TSTP Solution File: SEU463^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU463^1 : 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 : n011.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 03:49:00 EDT 2024
% Result : Theorem 0.24s 0.46s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU463^1 : TPTP v8.2.0. Released v3.6.0.
% 0.08/0.16 % 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
% 0.17/0.38 % Computer : n011.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Sun May 19 18:11:23 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.17/0.38 This is a TH0_THM_EQU_NAR problem
% 0.17/0.38 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
% 0.17/0.40 % (5283)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)
% 0.17/0.40 % (5282)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.17/0.40 % (5280)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)
% 0.17/0.40 % (5280)Instruction limit reached!
% 0.17/0.40 % (5280)------------------------------
% 0.17/0.40 % (5280)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.40 % (5276)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.17/0.40 % (5280)Termination reason: Unknown
% 0.17/0.40 % (5277)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)
% 0.17/0.40 % (5280)Termination phase: shuffling
% 0.17/0.40
% 0.17/0.40 % (5280)Memory used [KB]: 1023
% 0.17/0.40 % (5280)Time elapsed: 0.002 s
% 0.17/0.40 % (5280)Instructions burned: 2 (million)
% 0.17/0.40 % (5280)------------------------------
% 0.17/0.40 % (5280)------------------------------
% 0.17/0.40 % (5283)Instruction limit reached!
% 0.17/0.40 % (5283)------------------------------
% 0.17/0.40 % (5283)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.40 % (5283)Termination reason: Unknown
% 0.17/0.40 % (5283)Termination phase: shuffling
% 0.17/0.40
% 0.17/0.40 % (5283)Memory used [KB]: 1023
% 0.17/0.40 % (5283)Time elapsed: 0.003 s
% 0.17/0.40 % (5283)Instructions burned: 3 (million)
% 0.17/0.40 % (5283)------------------------------
% 0.17/0.40 % (5283)------------------------------
% 0.17/0.40 % (5277)Instruction limit reached!
% 0.17/0.40 % (5277)------------------------------
% 0.17/0.40 % (5277)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.40 % (5277)Termination reason: Unknown
% 0.17/0.40 % (5277)Termination phase: shuffling
% 0.17/0.40
% 0.17/0.40 % (5277)Memory used [KB]: 1023
% 0.17/0.40 % (5279)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.17/0.40 % (5277)Time elapsed: 0.004 s
% 0.17/0.40 % (5277)Instructions burned: 4 (million)
% 0.17/0.40 % (5277)------------------------------
% 0.17/0.40 % (5277)------------------------------
% 0.17/0.41 % (5279)Instruction limit reached!
% 0.17/0.41 % (5279)------------------------------
% 0.17/0.41 % (5279)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.41 % (5279)Termination reason: Unknown
% 0.17/0.41 % (5279)Termination phase: shuffling
% 0.17/0.41
% 0.17/0.41 % (5279)Memory used [KB]: 1023
% 0.17/0.41 % (5279)Time elapsed: 0.003 s
% 0.17/0.41 % (5279)Instructions burned: 2 (million)
% 0.17/0.41 % (5279)------------------------------
% 0.17/0.41 % (5279)------------------------------
% 0.17/0.41 % (5278)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)
% 0.17/0.41 % (5282)Instruction limit reached!
% 0.17/0.41 % (5282)------------------------------
% 0.17/0.41 % (5282)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.41 % (5282)Termination reason: Unknown
% 0.17/0.41 % (5282)Termination phase: Saturation
% 0.17/0.41 % (5281)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)
% 0.17/0.41
% 0.17/0.41 % (5282)Memory used [KB]: 5628
% 0.17/0.41 % (5282)Time elapsed: 0.010 s
% 0.17/0.41 % (5282)Instructions burned: 18 (million)
% 0.17/0.41 % (5282)------------------------------
% 0.17/0.41 % (5282)------------------------------
% 0.17/0.42 % (5284)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)
% 0.24/0.42 % (5287)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)
% 0.24/0.42 % (5286)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)
% 0.24/0.42 % (5286)Instruction limit reached!
% 0.24/0.42 % (5286)------------------------------
% 0.24/0.42 % (5286)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.42 % (5286)Termination reason: Unknown
% 0.24/0.42 % (5286)Termination phase: shuffling
% 0.24/0.42
% 0.24/0.42 % (5286)Memory used [KB]: 1023
% 0.24/0.42 % (5286)Time elapsed: 0.004 s
% 0.24/0.42 % (5286)Instructions burned: 3 (million)
% 0.24/0.42 % (5286)------------------------------
% 0.24/0.42 % (5286)------------------------------
% 0.24/0.42 % (5285)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)
% 0.24/0.42 % (5278)Instruction limit reached!
