TSTP Solution File: SYO459^4 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO459^4 : 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 : n002.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 09:04:48 EDT 2024
% Result : Theorem 0.24s 0.42s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SYO459^4 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.16 % 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
% 0.16/0.37 % Computer : n002.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 09:13:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.16/0.37 This is a TH0_THM_EQU_NAR problem
% 0.16/0.38 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/sandbox2/benchmark/theBenchmark.p
% 0.16/0.40 % (23829)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.16/0.40 % (23823)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.16/0.40 % (23824)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)
% 0.16/0.40 % (23830)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)
% 0.16/0.40 % (23824)Instruction limit reached!
% 0.16/0.40 % (23824)------------------------------
% 0.16/0.40 % (23824)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (23824)Termination reason: Unknown
% 0.16/0.40 % (23824)Termination phase: shuffling
% 0.16/0.40
% 0.16/0.40 % (23824)Memory used [KB]: 1023
% 0.16/0.40 % (23824)Time elapsed: 0.004 s
% 0.16/0.40 % (23824)Instructions burned: 4 (million)
% 0.16/0.40 % (23824)------------------------------
% 0.16/0.40 % (23824)------------------------------
% 0.16/0.40 % (23830)Instruction limit reached!
% 0.16/0.40 % (23830)------------------------------
% 0.16/0.40 % (23830)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (23830)Termination reason: Unknown
% 0.16/0.40 % (23830)Termination phase: shuffling
% 0.16/0.40
% 0.16/0.40 % (23830)Memory used [KB]: 1023
% 0.16/0.40 % (23830)Time elapsed: 0.004 s
% 0.16/0.40 % (23830)Instructions burned: 3 (million)
% 0.16/0.40 % (23830)------------------------------
% 0.16/0.40 % (23830)------------------------------
% 0.16/0.40 % (23825)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)
% 0.16/0.41 % (23829)Instruction limit reached!
% 0.16/0.41 % (23829)------------------------------
% 0.16/0.41 % (23829)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (23828)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)
% 0.16/0.41 % (23829)Termination reason: Unknown
% 0.16/0.41 % (23829)Termination phase: Saturation
% 0.16/0.41
% 0.16/0.41 % (23829)Memory used [KB]: 5628
% 0.16/0.41 % (23829)Time elapsed: 0.012 s
% 0.16/0.41 % (23829)Instructions burned: 19 (million)
% 0.16/0.41 % (23829)------------------------------
% 0.16/0.41 % (23829)------------------------------
% 0.16/0.41 % (23827)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)
% 0.16/0.41 % (23827)Instruction limit reached!
% 0.16/0.41 % (23827)------------------------------
% 0.16/0.41 % (23827)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (23827)Termination reason: Unknown
% 0.16/0.41 % (23827)Termination phase: shuffling
% 0.16/0.41
% 0.16/0.41 % (23827)Memory used [KB]: 1023
% 0.16/0.41 % (23827)Time elapsed: 0.002 s
% 0.16/0.41 % (23827)Instructions burned: 2 (million)
% 0.16/0.41 % (23827)------------------------------
% 0.16/0.41 % (23827)------------------------------
% 0.16/0.41 % (23826)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.41 % (23826)Instruction limit reached!
% 0.16/0.41 % (23826)------------------------------
% 0.16/0.41 % (23826)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (23826)Termination reason: Unknown
% 0.16/0.41 % (23826)Termination phase: shuffling
% 0.16/0.41
% 0.16/0.41 % (23826)Memory used [KB]: 1023
% 0.16/0.41 % (23826)Time elapsed: 0.003 s
% 0.16/0.41 % (23826)Instructions burned: 2 (million)
% 0.16/0.41 % (23826)------------------------------
% 0.16/0.41 % (23826)------------------------------
% 0.16/0.41 % (23831)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)
% 0.16/0.41 % (23828)Refutation not found, incomplete strategy
% 0.16/0.41 % (23828)------------------------------
% 0.16/0.41 % (23828)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (23828)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.41
% 0.16/0.41
% 0.16/0.41 % (23828)Memory used [KB]: 5628
% 0.16/0.41 % (23828)Time elapsed: 0.030 s
% 0.16/0.41 % (23828)Instructions burned: 16 (million)
% 0.16/0.41 % (23828)------------------------------
% 0.16/0.41 % (23828)------------------------------
% 0.24/0.42 % (23823)First to succeed.
