TSTP Solution File: SYO450^4 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO450^4 : TPTP v8.2.0. Released v4.0.0.
% 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 : n027.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 09:04:30 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYO450^4 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 08:33:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 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
% 0.14/0.38 % (21780)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (21783)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (21780)Instruction limit reached!
% 0.14/0.38 % (21780)------------------------------
% 0.14/0.38 % (21780)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (21780)Termination reason: Unknown
% 0.14/0.38 % (21780)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (21780)Memory used [KB]: 1023
% 0.14/0.38 % (21780)Time elapsed: 0.003 s
% 0.14/0.38 % (21780)Instructions burned: 2 (million)
% 0.14/0.38 % (21780)------------------------------
% 0.14/0.38 % (21780)------------------------------
% 0.14/0.38 % (21782)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)
% 0.14/0.38 % (21779)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)
% 0.14/0.38 % (21778)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)
% 0.14/0.38 % (21784)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)
% 0.14/0.38 % (21778)Instruction limit reached!
% 0.14/0.38 % (21778)------------------------------
% 0.14/0.38 % (21778)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (21778)Termination reason: Unknown
% 0.14/0.38 % (21778)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (21778)Memory used [KB]: 1023
% 0.14/0.38 % (21778)Time elapsed: 0.003 s
% 0.14/0.38 % (21784)Instruction limit reached!
% 0.14/0.38 % (21784)------------------------------
% 0.14/0.38 % (21784)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (21784)Termination reason: Unknown
% 0.14/0.38 % (21784)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (21784)Memory used [KB]: 1023
% 0.14/0.38 % (21784)Time elapsed: 0.004 s
% 0.14/0.38 % (21784)Instructions burned: 4 (million)
% 0.14/0.38 % (21784)------------------------------
% 0.14/0.38 % (21784)------------------------------
% 0.14/0.38 % (21778)Instructions burned: 5 (million)
% 0.14/0.38 % (21778)------------------------------
% 0.14/0.38 % (21778)------------------------------
% 0.14/0.38 % (21777)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (21781)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)
% 0.14/0.38 % (21781)Instruction limit reached!
% 0.14/0.38 % (21781)------------------------------
% 0.14/0.38 % (21781)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (21781)Termination reason: Unknown
% 0.14/0.38 % (21781)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (21781)Memory used [KB]: 1023
% 0.14/0.38 % (21781)Time elapsed: 0.003 s
% 0.14/0.38 % (21781)Instructions burned: 3 (million)
% 0.14/0.38 % (21781)------------------------------
% 0.14/0.38 % (21781)------------------------------
% 0.14/0.38 % (21782)Refutation not found, incomplete strategy
% 0.14/0.38 % (21782)------------------------------
% 0.14/0.38 % (21782)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (21782)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.38
% 0.14/0.38
% 0.14/0.38 % (21782)Memory used [KB]: 5628
% 0.14/0.38 % (21782)Time elapsed: 0.010 s
% 0.14/0.38 % (21782)Instructions burned: 15 (million)
% 0.14/0.38 % (21782)------------------------------
% 0.14/0.38 % (21782)------------------------------
% 0.14/0.39 % (21783)Instruction limit reached!
% 0.14/0.39 % (21783)------------------------------
% 0.14/0.39 % (21783)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (21783)Termination reason: Unknown
% 0.14/0.39 % (21783)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (21783)Memory used [KB]: 5628
% 0.14/0.39 % (21783)Time elapsed: 0.011 s
% 0.14/0.39 % (21783)Instructions burned: 18 (million)
% 0.14/0.39 % (21783)------------------------------
% 0.14/0.39 % (21783)------------------------------
% 0.14/0.39 % (21779)Instruction limit reached!
% 0.14/0.39 % (21779)------------------------------
% 0.14/0.39 % (21779)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (21779)Termination reason: Unknown
% 0.14/0.39 % (21779)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (21779)Memory used [KB]: 5756
% 0.14/0.39 % (21779)Time elapsed: 0.018 s
% 0.14/0.39 % (21779)Instructions burned: 27 (million)
% 0.14/0.39 % (21779)------------------------------
% 0.14/0.39 % (21779)------------------------------
% 0.14/0.40 % (21786)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)
% 0.14/0.40 % (21777)First to succeed.