% 0.24/0.42 % (5278)------------------------------
% 0.24/0.42 % (5278)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.42 % (5278)Termination reason: Unknown
% 0.24/0.42 % (5278)Termination phase: Saturation
% 0.24/0.42
% 0.24/0.42 % (5278)Memory used [KB]: 5756
% 0.24/0.42 % (5278)Time elapsed: 0.019 s
% 0.24/0.42 % (5278)Instructions burned: 28 (million)
% 0.24/0.42 % (5278)------------------------------
% 0.24/0.42 % (5278)------------------------------
% 0.24/0.43 % (5288)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.24/0.43 % (5288)Instruction limit reached!
% 0.24/0.43 % (5288)------------------------------
% 0.24/0.43 % (5288)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.43 % (5288)Termination reason: Unknown
% 0.24/0.43 % (5288)Termination phase: Property scanning
% 0.24/0.43
% 0.24/0.43 % (5288)Memory used [KB]: 1023
% 0.24/0.43 % (5288)Time elapsed: 0.005 s
% 0.24/0.43 % (5288)Instructions burned: 8 (million)
% 0.24/0.43 % (5288)------------------------------
% 0.24/0.43 % (5288)------------------------------
% 0.24/0.43 % (5284)Instruction limit reached!
% 0.24/0.43 % (5284)------------------------------
% 0.24/0.43 % (5284)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.43 % (5284)Termination reason: Unknown
% 0.24/0.43 % (5284)Termination phase: Saturation
% 0.24/0.43
% 0.24/0.43 % (5284)Memory used [KB]: 5756
% 0.24/0.43 % (5284)Time elapsed: 0.018 s
% 0.24/0.43 % (5284)Instructions burned: 37 (million)
% 0.24/0.43 % (5284)------------------------------
% 0.24/0.43 % (5284)------------------------------
% 0.24/0.44 % (5285)Instruction limit reached!
% 0.24/0.44 % (5285)------------------------------
% 0.24/0.44 % (5285)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.44 % (5285)Termination reason: Unknown
% 0.24/0.44 % (5285)Termination phase: Saturation
% 0.24/0.44
% 0.24/0.44 % (5285)Memory used [KB]: 5628
% 0.24/0.44 % (5285)Time elapsed: 0.015 s
% 0.24/0.44 % (5285)Instructions burned: 16 (million)
% 0.24/0.44 % (5285)------------------------------
% 0.24/0.44 % (5285)------------------------------
% 0.24/0.44 % (5290)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)
% 0.24/0.44 % (5291)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)
% 0.24/0.44 % (5290)Instruction limit reached!
% 0.24/0.44 % (5290)------------------------------
% 0.24/0.44 % (5290)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.44 % (5290)Termination reason: Unknown
% 0.24/0.44 % (5290)Termination phase: shuffling
% 0.24/0.44
% 0.24/0.44 % (5290)Memory used [KB]: 1023
% 0.24/0.44 % (5290)Time elapsed: 0.005 s
% 0.24/0.44 % (5290)Instructions burned: 4 (million)
% 0.24/0.44 % (5290)------------------------------
% 0.24/0.44 % (5290)------------------------------
% 0.24/0.45 % (5291)Instruction limit reached!
% 0.24/0.45 % (5291)------------------------------
% 0.24/0.45 % (5291)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.45 % (5291)Termination reason: Unknown
% 0.24/0.45 % (5291)Termination phase: shuffling
% 0.24/0.45
% 0.24/0.45 % (5291)Memory used [KB]: 1023
% 0.24/0.45 % (5291)Time elapsed: 0.003 s
% 0.24/0.45 % (5291)Instructions burned: 4 (million)
% 0.24/0.45 % (5291)------------------------------
% 0.24/0.45 % (5291)------------------------------
% 0.24/0.45 % (5292)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)
% 0.24/0.45 % (5289)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.24/0.45 % (5287)First to succeed.
% 0.24/0.45 % (5292)Instruction limit reached!
% 0.24/0.45 % (5292)------------------------------
% 0.24/0.45 % (5292)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.45 % (5292)Termination reason: Unknown
% 0.24/0.45 % (5292)Termination phase: Property scanning
% 0.24/0.45
% 0.24/0.45 % (5292)Memory used [KB]: 1023
% 0.24/0.45 % (5292)Time elapsed: 0.005 s
% 0.24/0.45 % (5292)Instructions burned: 7 (million)
% 0.24/0.45 % (5292)------------------------------
% 0.24/0.45 % (5292)------------------------------
% 0.24/0.46 % (5287)Refutation found. Thanks to Tanya!
% 0.24/0.46 % SZS status Theorem for theBenchmark
% 0.24/0.46 % SZS output start Proof for theBenchmark
% 0.24/0.46 thf(func_def_0, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_2, type, inv: ($i > $i > $o) > $i > $i > $o).
% 0.24/0.46 thf(func_def_3, type, idem: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_4, type, infl: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_5, type, mono: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_6, type, refl: ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_7, type, irrefl: ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_8, type, rc: ($i > $i > $o) > $i > $i > $o).
% 0.24/0.46 thf(func_def_9, type, symm: ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_10, type, antisymm: ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_11, type, asymm: ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_12, type, sc: ($i > $i > $o) > $i > $i > $o).