% 0.24/0.42 % (23832)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 % (23825)Also succeeded, but the first one will report.
% 0.24/0.42 % (23833)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 % (23823)Refutation found. Thanks to Tanya!
% 0.24/0.42 % SZS status Theorem for theBenchmark
% 0.24/0.42 % SZS output start Proof for theBenchmark
% 0.24/0.42 thf(type_def_5, type, mu: $tType).
% 0.24/0.42 thf(func_def_0, type, mu: $tType).
% 0.24/0.42 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.24/0.42 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.42 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.24/0.42 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.42 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.42 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.42 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.42 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.42 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.42 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.24/0.42 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.24/0.42 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.24/0.42 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.24/0.42 thf(func_def_15, type, mtrue: $i > $o).
% 0.24/0.42 thf(func_def_16, type, mfalse: $i > $o).
% 0.24/0.42 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.24/0.42 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.24/0.42 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.24/0.42 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.24/0.42 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.24/0.42 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.24/0.42 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.24/0.42 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.24/0.42 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.24/0.42 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.24/0.42 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.24/0.42 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.24/0.42 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.24/0.42 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.24/0.42 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.24/0.42 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.24/0.42 thf(func_def_33, type, rel_b: $i > $i > $o).
% 0.24/0.42 thf(func_def_34, type, mbox_b: ($i > $o) > $i > $o).
% 0.24/0.42 thf(func_def_35, type, mdia_b: ($i > $o) > $i > $o).
% 0.24/0.42 thf(func_def_36, type, p: $i > $o).
% 0.24/0.42 thf(func_def_54, type, sK2: $i > $i).
% 0.24/0.42 thf(func_def_55, type, sK3: $i > $i).
% 0.24/0.42 thf(f384,plain,(
% 0.24/0.42 $false),
% 0.24/0.42 inference(avatar_sat_refutation,[],[f247,f362,f377,f383])).
% 0.24/0.42 thf(f383,plain,(
% 0.24/0.42 ~spl0_6),
% 0.24/0.42 inference(avatar_contradiction_clause,[],[f382])).
% 0.24/0.42 thf(f382,plain,(
% 0.24/0.42 $false | ~spl0_6),
% 0.24/0.42 inference(trivial_inequality_removal,[],[f378])).
% 0.24/0.42 thf(f378,plain,(
% 0.24/0.42 ($false = $true) | ~spl0_6),
% 0.24/0.42 inference(superposition,[],[f360,f292])).
% 0.24/0.42 thf(f292,plain,(
% 0.24/0.42 ($false = (p @ (sK3 @ sK4)))),
% 0.24/0.42 inference(trivial_inequality_removal,[],[f284])).
% 0.24/0.42 thf(f284,plain,(
% 0.24/0.42 ($false = $true) | ($false = (p @ (sK3 @ sK4)))),
% 0.24/0.42 inference(superposition,[],[f189,f275])).
% 0.24/0.42 thf(f275,plain,(
% 0.24/0.42 ( ! [X0 : $i] : (($false = (rel_b @ sK1 @ X0)) | ($false = (p @ (sK3 @ X0)))) )),
% 0.24/0.42 inference(trivial_inequality_removal,[],[f274])).
% 0.24/0.42 thf(f274,plain,(
% 0.24/0.42 ( ! [X0 : $i] : (($false = (rel_b @ sK1 @ X0)) | ($false = (p @ (sK3 @ X0))) | ($false = $true)) )),
% 0.24/0.42 inference(duplicate_literal_removal,[],[f268])).
% 0.24/0.42 thf(f268,plain,(
% 0.24/0.42 ( ! [X0 : $i] : (($false = (p @ (sK3 @ X0))) | ($false = (rel_b @ sK1 @ X0)) | ($false = $true) | ($false = (rel_b @ sK1 @ X0))) )),
% 0.24/0.42 inference(superposition,[],[f173,f263])).