% 0.14/0.40 % (21789)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.40 % (21790)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.40 % (21777)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% 0.14/0.40 thf(type_def_5, type, mu: $tType).
% 0.14/0.40 thf(func_def_0, type, mu: $tType).
% 0.14/0.40 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.14/0.40 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_15, type, mtrue: $i > $o).
% 0.14/0.40 thf(func_def_16, type, mfalse: $i > $o).
% 0.14/0.40 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_33, type, rel_b: $i > $i > $o).
% 0.14/0.40 thf(func_def_34, type, mbox_b: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_35, type, mdia_b: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_36, type, p: $i > $o).
% 0.14/0.40 thf(func_def_37, type, q: $i > $o).
% 0.14/0.40 thf(func_def_38, type, r: $i > $o).
% 0.14/0.40 thf(func_def_56, type, sK2: $i > $i).
% 0.14/0.40 thf(f378,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(avatar_sat_refutation,[],[f283,f289,f302,f309,f361,f370,f377])).
% 0.14/0.40 thf(f377,plain,(
% 0.14/0.40 ~spl0_6 | ~spl0_12),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f376])).
% 0.14/0.40 thf(f376,plain,(
% 0.14/0.40 $false | (~spl0_6 | ~spl0_12)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f373])).
% 0.14/0.40 thf(f373,plain,(
% 0.14/0.40 ($false = $true) | (~spl0_6 | ~spl0_12)),
% 0.14/0.40 inference(superposition,[],[f287,f356])).
% 0.14/0.40 thf(f356,plain,(
% 0.14/0.40 ((r @ (sK2 @ sK1)) = $true) | ~spl0_12),
% 0.14/0.40 inference(avatar_component_clause,[],[f354])).
% 0.14/0.40 thf(f354,plain,(
% 0.14/0.40 spl0_12 <=> ((r @ (sK2 @ sK1)) = $true)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_12])])).
% 0.14/0.40 thf(f287,plain,(
% 0.14/0.40 ((r @ (sK2 @ sK1)) = $false) | ~spl0_6),
% 0.14/0.40 inference(avatar_component_clause,[],[f285])).
% 0.14/0.40 thf(f285,plain,(
% 0.14/0.40 spl0_6 <=> ((r @ (sK2 @ sK1)) = $false)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.14/0.40 thf(f370,plain,(
% 0.14/0.40 ~spl0_3 | ~spl0_11),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f369])).
% 0.14/0.40 thf(f369,plain,(
% 0.14/0.40 $false | (~spl0_3 | ~spl0_11)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f365])).
% 0.14/0.40 thf(f365,plain,(
% 0.14/0.40 ($false = $true) | (~spl0_3 | ~spl0_11)),
% 0.14/0.40 inference(superposition,[],[f352,f272])).
% 0.14/0.40 thf(f272,plain,(
% 0.14/0.40 ((q @ (sK2 @ sK1)) = $true) | ~spl0_3),
% 0.14/0.40 inference(avatar_component_clause,[],[f270])).
% 0.14/0.40 thf(f270,plain,(
% 0.14/0.40 spl0_3 <=> ((q @ (sK2 @ sK1)) = $true)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.14/0.40 thf(f352,plain,(
% 0.14/0.40 ((q @ (sK2 @ sK1)) = $false) | ~spl0_11),
% 0.14/0.40 inference(avatar_component_clause,[],[f350])).
% 0.14/0.40 thf(f350,plain,(
% 0.14/0.40 spl0_11 <=> ((q @ (sK2 @ sK1)) = $false)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_11])])).
% 0.14/0.40 thf(f361,plain,(
% 0.14/0.40 spl0_11 | spl0_12 | spl0_2),
% 0.14/0.40 inference(avatar_split_clause,[],[f360,f266,f354,f350])).
% 0.14/0.40 thf(f266,plain,(
% 0.14/0.40 spl0_2 <=> ((p @ sK1) = $false)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.14/0.40 thf(f360,plain,(
% 0.14/0.40 ((q @ (sK2 @ sK1)) = $false) | ((r @ (sK2 @ sK1)) = $true) | spl0_2),
% 0.14/0.40 inference(subsumption_resolution,[],[f329,f267])).