% 0.24/0.46 thf(func_def_13, type, trans: ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_14, type, tc: ($i > $i > $o) > $i > $i > $o).
% 0.24/0.46 thf(func_def_15, type, trc: ($i > $i > $o) > $i > $i > $o).
% 0.24/0.46 thf(func_def_16, type, trsc: ($i > $i > $o) > $i > $i > $o).
% 0.24/0.46 thf(func_def_17, type, po: ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_18, type, so: ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_19, type, total: ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_20, type, term: ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_21, type, ind: ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_22, type, innf: ($i > $i > $o) > $i > $o).
% 0.24/0.46 thf(func_def_23, type, nfof: ($i > $i > $o) > $i > $i > $o).
% 0.24/0.46 thf(func_def_24, type, norm: ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_25, type, join: ($i > $i > $o) > $i > $i > $o).
% 0.24/0.46 thf(func_def_26, type, lconfl: ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_27, type, sconfl: ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_28, type, confl: ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_29, type, cr: ($i > $i > $o) > $o).
% 0.24/0.46 thf(func_def_48, type, ph1: !>[X0: $tType]:(X0)).
% 0.24/0.46 thf(func_def_51, type, sK4: $i > $i > $o).
% 0.24/0.46 thf(func_def_53, type, sK6: $i > $i > $o).
% 0.24/0.46 thf(func_def_54, type, sK7: $i > $i > $o).
% 0.24/0.46 thf(f299,plain,(
% 0.24/0.46 $false),
% 0.24/0.46 inference(avatar_sat_refutation,[],[f292,f296])).
% 0.24/0.46 thf(f296,plain,(
% 0.24/0.46 spl0_2),
% 0.24/0.46 inference(avatar_split_clause,[],[f234,f208])).
% 0.24/0.46 thf(f208,plain,(
% 0.24/0.46 spl0_2 <=> ((sK4 @ sK5 @ sK3) = $true)),
% 0.24/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.24/0.46 thf(f234,plain,(
% 0.24/0.46 ((sK4 @ sK5 @ sK3) = $true)),
% 0.24/0.46 inference(boolean_simplification,[],[f233])).
% 0.24/0.46 thf(f233,plain,(
% 0.24/0.46 ($true = ($true => (sK4 @ sK5 @ sK3)))),
% 0.24/0.46 inference(forward_demodulation,[],[f231,f159])).
% 0.24/0.46 thf(f159,plain,(
% 0.24/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK6 @ Y0 @ Y1) => (sK4 @ Y0 @ Y1)))))))),
% 0.24/0.46 inference(binary_proxy_clausification,[],[f152])).
% 0.24/0.46 thf(f152,plain,(
% 0.24/0.46 (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK4 @ Y0 @ Y2) & (sK4 @ Y1 @ Y0)) => (sK4 @ Y1 @ Y2)))))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK6 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK5))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK6 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK5 @ sK3))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK6 @ Y0 @ Y1) => (sK4 @ Y0 @ Y1))))))) = $true)),
% 0.24/0.46 inference(binary_proxy_clausification,[],[f150])).
% 0.24/0.46 thf(f150,plain,(
% 0.24/0.46 ($false = (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK4 @ Y0 @ Y2) & (sK4 @ Y1 @ Y0)) => (sK4 @ Y1 @ Y2)))))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK6 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK5))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK6 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK5 @ sK3))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK6 @ Y0 @ Y1) => (sK4 @ Y0 @ Y1))))))) => (sK4 @ sK2 @ sK3)))),
% 0.24/0.46 inference(beta_eta_normalization,[],[f149])).
% 0.24/0.46 thf(f149,plain,(
% 0.24/0.46 ($false = ((^[Y0 : $i > $i > $o]: (((((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((sK4 @ Y1 @ Y3) & (sK4 @ Y2 @ Y1)) => (sK4 @ Y2 @ Y3)))))))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK2 @ sK5))))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK5 @ sK3))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (sK4 @ Y1 @ Y2))))))) => (sK4 @ sK2 @ sK3))) @ sK6))),
% 0.24/0.46 inference(sigma_clausification,[],[f148])).
% 0.24/0.46 thf(f148,plain,(
% 0.24/0.46 ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((sK4 @ Y1 @ Y3) & (sK4 @ Y2 @ Y1)) => (sK4 @ Y2 @ Y3)))))))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK2 @ sK5))))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK5 @ sK3))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (sK4 @ Y1 @ Y2))))))) => (sK4 @ sK2 @ sK3)))))),
% 0.24/0.46 inference(beta_eta_normalization,[],[f147])).
% 0.24/0.46 thf(f147,plain,(
% 0.24/0.46 ($false = ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((sK4 @ Y2 @ Y4) & (sK4 @ Y3 @ Y2)) => (sK4 @ Y3 @ Y4)))))))) & (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ sK2 @ Y0))))) & (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ sK3))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) => (sK4 @ Y2 @ Y3))))))) => (sK4 @ sK2 @ sK3))))) @ sK5))),
% 0.24/0.46 inference(sigma_clausification,[],[f146])).