% 0.24/0.42 thf(f263,plain,(
% 0.24/0.42 ( ! [X0 : $i,X1 : $i] : (($false = (rel_b @ X1 @ (sK2 @ X0))) | ($false = (p @ (sK3 @ X1))) | ($false = (rel_b @ sK1 @ X0))) )),
% 0.24/0.42 inference(trivial_inequality_removal,[],[f254])).
% 0.24/0.42 thf(f254,plain,(
% 0.24/0.42 ( ! [X0 : $i,X1 : $i] : (($false = (rel_b @ X1 @ (sK2 @ X0))) | ($false = (p @ (sK3 @ X1))) | ($false = $true) | ($false = (rel_b @ sK1 @ X0))) )),
% 0.24/0.42 inference(superposition,[],[f182,f200])).
% 0.24/0.42 thf(f200,plain,(
% 0.24/0.42 ( ! [X2 : $i,X1 : $i] : (($true = (rel_b @ X1 @ X2)) | ($false = (rel_b @ X2 @ X1))) )),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f199])).
% 0.24/0.42 thf(f199,plain,(
% 0.24/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((rel_b @ X2 @ X1) => (rel_b @ X1 @ X2)))) )),
% 0.24/0.42 inference(beta_eta_normalization,[],[f198])).
% 0.24/0.42 thf(f198,plain,(
% 0.24/0.42 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((rel_b @ Y0 @ X1) => (rel_b @ X1 @ Y0))) @ X2) = $true)) )),
% 0.24/0.42 inference(pi_clausification,[],[f197])).
% 0.24/0.42 thf(f197,plain,(
% 0.24/0.42 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((rel_b @ Y0 @ X1) => (rel_b @ X1 @ Y0)))) = $true)) )),
% 0.24/0.42 inference(beta_eta_normalization,[],[f196])).
% 0.24/0.42 thf(f196,plain,(
% 0.24/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_b @ Y1 @ Y0) => (rel_b @ Y0 @ Y1))))) @ X1))) )),
% 0.24/0.42 inference(pi_clausification,[],[f195])).
% 0.24/0.42 thf(f195,plain,(
% 0.24/0.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_b @ Y1 @ Y0) => (rel_b @ Y0 @ Y1)))))) = $true)),
% 0.24/0.42 inference(beta_eta_normalization,[],[f155])).
% 0.24/0.42 thf(f155,plain,(
% 0.24/0.42 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))) @ rel_b))),
% 0.24/0.42 inference(definition_unfolding,[],[f126,f114])).
% 0.24/0.42 thf(f114,plain,(
% 0.24/0.42 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.24/0.42 inference(cnf_transformation,[],[f81])).
% 0.24/0.42 thf(f81,plain,(
% 0.24/0.42 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.24/0.42 inference(fool_elimination,[],[f80])).
% 0.24/0.42 thf(f80,plain,(
% 0.24/0.42 ((^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)))) = msymmetric)),
% 0.24/0.42 inference(rectify,[],[f19])).
% 0.24/0.42 thf(f19,axiom,(
% 0.24/0.42 ((^[X6 : $i > $i > $o] : (! [X8,X9] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))) = msymmetric)),
% 0.24/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric)).
% 0.24/0.42 thf(f126,plain,(
% 0.24/0.42 ((msymmetric @ rel_b) = $true)),
% 0.24/0.42 inference(cnf_transformation,[],[f87])).
% 0.24/0.42 thf(f87,plain,(
% 0.24/0.42 ((msymmetric @ rel_b) = $true)),
% 0.24/0.42 inference(fool_elimination,[],[f86])).
% 0.24/0.42 thf(f86,plain,(
% 0.24/0.42 (msymmetric @ rel_b)),
% 0.24/0.42 inference(rectify,[],[f35])).