% 0.14/0.40 thf(f267,plain,(
% 0.14/0.40 ((p @ sK1) != $false) | spl0_2),
% 0.14/0.40 inference(avatar_component_clause,[],[f266])).
% 0.14/0.40 thf(f329,plain,(
% 0.14/0.40 ((r @ (sK2 @ sK1)) = $true) | ((q @ (sK2 @ sK1)) = $false) | ((p @ sK1) = $false)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f323])).
% 0.14/0.40 thf(f323,plain,(
% 0.14/0.40 ((p @ sK1) = $false) | ($false = $true) | ((q @ (sK2 @ sK1)) = $false) | ((r @ (sK2 @ sK1)) = $true)),
% 0.14/0.40 inference(superposition,[],[f201,f159])).
% 0.14/0.40 thf(f159,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_b @ X1 @ X1) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f158])).
% 0.14/0.40 thf(f158,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: (rel_b @ Y0 @ Y0)) @ X1) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f157])).
% 0.14/0.40 thf(f157,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: (rel_b @ Y0 @ Y0))) = $true)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f156])).
% 0.14/0.40 thf(f156,plain,(
% 0.14/0.40 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_b) = $true)),
% 0.14/0.40 inference(definition_unfolding,[],[f140,f143])).
% 0.14/0.40 thf(f143,plain,(
% 0.14/0.40 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f87])).
% 0.14/0.40 thf(f87,plain,(
% 0.14/0.40 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f86])).
% 0.14/0.40 thf(f86,plain,(
% 0.14/0.40 ((^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))) = mreflexive)),
% 0.14/0.40 inference(rectify,[],[f18])).
% 0.14/0.40 thf(f18,axiom,(
% 0.14/0.40 ((^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))) = mreflexive)),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
% 0.14/0.40 thf(f140,plain,(
% 0.14/0.40 ((mreflexive @ rel_b) = $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f56])).
% 0.14/0.40 thf(f56,plain,(
% 0.14/0.40 ((mreflexive @ rel_b) = $true)),
% 0.14/0.40 inference(fool_elimination,[],[f55])).
% 0.14/0.40 thf(f55,plain,(
% 0.14/0.40 (mreflexive @ rel_b)),
% 0.14/0.40 inference(rectify,[],[f34])).
% 0.14/0.40 thf(f34,axiom,(
% 0.14/0.40 (mreflexive @ rel_b)),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 0.14/0.40 thf(f201,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ((r @ (sK2 @ X1)) = $true) | ($false = (q @ (sK2 @ X1))) | ((p @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f200])).
% 0.14/0.40 thf(f200,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((p @ X1) = $false) | ((~ (q @ (sK2 @ X1))) = $true) | ($false = (rel_b @ sK1 @ X1)) | ((r @ (sK2 @ X1)) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f199])).
% 0.14/0.40 thf(f199,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((r @ (sK2 @ X1)) | (~ (q @ (sK2 @ X1))))) | ($false = (rel_b @ sK1 @ X1)) | ((p @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f198])).
% 0.14/0.40 thf(f198,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (~ ((r @ (sK2 @ X1)) | (~ (q @ (sK2 @ X1)))))) | ((p @ X1) = $false) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f196])).
% 0.14/0.40 thf(f196,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((p @ X1) = $false) | ($false = (rel_b @ sK1 @ X1)) | ($false = ((~ ((r @ (sK2 @ X1)) | (~ (q @ (sK2 @ X1))))) | (~ (rel_b @ X1 @ (sK2 @ X1)))))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f195])).
% 0.14/0.40 thf(f195,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((p @ X1) = $false) | ($false = ((^[Y0 : $i]: ((~ ((r @ Y0) | (~ (q @ Y0)))) | (~ (rel_b @ X1 @ Y0)))) @ (sK2 @ X1))) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.14/0.40 inference(sigma_clausification,[],[f194])).
% 0.14/0.40 thf(f194,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((p @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ ((r @ Y0) | (~ (q @ Y0)))) | (~ (rel_b @ X1 @ Y0))))) = $false) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f193])).
% 0.14/0.40 thf(f193,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((p @ X1) = $false) | ($false = (rel_b @ sK1 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((r @ Y0) | (~ (q @ Y0)))) | (~ (rel_b @ X1 @ Y0)))))) = $true)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f192])).
