15/0.35 thf(f188,plain,(
% 0.15/0.35 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((sK2 @ Y0 @ X1) => (~ (sK2 @ X1 @ Y0)))) @ X2))) ) | ~spl0_3),
% 0.15/0.35 inference(pi_clausification,[],[f185])).
% 0.15/0.35 thf(f185,plain,(
% 0.15/0.35 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0 @ X1) => (~ (sK2 @ X1 @ Y0))))))) ) | ~spl0_3),
% 0.15/0.35 inference(beta_eta_normalization,[],[f184])).
% 0.15/0.35 thf(f184,plain,(
% 0.15/0.35 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1)))))) @ X1))) ) | ~spl0_3),
% 0.15/0.35 inference(pi_clausification,[],[f181])).
% 0.15/0.35 thf(f181,plain,(
% 0.15/0.35 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1)))))))) | ~spl0_3),
% 0.15/0.35 inference(binary_proxy_clausification,[],[f155])).
% 0.15/0.35 thf(f155,plain,(
% 0.15/0.35 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0)))))))))) | ~spl0_3),
% 0.15/0.35 inference(avatar_component_clause,[],[f154])).
% 0.15/0.35 thf(f154,plain,(
% 0.15/0.35 spl0_3 <=> ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))))))),
% 0.15/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.15/0.35 thf(f172,plain,(
% 0.15/0.35 spl0_5 | spl0_6 | ~spl0_1),
% 0.15/0.35 inference(avatar_split_clause,[],[f165,f147,f170,f167])).
% 0.15/0.35 thf(f147,plain,(
% 0.15/0.35 spl0_1 <=> (((!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))))) = $false)),
% 0.15/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.15/0.35 thf(f165,plain,(
% 0.15/0.35 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0)))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0 @ Y0)))) = $false) | ~spl0_1),
% 0.15/0.35 inference(binary_proxy_clausification,[],[f148])).
% 0.15/0.35 thf(f148,plain,(
% 0.15/0.35 (((!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))))) = $false) | ~spl0_1),
% 0.15/0.35 inference(avatar_component_clause,[],[f147])).
% 0.15/0.35 thf(f163,plain,(
% 0.15/0.35 ~spl0_2 | ~spl0_3),
% 0.15/0.35 inference(avatar_contradiction_clause,[],[f162])).
% 0.15/0.35 thf(f162,plain,(
% 0.15/0.35 $false | (~spl0_2 | ~spl0_3)),
% 0.15/0.35 inference(trivial_inequality_removal,[],[f161])).
% 0.15/0.35 thf(f161,plain,(
% 0.15/0.35 ($true = $false) | (~spl0_2 | ~spl0_3)),
% 0.15/0.35 inference(backward_demodulation,[],[f155,f151])).
% 0.15/0.35 thf(f159,plain,(
% 0.15/0.35 spl0_3 | spl0_4),
% 0.15/0.35 inference(avatar_split_clause,[],[f144,f157,f154])).
% 0.15/0.35 thf(f144,plain,(
% 0.15/0.35 ($true = ((!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0)))))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))))))),
% 0.15/0.35 inference(binary_proxy_clausification,[],[f143])).
% 0.15/0.35 thf(f152,plain,(
% 0.15/0.35 spl0_1 | spl0_2),
% 0.15/0.35 inference(avatar_split_clause,[],[f145,f150,f147])).
% 0.15/0.35 thf(f145,plain,(
% 0.15/0.35 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (~ (sK2 @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: (~ (sK2 @ Y0 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))))) = $false)),
% 0.15/0.35 inference(binary_proxy_clausification,[],[f143])).
% 0.15/0.35 % SZS output end Proof for theBenchmark
% 0.15/0.35 % (28284)------------------------------
% 0.15/0.35 % (28284)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.35 % (28284)Termination reason: Refutation
% 0.15/0.35
% 0.15/0.35 % (28284)Memory used [KB]: 5756
% 0.15/0.35 % (28284)Time elapsed: 0.021 s
% 0.15/0.35 % (28284)Instructions burned: 31 (million)
% 0.15/0.35 % (28284)------------------------------
% 0.15/0.35 % (28284)------------------------------
% 0.15/0.35 % (28272)Success in time 0.035 s
% 0.15/0.35 % Vampire---4.8 exiting
%------------------------------------------------------------------------------