% 0.24/0.42 thf(f35,axiom,(
% 0.24/0.42 (msymmetric @ rel_b)),
% 0.24/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 0.24/0.42 thf(f182,plain,(
% 0.24/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (rel_b @ (sK2 @ X1) @ X2)) | ($false = (p @ (sK3 @ X2))) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f181])).
% 0.24/0.42 thf(f181,plain,(
% 0.24/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ($false = ((~ (rel_b @ X2 @ (sK3 @ X2))) | (p @ (sK3 @ X2)))) | ($false = (rel_b @ (sK2 @ X1) @ X2))) )),
% 0.24/0.42 inference(beta_eta_normalization,[],[f180])).
% 0.24/0.42 thf(f180,plain,(
% 0.24/0.42 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((~ (rel_b @ X2 @ Y0)) | (p @ Y0))) @ (sK3 @ X2))) | ($false = (rel_b @ (sK2 @ X1) @ X2)) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.24/0.42 inference(sigma_clausification,[],[f179])).
% 0.24/0.42 thf(f179,plain,(
% 0.24/0.42 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ X2 @ Y0)) | (p @ Y0)))) = $false) | ($false = (rel_b @ (sK2 @ X1) @ X2)) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.24/0.42 inference(not_proxy_clausification,[],[f178])).
% 0.24/0.42 thf(f178,plain,(
% 0.24/0.42 ( ! [X2 : $i,X1 : $i] : (((~ (rel_b @ (sK2 @ X1) @ X2)) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ X2 @ Y0)) | (p @ Y0)))) = $false) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.24/0.42 inference(not_proxy_clausification,[],[f177])).
% 0.24/0.42 thf(f177,plain,(
% 0.24/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ X2 @ Y0)) | (p @ Y0)))))) | ((~ (rel_b @ (sK2 @ X1) @ X2)) = $true)) )),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f176])).
% 0.24/0.42 thf(f176,plain,(
% 0.24/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ($true = ((~ (rel_b @ (sK2 @ X1) @ X2)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ X2 @ Y0)) | (p @ Y0)))))))) )),
% 0.24/0.42 inference(beta_eta_normalization,[],[f175])).
% 0.24/0.42 thf(f175,plain,(
% 0.24/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | (((^[Y0 : $i]: ((~ (rel_b @ (sK2 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1))))))) @ X2) = $true)) )),
% 0.24/0.42 inference(pi_clausification,[],[f174])).
% 0.24/0.42 thf(f174,plain,(
% 0.24/0.42 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ (sK2 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))) = $true) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.24/0.42 inference(not_proxy_clausification,[],[f171])).
% 0.24/0.42 thf(f171,plain,(
% 0.24/0.42 ( ! [X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ (sK2 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1))))))))))) )),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f170])).
% 0.24/0.42 thf(f170,plain,(
% 0.24/0.42 ( ! [X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ($false = ((~ (rel_b @ X1 @ (sK2 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ (sK2 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))))))) )),
% 0.24/0.42 inference(beta_eta_normalization,[],[f169])).
% 0.24/0.42 thf(f169,plain,(
% 0.24/0.42 ( ! [X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | (((^[Y0 : $i]: ((~ (rel_b @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2))))))))))) @ (sK2 @ X1)) = $false)) )),
% 0.24/0.42 inference(sigma_clausification,[],[f168])).
% 0.24/0.42 thf(f168,plain,(
% 0.24/0.42 ( ! [X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2)))))))))))) = $false)) )),
% 0.24/0.42 inference(not_proxy_clausification,[],[f167])).
% 0.24/0.42 thf(f167,plain,(
% 0.24/0.42 ( ! [X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2))))))))))))))) )),
% 0.24/0.42 inference(not_proxy_clausification,[],[f166])).
% 0.24/0.42 thf(f166,plain,(
% 0.24/0.42 ( ! [X1 : $i] : (($true = (~ (rel_b @ sK1 @ X1))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2))))))))))))))) )),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f165])).
% 0.24/0.42 thf(f165,plain,(
% 0.24/0.42 ( ! [X1 : $i] : (($true = ((~ (rel_b @ sK1 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2)))))))))))))))) )),
% 0.24/0.42 inference(beta_eta_normalization,[],[f164])).