% 0.14/0.40 thf(f192,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ((~ (p @ X1)) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((r @ Y0) | (~ (q @ Y0)))) | (~ (rel_b @ X1 @ Y0)))))) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f191])).
% 0.14/0.40 thf(f191,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((r @ Y0) | (~ (q @ Y0)))) | (~ (rel_b @ X1 @ Y0)))))) | (~ (p @ X1))) = $true) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f190])).
% 0.14/0.40 thf(f190,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((~ (rel_b @ sK1 @ X1)) = $true) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((r @ Y0) | (~ (q @ Y0)))) | (~ (rel_b @ X1 @ Y0)))))) | (~ (p @ X1))) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f189])).
% 0.14/0.40 thf(f189,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((r @ Y0) | (~ (q @ Y0)))) | (~ (rel_b @ X1 @ Y0)))))) | (~ (p @ X1))) | (~ (rel_b @ sK1 @ X1))) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f188])).
% 0.14/0.40 thf(f188,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((r @ Y1) | (~ (q @ Y1)))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (p @ Y0))) | (~ (rel_b @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f187])).
% 0.14/0.40 thf(f187,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((r @ Y1) | (~ (q @ Y1)))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (p @ Y0))) | (~ (rel_b @ sK1 @ Y0))))) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f163])).
% 0.14/0.40 thf(f163,plain,(
% 0.14/0.40 ($false = (~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((r @ Y1) | (~ (q @ Y1)))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (p @ Y0))) | (~ (rel_b @ sK1 @ Y0)))))))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f162])).
% 0.14/0.40 thf(f162,plain,(
% 0.14/0.40 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (r @ Y1)) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1))))))) | (~ (q @ Y0)))) | (~ (rel_b @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((r @ Y1) | (~ (q @ Y1)))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (p @ Y0))) | (~ (rel_b @ sK1 @ Y0))))))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f161])).
% 0.14/0.40 thf(f161,plain,(
% 0.14/0.40 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (((~ (!! @ $i @ (^[Y2 : $i]: ((~ (r @ Y2)) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_b @ Y1 @ Y2))))))) | (~ (q @ Y1)))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((~ ((r @ Y2) | (~ (q @ Y2)))) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (p @ Y1))) | (~ (rel_b @ Y0 @ Y1)))))))) @ sK1) = $false)),
% 0.14/0.40 inference(sigma_clausification,[],[f160])).
% 0.14/0.40 thf(f160,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (((~ (!! @ $i @ (^[Y2 : $i]: ((~ (r @ Y2)) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_b @ Y1 @ Y2))))))) | (~ (q @ Y1)))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((~ ((r @ Y2) | (~ (q @ Y2)))) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (p @ Y1))) | (~ (rel_b @ Y0 @ Y1))))))))) != $true)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f155])).
% 0.14/0.40 thf(f155,plain,(
% 0.14/0.40 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ p @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_b @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ q @ r)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_b @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ q @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_b @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ r)))))))),
% 0.14/0.40 inference(definition_unfolding,[],[f139,f109,f145,f122,f145,f153,f145,f153,f145,f145,f122,f153])).
% 0.14/0.40 thf(f153,plain,(
% 0.14/0.40 (mdia_b = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_b @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.14/0.40 inference(definition_unfolding,[],[f119,f116,f122,f116])).
% 0.14/0.40 thf(f116,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f61])).
% 0.14/0.40 thf(f61,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(fool_elimination,[],[f60])).
% 0.14/0.40 thf(f60,plain,(
% 0.14/0.40 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.14/0.40 inference(rectify,[],[f3])).
% 0.14/0.40 thf(f3,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.14/0.40 thf(f119,plain,(
% 0.14/0.40 (mdia_b = (^[Y0 : $i > $o]: (mnot @ (mbox_b @ (mnot @ Y0)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f52])).
% 0.14/0.40 thf(f52,plain,(
% 0.14/0.40 (mdia_b = (^[Y0 : $i > $o]: (mnot @ (mbox_b @ (mnot @ Y0)))))),
% 0.14/0.40 inference(fool_elimination,[],[f51])).
% 0.14/0.40 thf(f51,plain,(
% 0.14/0.40 (mdia_b = (^[X0 : $i > $o] : (mnot @ (mbox_b @ (mnot @ X0)))))),
% 0.14/0.40 inference(rectify,[],[f33])).