% 0.24/0.46 thf(f146,plain,(
% 0.24/0.46 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((sK4 @ Y2 @ Y4) & (sK4 @ Y3 @ Y2)) => (sK4 @ Y3 @ Y4)))))))) & (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ sK2 @ Y0))))) & (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ sK3))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) => (sK4 @ Y2 @ Y3))))))) => (sK4 @ sK2 @ sK3)))))))),
% 0.24/0.46 inference(beta_eta_normalization,[],[f145])).
% 0.24/0.46 thf(f145,plain,(
% 0.24/0.46 ($false = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y0 @ Y3 @ Y5) & (Y0 @ Y4 @ Y3)) => (Y0 @ Y4 @ Y5)))))))) & (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ sK2 @ Y1))))) & (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ sK3))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) => (Y0 @ Y3 @ Y4))))))) => (Y0 @ sK2 @ sK3))))))) @ sK4))),
% 0.24/0.46 inference(sigma_clausification,[],[f144])).
% 0.24/0.46 thf(f144,plain,(
% 0.24/0.46 ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y0 @ Y3 @ Y5) & (Y0 @ Y4 @ Y3)) => (Y0 @ Y4 @ Y5)))))))) & (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ sK2 @ Y1))))) & (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ sK3))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) => (Y0 @ Y3 @ Y4))))))) => (Y0 @ sK2 @ sK3)))))))))),
% 0.24/0.46 inference(beta_eta_normalization,[],[f143])).
% 0.24/0.46 thf(f143,plain,(
% 0.24/0.46 ($false = ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y1 @ Y4 @ Y6) & (Y1 @ Y5 @ Y4)) => (Y1 @ Y5 @ Y6)))))))) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ sK2 @ Y2))))) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y2 @ Y0))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) => (Y1 @ Y4 @ Y5))))))) => (Y1 @ sK2 @ Y0))))))))) @ sK3))),
% 0.24/0.46 inference(sigma_clausification,[],[f142])).
% 0.24/0.46 thf(f142,plain,(
% 0.24/0.46 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y1 @ Y4 @ Y6) & (Y1 @ Y5 @ Y4)) => (Y1 @ Y5 @ Y6)))))))) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ sK2 @ Y2))))) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y2 @ Y0))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) => (Y1 @ Y4 @ Y5))))))) => (Y1 @ sK2 @ Y0)))))))))))),
% 0.24/0.46 inference(beta_eta_normalization,[],[f141])).
% 0.24/0.46 thf(f141,plain,(
% 0.24/0.46 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y2 @ Y5 @ Y7) & (Y2 @ Y6 @ Y5)) => (Y2 @ Y6 @ Y7)))))))) & (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y8))))))))) => (Y5 @ Y0 @ Y3))))) & (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y8))))))))) => (Y5 @ Y3 @ Y1))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) => (Y2 @ Y5 @ Y6))))))) => (Y2 @ Y0 @ Y1))))))))))) @ sK2))),
% 0.24/0.46 inference(sigma_clausification,[],[f138])).
% 0.24/0.46 thf(f138,plain,(
% 0.24/0.46 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y2 @ Y5 @ Y7) & (Y2 @ Y6 @ Y5)) => (Y2 @ Y6 @ Y7)))))))) & (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y8))))))))) => (Y5 @ Y0 @ Y3))))) & (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y8))))))))) => (Y5 @ Y3 @ Y1))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) => (Y2 @ Y5 @ Y6))))))) => (Y2 @ Y0 @ Y1)))))))))))))),
% 0.24/0.46 inference(not_proxy_clausification,[],[f137])).
% 0.24/0.46 thf(f137,plain,(
% 0.24/0.46 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y2 @ Y5 @ Y7) & (Y2 @ Y6 @ Y5)) => (Y2 @ Y6 @ Y7)))))))) & (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y8))))))))) => (Y5 @ Y0 @ Y3))))) & (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y8))))))))) => (Y5 @ Y3 @ Y1))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) => (Y2 @ Y5 @ Y6))))))) => (Y2 @ Y0 @ Y1))))))))))))) = $true)),
% 0.24/0.46 inference(beta_eta_normalization,[],[f136])).