% 0.24/0.42 thf(f164,plain,(
% 0.24/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3))))))))))))))) @ X1) = $true)) )),
% 0.24/0.42 inference(pi_clausification,[],[f163])).
% 0.24/0.42 thf(f163,plain,(
% 0.24/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3)))))))))))))))))),
% 0.24/0.42 inference(not_proxy_clausification,[],[f162])).
% 0.24/0.42 thf(f162,plain,(
% 0.24/0.42 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3))))))))))))))))))),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f160])).
% 0.24/0.42 thf(f160,plain,(
% 0.24/0.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (p @ Y3))))))))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1))))))))))),
% 0.24/0.42 inference(beta_eta_normalization,[],[f159])).
% 0.24/0.42 thf(f159,plain,(
% 0.24/0.42 ($false = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (p @ Y4))))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2)))))))))) @ sK1))),
% 0.24/0.42 inference(sigma_clausification,[],[f158])).
% 0.24/0.42 thf(f158,plain,(
% 0.24/0.42 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (p @ Y4))))))))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2))))))))))) != $true)),
% 0.24/0.42 inference(boolean_simplification,[],[f157])).
% 0.24/0.42 thf(f157,plain,(
% 0.24/0.42 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_b @ Y3 @ Y4)) | (p @ Y4))))))))))))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (p @ Y2))))))))))))))),
% 0.24/0.42 inference(beta_eta_normalization,[],[f154])).
% 0.24/0.42 thf(f154,plain,(
% 0.24/0.42 ($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 > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p)))))))),
% 0.24/0.42 inference(definition_unfolding,[],[f122,f116,f145,f153,f135,f153,f135,f153,f135])).
% 0.24/0.42 thf(f135,plain,(
% 0.24/0.42 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.24/0.42 inference(cnf_transformation,[],[f77])).
% 0.24/0.42 thf(f77,plain,(
% 0.24/0.42 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.24/0.42 inference(fool_elimination,[],[f76])).
% 0.24/0.42 thf(f76,plain,(
% 0.24/0.42 (mbox_b = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_b @ X1 @ X2)))))),
% 0.24/0.42 inference(rectify,[],[f32])).
% 0.24/0.42 thf(f32,axiom,(
% 0.24/0.42 (mbox_b = (^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_b @ X2 @ X7)))))),
% 0.24/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_b)).
% 0.24/0.42 thf(f153,plain,(
% 0.24/0.42 (mdia_b = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_b @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.24/0.42 inference(definition_unfolding,[],[f139,f125,f135,f125])).
% 0.24/0.42 thf(f125,plain,(
% 0.24/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.24/0.42 inference(cnf_transformation,[],[f91])).
% 0.24/0.42 thf(f91,plain,(
% 0.24/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.24/0.42 inference(fool_elimination,[],[f90])).
% 0.24/0.42 thf(f90,plain,(
% 0.24/0.42 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.24/0.42 inference(rectify,[],[f3])).
% 0.24/0.42 thf(f3,axiom,(
% 0.24/0.42 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.24/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.24/0.42 thf(f139,plain,(
% 0.24/0.42 (mdia_b = (^[Y0 : $i > $o]: (mnot @ (mbox_b @ (mnot @ Y0)))))),
% 0.24/0.42 inference(cnf_transformation,[],[f50])).
% 0.24/0.42 thf(f50,plain,(
% 0.24/0.42 (mdia_b = (^[Y0 : $i > $o]: (mnot @ (mbox_b @ (mnot @ Y0)))))),
% 0.24/0.42 inference(fool_elimination,[],[f49])).
% 0.24/0.42 thf(f49,plain,(
% 0.24/0.42 ((^[X0 : $i > $o] : (mnot @ (mbox_b @ (mnot @ X0)))) = mdia_b)),
% 0.24/0.42 inference(rectify,[],[f33])).
% 0.24/0.42 thf(f33,axiom,(
% 0.24/0.42 ((^[X3 : $i > $o] : (mnot @ (mbox_b @ (mnot @ X3)))) = mdia_b)),
% 0.24/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_b)).