% 0.14/0.40 thf(f33,axiom,(
% 0.14/0.40 (mdia_b = (^[X3 : $i > $o] : (mnot @ (mbox_b @ (mnot @ X3)))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_b)).
% 0.14/0.40 thf(f122,plain,(
% 0.14/0.40 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f99])).
% 0.14/0.40 thf(f99,plain,(
% 0.14/0.40 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f98])).
% 0.14/0.40 thf(f98,plain,(
% 0.14/0.40 (mbox_b = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_b @ X1 @ X2) | (X0 @ X2)))))),
% 0.14/0.40 inference(rectify,[],[f32])).
% 0.14/0.40 thf(f32,axiom,(
% 0.14/0.40 (mbox_b = (^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_b @ X2 @ X7) | (X3 @ X7)))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_b)).
% 0.14/0.40 thf(f145,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.14/0.40 inference(definition_unfolding,[],[f125,f135,f116])).
% 0.14/0.40 thf(f135,plain,(
% 0.14/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f40])).
% 0.14/0.40 thf(f40,plain,(
% 0.14/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f39])).
% 0.14/0.40 thf(f39,plain,(
% 0.14/0.40 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.14/0.40 inference(rectify,[],[f4])).
% 0.14/0.40 thf(f4,axiom,(
% 0.14/0.40 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.14/0.40 thf(f125,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f75])).
% 0.14/0.40 thf(f75,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f74])).
% 0.14/0.40 thf(f74,plain,(
% 0.14/0.40 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.14/0.40 inference(rectify,[],[f6])).
% 0.14/0.40 thf(f6,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.40 thf(f109,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f95])).
% 0.14/0.40 thf(f95,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f94])).
% 0.14/0.40 thf(f94,plain,(
% 0.14/0.40 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.14/0.40 inference(rectify,[],[f28])).
% 0.14/0.40 thf(f28,axiom,(
% 0.14/0.40 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.40 thf(f139,plain,(
% 0.14/0.40 ((mvalid @ (mimplies @ (mbox_b @ (mimplies @ p @ (mdia_b @ (mimplies @ q @ r)))) @ (mdia_b @ (mimplies @ q @ (mimplies @ (mbox_b @ p) @ (mdia_b @ r)))))) != $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f107])).
% 0.14/0.40 thf(f107,plain,(
% 0.14/0.40 ((mvalid @ (mimplies @ (mbox_b @ (mimplies @ p @ (mdia_b @ (mimplies @ q @ r)))) @ (mdia_b @ (mimplies @ q @ (mimplies @ (mbox_b @ p) @ (mdia_b @ r)))))) != $true)),
% 0.14/0.40 inference(flattening,[],[f106])).
% 0.14/0.40 thf(f106,plain,(
% 0.14/0.40 ~((mvalid @ (mimplies @ (mbox_b @ (mimplies @ p @ (mdia_b @ (mimplies @ q @ r)))) @ (mdia_b @ (mimplies @ q @ (mimplies @ (mbox_b @ p) @ (mdia_b @ r)))))) = $true)),
% 0.14/0.40 inference(fool_elimination,[],[f105])).
% 0.14/0.40 thf(f105,plain,(
% 0.14/0.40 ~(mvalid @ (mimplies @ (mbox_b @ (mimplies @ p @ (mdia_b @ (mimplies @ q @ r)))) @ (mdia_b @ (mimplies @ q @ (mimplies @ (mbox_b @ p) @ (mdia_b @ r))))))),
% 0.14/0.40 inference(rectify,[],[f37])).
% 0.14/0.40 thf(f37,negated_conjecture,(
% 0.14/0.40 ~(mvalid @ (mimplies @ (mbox_b @ (mimplies @ p @ (mdia_b @ (mimplies @ q @ r)))) @ (mdia_b @ (mimplies @ q @ (mimplies @ (mbox_b @ p) @ (mdia_b @ r))))))),
% 0.14/0.40 inference(negated_conjecture,[],[f36])).