% 0.24/0.46 thf(f136,plain,(
% 0.24/0.46 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((((((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y8))))))))) @ Y2) & ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (!! @ ($i > $i > $o) @ (^[Y8 : $i > $i > $o]: ((((^[Y9 : $i > $i > $o]: ((^[Y10 : $i > $i > $o]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: ((Y9 @ Y11 @ Y12) => (Y10 @ Y11 @ Y12))))))))) @ Y5 @ Y8) & ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: (((Y9 @ Y10 @ Y12) & (Y9 @ Y11 @ Y10)) => (Y9 @ Y11 @ Y12))))))))) @ Y8)) => (Y8 @ Y6 @ Y7))))))))) @ Y4 @ Y0 @ Y3)) & ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (!! @ ($i > $i > $o) @ (^[Y8 : $i > $i > $o]: ((((^[Y9 : $i > $i > $o]: ((^[Y10 : $i > $i > $o]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: ((Y9 @ Y11 @ Y12) => (Y10 @ Y11 @ Y12))))))))) @ Y5 @ Y8) & ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: (((Y9 @ Y10 @ Y12) & (Y9 @ Y11 @ Y10)) => (Y9 @ Y11 @ Y12))))))))) @ Y8)) => (Y8 @ Y6 @ Y7))))))))) @ Y4 @ Y3 @ Y1)) & ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i > $i > $o]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y5 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))))) @ Y4 @ Y2)) => (Y2 @ Y0 @ Y1))))))))))))))),
% 0.24/0.46 inference(definition_unfolding,[],[f114,f109,f123,f123,f119])).
% 0.24/0.46 thf(f119,plain,(
% 0.24/0.46 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 0.24/0.46 inference(cnf_transformation,[],[f57])).
% 0.24/0.46 thf(f57,plain,(
% 0.24/0.46 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 0.24/0.46 inference(fool_elimination,[],[f56])).
% 0.24/0.46 thf(f56,plain,(
% 0.24/0.46 ((^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X3 @ X2) => (X1 @ X3 @ X2)))) = subrel)),
% 0.24/0.46 inference(rectify,[],[f1])).
% 0.24/0.46 thf(f1,axiom,(
% 0.24/0.46 ((^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X3,X2] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))) = subrel)),
% 0.24/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subrel)).
% 0.24/0.46 thf(f123,plain,(
% 0.24/0.46 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))))) @ Y0 @ Y3) & ((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.24/0.46 inference(definition_unfolding,[],[f116,f119,f109])).
% 0.24/0.46 thf(f116,plain,(
% 0.24/0.46 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((subrel @ Y0 @ Y3) & (trans @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.24/0.46 inference(cnf_transformation,[],[f38])).
% 0.24/0.46 thf(f38,plain,(
% 0.24/0.46 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((subrel @ Y0 @ Y3) & (trans @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.24/0.46 inference(fool_elimination,[],[f37])).
% 0.24/0.46 thf(f37,plain,(
% 0.24/0.46 (tc = (^[X0 : $i > $i > $o, X1 : $i, X2 : $i] : (! [X3 : $i > $i > $o] : (((trans @ X3) & (subrel @ X0 @ X3)) => (X3 @ X1 @ X2)))))),
% 0.24/0.46 inference(rectify,[],[f14])).
% 0.24/0.46 thf(f14,axiom,(
% 0.24/0.46 (tc = (^[X0 : $i > $i > $o, X2 : $i, X3 : $i] : (! [X1 : $i > $i > $o] : (((trans @ X1) & (subrel @ X0 @ X1)) => (X1 @ X2 @ X3)))))),
% 0.24/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure)).
% 0.24/0.46 thf(f109,plain,(
% 0.24/0.46 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))))),
% 0.24/0.46 inference(cnf_transformation,[],[f50])).
% 0.24/0.46 thf(f50,plain,(
% 0.24/0.46 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))))),
% 0.24/0.46 inference(fool_elimination,[],[f49])).
% 0.24/0.46 thf(f49,plain,(
% 0.24/0.46 (trans = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X1)) => (X0 @ X2 @ X1)))))),
% 0.24/0.46 inference(rectify,[],[f13])).
% 0.24/0.46 thf(f13,axiom,(
% 0.24/0.46 (trans = (^[X0 : $i > $i > $o] : (! [X5,X2,X3] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X5)) => (X0 @ X2 @ X5)))))),
% 0.24/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive)).
% 0.24/0.46 thf(f114,plain,(
% 0.24/0.46 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((trans @ Y2) & (tc @ Y4 @ Y0 @ Y3)) & (tc @ Y4 @ Y3 @ Y1)) & (subrel @ Y4 @ Y2)) => (Y2 @ Y0 @ Y1))))))))))))))),
% 0.24/0.46 inference(cnf_transformation,[],[f34])).
% 0.24/0.46 thf(f34,plain,(
% 0.24/0.46 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((trans @ Y2) & (tc @ Y4 @ Y0 @ Y3)) & (tc @ Y4 @ Y3 @ Y1)) & (subrel @ Y4 @ Y2)) => (Y2 @ Y0 @ Y1))))))))))))))),
% 0.24/0.46 inference(fool_elimination,[],[f33])).
% 0.24/0.46 thf(f33,plain,(
% 0.24/0.46 ~! [X0 : $i > $i > $o,X1,X2 : $i > $i > $o,X3,X4] : (((subrel @ X0 @ X2) & (tc @ X0 @ X1 @ X3) & (tc @ X0 @ X4 @ X1) & (trans @ X2)) => (X2 @ X4 @ X3))),
% 0.24/0.46 inference(rectify,[],[f31])).