% 0.24/0.42 thf(f145,plain,(
% 0.24/0.42 (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)))))),
% 0.24/0.42 inference(definition_unfolding,[],[f113,f134,f125])).
% 0.24/0.42 thf(f134,plain,(
% 0.24/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.24/0.42 inference(cnf_transformation,[],[f104])).
% 0.24/0.42 thf(f104,plain,(
% 0.24/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.24/0.42 inference(fool_elimination,[],[f103])).
% 0.24/0.42 thf(f103,plain,(
% 0.24/0.42 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.24/0.42 inference(rectify,[],[f4])).
% 0.24/0.42 thf(f4,axiom,(
% 0.24/0.42 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.24/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.24/0.42 thf(f113,plain,(
% 0.24/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.24/0.42 inference(cnf_transformation,[],[f59])).
% 0.24/0.42 thf(f59,plain,(
% 0.24/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.24/0.42 inference(fool_elimination,[],[f58])).
% 0.24/0.42 thf(f58,plain,(
% 0.24/0.42 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.24/0.42 inference(rectify,[],[f6])).
% 0.24/0.42 thf(f6,axiom,(
% 0.24/0.42 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.24/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.24/0.42 thf(f116,plain,(
% 0.24/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.24/0.42 inference(cnf_transformation,[],[f63])).
% 0.24/0.42 thf(f63,plain,(
% 0.24/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.24/0.42 inference(fool_elimination,[],[f62])).
% 0.24/0.42 thf(f62,plain,(
% 0.24/0.42 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.24/0.42 inference(rectify,[],[f28])).
% 0.24/0.42 thf(f28,axiom,(
% 0.24/0.42 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.24/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.24/0.42 thf(f122,plain,(
% 0.24/0.42 ((mvalid @ (mimplies @ (mdia_b @ (mbox_b @ p)) @ (mdia_b @ (mbox_b @ (mdia_b @ (mbox_b @ p)))))) != $true)),
% 0.24/0.42 inference(cnf_transformation,[],[f107])).
% 0.24/0.42 thf(f107,plain,(
% 0.24/0.42 ((mvalid @ (mimplies @ (mdia_b @ (mbox_b @ p)) @ (mdia_b @ (mbox_b @ (mdia_b @ (mbox_b @ p)))))) != $true)),
% 0.24/0.42 inference(flattening,[],[f75])).
% 0.24/0.42 thf(f75,plain,(
% 0.24/0.42 ~((mvalid @ (mimplies @ (mdia_b @ (mbox_b @ p)) @ (mdia_b @ (mbox_b @ (mdia_b @ (mbox_b @ p)))))) = $true)),
% 0.24/0.42 inference(fool_elimination,[],[f74])).
% 0.24/0.42 thf(f74,plain,(
% 0.24/0.42 ~(mvalid @ (mimplies @ (mdia_b @ (mbox_b @ p)) @ (mdia_b @ (mbox_b @ (mdia_b @ (mbox_b @ p))))))),
% 0.24/0.42 inference(rectify,[],[f37])).
% 0.24/0.42 thf(f37,negated_conjecture,(
% 0.24/0.42 ~(mvalid @ (mimplies @ (mdia_b @ (mbox_b @ p)) @ (mdia_b @ (mbox_b @ (mdia_b @ (mbox_b @ p))))))),
% 0.24/0.42 inference(negated_conjecture,[],[f36])).
% 0.24/0.42 thf(f36,conjecture,(
% 0.24/0.42 (mvalid @ (mimplies @ (mdia_b @ (mbox_b @ p)) @ (mdia_b @ (mbox_b @ (mdia_b @ (mbox_b @ p))))))),
% 0.24/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.24/0.42 thf(f173,plain,(
% 0.24/0.42 ( ! [X1 : $i] : (($true = (rel_b @ X1 @ (sK2 @ X1))) | ($false = (rel_b @ sK1 @ X1))) )),
% 0.24/0.42 inference(not_proxy_clausification,[],[f172])).