% 0.14/0.40 thf(f36,conjecture,(
% 0.14/0.40 (mvalid @ (mimplies @ (mbox_b @ (mimplies @ p @ (mdia_b @ (mimplies @ q @ r)))) @ (mdia_b @ (mimplies @ q @ (mimplies @ (mbox_b @ p) @ (mdia_b @ r))))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.14/0.40 thf(f309,plain,(
% 0.14/0.40 ~spl0_1),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f308])).
% 0.14/0.40 thf(f308,plain,(
% 0.14/0.40 $false | ~spl0_1),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f305])).
% 0.14/0.40 thf(f305,plain,(
% 0.14/0.40 ($false = $true) | ~spl0_1),
% 0.14/0.40 inference(superposition,[],[f159,f264])).
% 0.14/0.40 thf(f264,plain,(
% 0.14/0.40 ((rel_b @ sK1 @ sK1) = $false) | ~spl0_1),
% 0.14/0.40 inference(avatar_component_clause,[],[f262])).
% 0.14/0.40 thf(f262,plain,(
% 0.14/0.40 spl0_1 <=> ((rel_b @ sK1 @ sK1) = $false)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.14/0.40 thf(f302,plain,(
% 0.14/0.40 ~spl0_2),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f301])).
% 0.14/0.40 thf(f301,plain,(
% 0.14/0.40 $false | ~spl0_2),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f297])).
% 0.14/0.40 thf(f297,plain,(
% 0.14/0.40 ($false = $true) | ~spl0_2),
% 0.14/0.40 inference(superposition,[],[f236,f268])).
% 0.14/0.40 thf(f268,plain,(
% 0.14/0.40 ((p @ sK1) = $false) | ~spl0_2),
% 0.14/0.40 inference(avatar_component_clause,[],[f266])).
% 0.14/0.40 thf(f236,plain,(
% 0.14/0.40 ((p @ sK1) = $true)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f234])).
% 0.14/0.40 thf(f234,plain,(
% 0.14/0.40 ((p @ sK1) = $true) | ($false = $true)),
% 0.14/0.40 inference(superposition,[],[f159,f232])).
% 0.14/0.40 thf(f232,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (($false = (rel_b @ sK1 @ X0)) | ((p @ X0) = $true)) )),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f227])).
% 0.14/0.40 thf(f227,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (((p @ X0) = $true) | ($false = $true) | ($false = (rel_b @ sK1 @ X0))) )),
% 0.14/0.40 inference(superposition,[],[f185,f159])).
% 0.14/0.40 thf(f185,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ((p @ X2) = $true) | ($false = (rel_b @ X1 @ X2))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f184])).
% 0.14/0.40 thf(f184,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((p @ X2) = $true) | ($false = (rel_b @ sK1 @ X1)) | ((~ (rel_b @ X1 @ X2)) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f183])).
% 0.14/0.40 thf(f183,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | (((p @ X2) | (~ (rel_b @ X1 @ X2))) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f182])).
% 0.14/0.40 thf(f182,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ X1 @ Y0)))) @ X2) = $true) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.14/0.40 inference(pi_clausification,[],[f181])).
% 0.14/0.40 thf(f181,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ X1 @ Y0))))) = $true) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f173])).
% 0.14/0.40 thf(f173,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ X1 @ Y0))))))) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f172])).
% 0.14/0.40 thf(f172,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_b @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ X1 @ Y0)))))))) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f170])).
% 0.14/0.40 thf(f170,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_b @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ X1 @ Y0))))))) | (~ (q @ X1))) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f169])).
% 0.14/0.40 thf(f169,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((~ (rel_b @ sK1 @ X1)) = $true) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_b @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ X1 @ Y0))))))) | (~ (q @ X1))) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f168])).
% 0.14/0.40 thf(f168,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_b @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ X1 @ Y0))))))) | (~ (q @ X1)))) = $true) | ((~ (rel_b @ sK1 @ X1)) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f167])).
% 0.14/0.40 thf(f167,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_b @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ X1 @ Y0))))))) | (~ (q @ X1)))) | (~ (rel_b @ sK1 @ X1))) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f166])).
% 0.14/0.40 thf(f166,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (r @ Y1)) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1))))))) | (~ (q @ Y0)))) | (~ (rel_b @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f165])).
% 0.14/0.40 thf(f165,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (r @ Y1)) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1))))))) | (~ (q @ Y0)))) | (~ (rel_b @ sK1 @ Y0))))) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f164])).