% 0.24/0.46 thf(f31,negated_conjecture,(
% 0.24/0.46 ~! [X0 : $i > $i > $o,X3,X1 : $i > $i > $o,X5,X2] : (((subrel @ X0 @ X1) & (tc @ X0 @ X3 @ X5) & (tc @ X0 @ X2 @ X3) & (trans @ X1)) => (X1 @ X2 @ X5))),
% 0.24/0.46 inference(negated_conjecture,[],[f30])).
% 0.24/0.46 thf(f30,conjecture,(
% 0.24/0.46 ! [X0 : $i > $i > $o,X3,X1 : $i > $i > $o,X5,X2] : (((subrel @ X0 @ X1) & (tc @ X0 @ X3 @ X5) & (tc @ X0 @ X2 @ X3) & (trans @ X1)) => (X1 @ X2 @ X5))),
% 0.24/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure_is_transitive3)).
% 0.24/0.46 thf(f231,plain,(
% 0.24/0.46 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK6 @ Y0 @ Y1) => (sK4 @ Y0 @ Y1)))))) => (sK4 @ sK5 @ sK3)))),
% 0.24/0.46 inference(boolean_simplification,[],[f230])).
% 0.24/0.46 thf(f230,plain,(
% 0.24/0.46 ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK6 @ Y0 @ Y1) => (sK4 @ Y0 @ Y1)))))) & $true) => (sK4 @ sK5 @ sK3)))),
% 0.24/0.46 inference(superposition,[],[f199,f224])).
% 0.24/0.46 thf(f224,plain,(
% 0.24/0.46 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK4 @ Y0 @ Y2) & (sK4 @ Y1 @ Y0)) => (sK4 @ Y1 @ Y2)))))))) = $true)),
% 0.24/0.46 inference(binary_proxy_clausification,[],[f216])).
% 0.24/0.46 thf(f216,plain,(
% 0.24/0.46 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK4 @ Y0 @ Y2) & (sK4 @ Y1 @ Y0)) => (sK4 @ Y1 @ Y2)))))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK7 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK5))))))),
% 0.24/0.46 inference(boolean_simplification,[],[f215])).
% 0.24/0.46 thf(f215,plain,(
% 0.24/0.46 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK4 @ Y0 @ Y2) & (sK4 @ Y1 @ Y0)) => (sK4 @ Y1 @ Y2)))))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK7 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK5))))) & $true) = $true)),
% 0.24/0.46 inference(backward_demodulation,[],[f169,f213])).
% 0.24/0.46 thf(f213,plain,(
% 0.24/0.46 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK7 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK5 @ sK3)))))),
% 0.24/0.46 inference(binary_proxy_clausification,[],[f169])).
% 0.24/0.46 thf(f169,plain,(
% 0.24/0.46 ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK4 @ Y0 @ Y2) & (sK4 @ Y1 @ Y0)) => (sK4 @ Y1 @ Y2)))))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK7 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK5))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK7 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK5 @ sK3))))))),
% 0.24/0.46 inference(binary_proxy_clausification,[],[f163])).
% 0.24/0.46 thf(f163,plain,(
% 0.24/0.46 ($true = ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK4 @ Y0 @ Y2) & (sK4 @ Y1 @ Y0)) => (sK4 @ Y1 @ Y2)))))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK7 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK5))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK7 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK5 @ sK3))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK7 @ Y0 @ Y1) => (sK4 @ Y0 @ Y1))))))))),
% 0.24/0.46 inference(not_proxy_clausification,[],[f158])).
% 0.24/0.46 thf(f158,plain,(
% 0.24/0.46 ($false = (~ ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK4 @ Y0 @ Y2) & (sK4 @ Y1 @ Y0)) => (sK4 @ Y1 @ Y2)))))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK7 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK5))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK7 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK5 @ sK3))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK7 @ Y0 @ Y1) => (sK4 @ Y0 @ Y1)))))))))),
% 0.24/0.46 inference(beta_eta_normalization,[],[f157])).
% 0.24/0.46 thf(f157,plain,(
% 0.24/0.46 ($false = ((^[Y0 : $i > $i > $o]: (~ ((((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((sK4 @ Y1 @ Y3) & (sK4 @ Y2 @ Y1)) => (sK4 @ Y2 @ Y3)))))))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK2 @ sK5))))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK5 @ sK3))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (sK4 @ Y1 @ Y2))))))))) @ sK7))),
% 0.24/0.46 inference(sigma_clausification,[],[f156])).
% 0.24/0.46 thf(f156,plain,(
% 0.24/0.46 ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (~ ((((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((sK4 @ Y1 @ Y3) & (sK4 @ Y2 @ Y1)) => (sK4 @ Y2 @ Y3)))))))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK2 @ sK5))))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK5 @ sK3))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (sK4 @ Y1 @ Y2)))))))))))),
% 0.24/0.46 inference(boolean_simplification,[],[f155])).