% 0.24/0.42 thf(f172,plain,(
% 0.24/0.42 ( ! [X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ($false = (~ (rel_b @ X1 @ (sK2 @ X1))))) )),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f170])).
% 0.24/0.42 thf(f189,plain,(
% 0.24/0.42 ((rel_b @ sK1 @ sK4) = $true)),
% 0.24/0.42 inference(not_proxy_clausification,[],[f188])).
% 0.24/0.42 thf(f188,plain,(
% 0.24/0.42 ((~ (rel_b @ sK1 @ sK4)) = $false)),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f186])).
% 0.24/0.42 thf(f186,plain,(
% 0.24/0.42 ($false = ((~ (rel_b @ sK1 @ sK4)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK4 @ Y0)) | (p @ Y0)))))))),
% 0.24/0.42 inference(beta_eta_normalization,[],[f185])).
% 0.24/0.42 thf(f185,plain,(
% 0.24/0.42 ($false = ((^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1))))))) @ sK4))),
% 0.24/0.42 inference(sigma_clausification,[],[f161])).
% 0.24/0.42 thf(f161,plain,(
% 0.24/0.42 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))))),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f160])).
% 0.24/0.42 thf(f360,plain,(
% 0.24/0.42 ($true = (p @ (sK3 @ sK4))) | ~spl0_6),
% 0.24/0.42 inference(avatar_component_clause,[],[f358])).
% 0.24/0.42 thf(f358,plain,(
% 0.24/0.42 spl0_6 <=> ($true = (p @ (sK3 @ sK4)))),
% 0.24/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.24/0.42 thf(f377,plain,(
% 0.24/0.42 spl0_2 | ~spl0_5),
% 0.24/0.42 inference(avatar_contradiction_clause,[],[f376])).
% 0.24/0.42 thf(f376,plain,(
% 0.24/0.42 $false | (spl0_2 | ~spl0_5)),
% 0.24/0.42 inference(subsumption_resolution,[],[f370,f235])).
% 0.24/0.42 thf(f235,plain,(
% 0.24/0.42 ($false != (rel_b @ sK1 @ sK4)) | spl0_2),
% 0.24/0.42 inference(avatar_component_clause,[],[f234])).
% 0.24/0.42 thf(f234,plain,(
% 0.24/0.42 spl0_2 <=> ($false = (rel_b @ sK1 @ sK4))),
% 0.24/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.24/0.42 thf(f370,plain,(
% 0.24/0.42 ($false = (rel_b @ sK1 @ sK4)) | ~spl0_5),
% 0.24/0.42 inference(trivial_inequality_removal,[],[f369])).
% 0.24/0.42 thf(f369,plain,(
% 0.24/0.42 ($false = $true) | ($false = (rel_b @ sK1 @ sK4)) | ~spl0_5),
% 0.24/0.42 inference(duplicate_literal_removal,[],[f364])).
% 0.24/0.42 thf(f364,plain,(
% 0.24/0.42 ($false = $true) | ($false = (rel_b @ sK1 @ sK4)) | ($false = (rel_b @ sK1 @ sK4)) | ~spl0_5),
% 0.24/0.42 inference(superposition,[],[f356,f173])).
% 0.24/0.42 thf(f356,plain,(
% 0.24/0.42 ( ! [X0 : $i] : (($false = (rel_b @ sK4 @ (sK2 @ X0))) | ($false = (rel_b @ sK1 @ X0))) ) | ~spl0_5),
% 0.24/0.42 inference(avatar_component_clause,[],[f355])).
% 0.24/0.42 thf(f355,plain,(
% 0.24/0.42 spl0_5 <=> ! [X0] : (($false = (rel_b @ sK4 @ (sK2 @ X0))) | ($false = (rel_b @ sK1 @ X0)))),
% 0.24/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.24/0.42 thf(f362,plain,(
% 0.24/0.42 spl0_5 | spl0_6),
% 0.24/0.42 inference(avatar_split_clause,[],[f340,f358,f355])).