% 0.14/0.40 thf(f164,plain,(
% 0.14/0.40 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (r @ Y1)) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1))))))) | (~ (q @ Y0)))) | (~ (rel_b @ sK1 @ Y0)))))))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f162])).
% 0.14/0.40 thf(f289,plain,(
% 0.14/0.40 spl0_2 | spl0_1 | spl0_6),
% 0.14/0.40 inference(avatar_split_clause,[],[f254,f285,f262,f266])).
% 0.14/0.40 thf(f254,plain,(
% 0.14/0.40 ((r @ (sK2 @ sK1)) = $false) | ((rel_b @ sK1 @ sK1) = $false) | ((p @ sK1) = $false)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f239])).
% 0.14/0.40 thf(f239,plain,(
% 0.14/0.40 ($false = $true) | ((rel_b @ sK1 @ sK1) = $false) | ((p @ sK1) = $false) | ((r @ (sK2 @ sK1)) = $false)),
% 0.14/0.40 inference(superposition,[],[f202,f222])).
% 0.14/0.40 thf(f222,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (($false = (rel_b @ sK1 @ X0)) | ((r @ X0) = $false)) )),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f218])).
% 0.14/0.40 thf(f218,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (($false = $true) | ($false = (rel_b @ sK1 @ X0)) | ((r @ X0) = $false)) )),
% 0.14/0.40 inference(superposition,[],[f159,f180])).
% 0.14/0.40 thf(f180,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ($false = (r @ X2)) | ($false = (rel_b @ X1 @ X2))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f179])).
% 0.14/0.40 thf(f179,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((~ (rel_b @ X1 @ X2)) = $true) | ($false = (r @ X2)) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f178])).
% 0.14/0.40 thf(f178,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ((~ (r @ X2)) = $true) | ((~ (rel_b @ X1 @ X2)) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f177])).
% 0.14/0.40 thf(f177,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : ((((~ (r @ X2)) | (~ (rel_b @ X1 @ X2))) = $true) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f176])).
% 0.14/0.40 thf(f176,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_b @ X1 @ Y0)))) @ X2) = $true) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.14/0.40 inference(pi_clausification,[],[f175])).
% 0.14/0.40 thf(f175,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_b @ X1 @ Y0))))) = $true)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f174])).
% 0.14/0.40 thf(f174,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_b @ X1 @ Y0))))))) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f172])).
% 0.14/0.40 thf(f202,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_b @ X1 @ (sK2 @ X1)) = $true) | ($false = (rel_b @ sK1 @ X1)) | ((p @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f197])).
% 0.14/0.40 thf(f197,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((p @ X1) = $false) | ($false = (~ (rel_b @ X1 @ (sK2 @ X1)))) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f196])).
% 0.14/0.40 thf(f283,plain,(
% 0.14/0.40 spl0_1 | spl0_3 | spl0_2),
% 0.14/0.40 inference(avatar_split_clause,[],[f256,f266,f270,f262])).
% 0.14/0.40 thf(f256,plain,(
% 0.14/0.40 ((rel_b @ sK1 @ sK1) = $false) | ((q @ (sK2 @ sK1)) = $true) | ((p @ sK1) = $false)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f247])).
% 0.14/0.40 thf(f247,plain,(
% 0.14/0.40 ((q @ (sK2 @ sK1)) = $true) | ($false = $true) | ((rel_b @ sK1 @ sK1) = $false) | ((p @ sK1) = $false)),
% 0.14/0.40 inference(superposition,[],[f186,f202])).
% 0.14/0.40 thf(f186,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ((q @ X1) = $true)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f171])).
% 0.14/0.40 thf(f171,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ($false = (~ (q @ X1)))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f170])).
% 0.14/0.40 % SZS output end Proof for theBenchmark
% 0.14/0.40 % (21777)------------------------------
% 0.14/0.40 % (21777)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (21777)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (21777)Memory used [KB]: 5884
% 0.14/0.40 % (21777)Time elapsed: 0.018 s
% 0.14/0.40 % (21777)Instructions burned: 25 (million)
% 0.14/0.40 % (21777)------------------------------
% 0.14/0.40 % (21777)------------------------------
% 0.14/0.40 % (21776)Success in time 0.037 s
% 0.14/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------