% 0.24/0.46 thf(f155,plain,(
% 0.24/0.46 ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((sK4 @ Y1 @ Y3) & (sK4 @ Y2 @ Y1)) => (sK4 @ Y2 @ Y3)))))))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK2 @ sK5))))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK5 @ sK3))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (sK4 @ Y1 @ Y2))))))) => $false))))),
% 0.24/0.46 inference(backward_demodulation,[],[f148,f154])).
% 0.24/0.46 thf(f154,plain,(
% 0.24/0.46 ($false = (sK4 @ sK2 @ sK3))),
% 0.24/0.46 inference(boolean_simplification,[],[f153])).
% 0.24/0.46 thf(f153,plain,(
% 0.24/0.46 ($false = ($true => (sK4 @ sK2 @ sK3)))),
% 0.24/0.46 inference(backward_demodulation,[],[f150,f152])).
% 0.24/0.46 thf(f199,plain,(
% 0.24/0.46 ( ! [X1 : $i > $i > $o] : (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK6 @ Y0 @ Y1) => (X1 @ Y0 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X1 @ Y0 @ Y2) & (X1 @ Y1 @ Y0)) => (X1 @ Y1 @ Y2))))))))) => (X1 @ sK5 @ sK3)) = $true)) )),
% 0.24/0.46 inference(beta_eta_normalization,[],[f198])).
% 0.24/0.46 thf(f198,plain,(
% 0.24/0.46 ( ! [X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK6 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK5 @ sK3))) @ X1))) )),
% 0.24/0.46 inference(pi_clausification,[],[f197])).
% 0.24/0.46 thf(f197,plain,(
% 0.24/0.46 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK6 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK5 @ sK3)))))),
% 0.24/0.46 inference(boolean_simplification,[],[f196])).
% 0.24/0.46 thf(f196,plain,(
% 0.24/0.46 ($true = ($true & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK6 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK5 @ sK3))))))),
% 0.24/0.46 inference(backward_demodulation,[],[f162,f195])).
% 0.24/0.46 thf(f195,plain,(
% 0.24/0.46 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK4 @ Y0 @ Y2) & (sK4 @ Y1 @ Y0)) => (sK4 @ Y1 @ Y2)))))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK6 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK5))))))),
% 0.24/0.46 inference(binary_proxy_clausification,[],[f162])).
% 0.24/0.46 thf(f162,plain,(
% 0.24/0.46 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK4 @ Y0 @ Y2) & (sK4 @ Y1 @ Y0)) => (sK4 @ Y1 @ Y2)))))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK6 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK5))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK6 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK5 @ sK3))))) = $true)),
% 0.24/0.46 inference(boolean_simplification,[],[f161])).
% 0.24/0.46 thf(f161,plain,(
% 0.24/0.46 ($true = ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK4 @ Y0 @ Y2) & (sK4 @ Y1 @ Y0)) => (sK4 @ Y1 @ Y2)))))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK6 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK5))))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK6 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK5 @ sK3))))) & $true))),
% 0.24/0.46 inference(backward_demodulation,[],[f152,f159])).
% 0.24/0.46 thf(f292,plain,(
% 0.24/0.46 ~spl0_2),
% 0.24/0.46 inference(avatar_contradiction_clause,[],[f291])).
% 0.24/0.46 thf(f291,plain,(
% 0.24/0.46 $false | ~spl0_2),
% 0.24/0.46 inference(trivial_inequality_removal,[],[f290])).
% 0.24/0.46 thf(f290,plain,(
% 0.24/0.46 ($false = $true) | ~spl0_2),
% 0.24/0.46 inference(forward_demodulation,[],[f284,f154])).
% 0.24/0.46 thf(f284,plain,(
% 0.24/0.46 ((sK4 @ sK2 @ sK3) = $true) | ~spl0_2),
% 0.24/0.46 inference(boolean_simplification,[],[f282])).
% 0.24/0.46 thf(f282,plain,(
% 0.24/0.46 ($true = ($true => (sK4 @ sK2 @ sK3))) | ~spl0_2),
% 0.24/0.46 inference(superposition,[],[f268,f209])).
% 0.24/0.46 thf(f209,plain,(
% 0.24/0.46 ((sK4 @ sK5 @ sK3) = $true) | ~spl0_2),
% 0.24/0.46 inference(avatar_component_clause,[],[f208])).
% 0.24/0.46 thf(f268,plain,(
% 0.24/0.46 ( ! [X0 : $i] : (($true = ((sK4 @ sK5 @ X0) => (sK4 @ sK2 @ X0)))) )),
% 0.24/0.46 inference(boolean_simplification,[],[f262])).
% 0.24/0.46 thf(f262,plain,(
% 0.24/0.46 ( ! [X0 : $i] : (($true = (((sK4 @ sK5 @ X0) & $true) => (sK4 @ sK2 @ X0)))) )),
% 0.24/0.46 inference(superposition,[],[f255,f245])).
% 0.24/0.46 thf(f245,plain,(
% 0.24/0.46 ($true = (sK4 @ sK2 @ sK5))),
% 0.24/0.46 inference(boolean_simplification,[],[f244])).
% 0.24/0.46 thf(f244,plain,(
% 0.24/0.46 (($true => (sK4 @ sK2 @ sK5)) = $true)),
% 0.24/0.46 inference(forward_demodulation,[],[f243,f224])).
% 0.24/0.46 thf(f243,plain,(
% 0.24/0.46 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK4 @ Y0 @ Y2) & (sK4 @ Y1 @ Y0)) => (sK4 @ Y1 @ Y2)))))))) => (sK4 @ sK2 @ sK5)) = $true)),
% 0.24/0.46 inference(boolean_simplification,[],[f241])).
% 0.24/0.46 thf(f241,plain,(
% 0.24/0.46 ($true = (($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK4 @ Y0 @ Y2) & (sK4 @ Y1 @ Y0)) => (sK4 @ Y1 @ Y2))))))))) => (sK4 @ sK2 @ sK5)))),
% 0.24/0.46 inference(superposition,[],[f236,f171])).
% 0.24/0.46 thf(f171,plain,(
% 0.24/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK7 @ Y0 @ Y1) => (sK4 @ Y0 @ Y1)))))))),
% 0.24/0.46 inference(boolean_simplification,[],[f170])).
% 0.24/0.46 thf(f170,plain,(
% 0.24/0.46 ($true = ($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK7 @ Y0 @ Y1) => (sK4 @ Y0 @ Y1))))))))),
% 0.24/0.46 inference(backward_demodulation,[],[f163,f169])).
% 0.24/0.46 thf(f236,plain,(
% 0.24/0.46 ( ! [X1 : $i > $i > $o] : (($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK7 @ Y0 @ Y1) => (X1 @ Y0 @ Y1)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X1 @ Y0 @ Y2) & (X1 @ Y1 @ Y0)) => (X1 @ Y1 @ Y2))))))))) => (X1 @ sK2 @ sK5)))) )),
% 0.24/0.46 inference(beta_eta_normalization,[],[f235])).
% 0.24/0.46 thf(f235,plain,(
% 0.24/0.46 ( ! [X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK7 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK5))) @ X1))) )),
% 0.24/0.46 inference(pi_clausification,[],[f227])).
% 0.24/0.46 thf(f227,plain,(
% 0.24/0.46 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK7 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK5)))))),
% 0.24/0.46 inference(boolean_simplification,[],[f225])).
% 0.24/0.46 thf(f225,plain,(
% 0.24/0.46 ($true = ($true & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK7 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK2 @ sK5))))))),
% 0.24/0.46 inference(backward_demodulation,[],[f216,f224])).
% 0.24/0.46 thf(f255,plain,(
% 0.24/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((sK4 @ X1 @ X3) & (sK4 @ X2 @ X1)) => (sK4 @ X2 @ X3)))) )),
% 0.24/0.46 inference(beta_eta_normalization,[],[f254])).
% 0.24/0.46 thf(f254,plain,(
% 0.24/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((sK4 @ X1 @ Y0) & (sK4 @ X2 @ X1)) => (sK4 @ X2 @ Y0))) @ X3) = $true)) )),
% 0.24/0.46 inference(pi_clausification,[],[f238])).
% 0.24/0.46 thf(f238,plain,(
% 0.24/0.46 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((sK4 @ X1 @ Y0) & (sK4 @ X2 @ X1)) => (sK4 @ X2 @ Y0)))))) )),
% 0.24/0.46 inference(beta_eta_normalization,[],[f237])).
% 0.24/0.46 thf(f237,plain,(
% 0.24/0.46 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK4 @ X1 @ Y1) & (sK4 @ Y0 @ X1)) => (sK4 @ Y0 @ Y1))))) @ X2))) )),
% 0.24/0.46 inference(pi_clausification,[],[f232])).
% 0.24/0.46 thf(f232,plain,(
% 0.24/0.46 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK4 @ X1 @ Y1) & (sK4 @ Y0 @ X1)) => (sK4 @ Y0 @ Y1)))))))) )),
% 0.24/0.46 inference(beta_eta_normalization,[],[f229])).
% 0.24/0.46 thf(f229,plain,(
% 0.24/0.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK4 @ Y0 @ Y2) & (sK4 @ Y1 @ Y0)) => (sK4 @ Y1 @ Y2))))))) @ X1))) )),
% 0.24/0.46 inference(pi_clausification,[],[f224])).
% 0.24/0.46 % SZS output end Proof for theBenchmark
% 0.24/0.46 % (5287)------------------------------
% 0.24/0.46 % (5287)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.46 % (5287)Termination reason: Refutation
% 0.24/0.46
% 0.24/0.46 % (5287)Memory used [KB]: 6012
% 0.24/0.46 % (5287)Time elapsed: 0.038 s
% 0.24/0.46 % (5287)Instructions burned: 61 (million)
% 0.24/0.46 % (5287)------------------------------
% 0.24/0.46 % (5287)------------------------------
% 0.24/0.46 % (5275)Success in time 0.052 s
% 0.24/0.46 % Vampire---4.8 exiting
%------------------------------------------------------------------------------