% 0.24/0.42 thf(f340,plain,(
% 0.24/0.42 ( ! [X0 : $i] : (($false = (rel_b @ sK1 @ X0)) | ($true = (p @ (sK3 @ sK4))) | ($false = (rel_b @ sK4 @ (sK2 @ X0)))) )),
% 0.24/0.42 inference(trivial_inequality_removal,[],[f336])).
% 0.24/0.42 thf(f336,plain,(
% 0.24/0.42 ( ! [X0 : $i] : (($false = $true) | ($false = (rel_b @ sK4 @ (sK2 @ X0))) | ($false = (rel_b @ sK1 @ X0)) | ($true = (p @ (sK3 @ sK4)))) )),
% 0.24/0.42 inference(superposition,[],[f194,f316])).
% 0.24/0.42 thf(f316,plain,(
% 0.24/0.42 ( ! [X0 : $i,X1 : $i] : (($true = (rel_b @ X1 @ (sK3 @ X1))) | ($false = (rel_b @ sK1 @ X0)) | ($false = (rel_b @ X1 @ (sK2 @ X0)))) )),
% 0.24/0.42 inference(trivial_inequality_removal,[],[f309])).
% 0.24/0.42 thf(f309,plain,(
% 0.24/0.42 ( ! [X0 : $i,X1 : $i] : (($false = (rel_b @ X1 @ (sK2 @ X0))) | ($true = (rel_b @ X1 @ (sK3 @ X1))) | ($false = (rel_b @ sK1 @ X0)) | ($false = $true)) )),
% 0.24/0.42 inference(superposition,[],[f200,f184])).
% 0.24/0.42 thf(f184,plain,(
% 0.24/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (rel_b @ (sK2 @ X1) @ X2)) | ($false = (rel_b @ sK1 @ X1)) | ((rel_b @ X2 @ (sK3 @ X2)) = $true)) )),
% 0.24/0.42 inference(not_proxy_clausification,[],[f183])).
% 0.24/0.42 thf(f183,plain,(
% 0.24/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (rel_b @ sK1 @ X1)) | ($false = (~ (rel_b @ X2 @ (sK3 @ X2)))) | ($false = (rel_b @ (sK2 @ X1) @ X2))) )),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f181])).
% 0.24/0.42 thf(f194,plain,(
% 0.24/0.42 ( ! [X1 : $i] : (($false = (rel_b @ sK4 @ X1)) | ((p @ X1) = $true)) )),
% 0.24/0.42 inference(not_proxy_clausification,[],[f193])).
% 0.24/0.42 thf(f193,plain,(
% 0.24/0.42 ( ! [X1 : $i] : (((p @ X1) = $true) | ((~ (rel_b @ sK4 @ X1)) = $true)) )),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f192])).
% 0.24/0.42 thf(f192,plain,(
% 0.24/0.42 ( ! [X1 : $i] : ((((~ (rel_b @ sK4 @ X1)) | (p @ X1)) = $true)) )),
% 0.24/0.42 inference(beta_eta_normalization,[],[f191])).
% 0.24/0.42 thf(f191,plain,(
% 0.24/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_b @ sK4 @ Y0)) | (p @ Y0))) @ X1))) )),
% 0.24/0.42 inference(pi_clausification,[],[f190])).
% 0.24/0.42 thf(f190,plain,(
% 0.24/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK4 @ Y0)) | (p @ Y0)))))),
% 0.24/0.42 inference(not_proxy_clausification,[],[f187])).
% 0.24/0.42 thf(f187,plain,(
% 0.24/0.42 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK4 @ Y0)) | (p @ Y0))))))),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f186])).
% 0.24/0.42 thf(f247,plain,(
% 0.24/0.42 ~spl0_2),
% 0.24/0.42 inference(avatar_contradiction_clause,[],[f246])).
% 0.24/0.42 thf(f246,plain,(
% 0.24/0.42 $false | ~spl0_2),
% 0.24/0.42 inference(trivial_inequality_removal,[],[f241])).
% 0.24/0.42 thf(f241,plain,(
% 0.24/0.42 ($false = $true) | ~spl0_2),
% 0.24/0.42 inference(superposition,[],[f189,f236])).
% 0.24/0.42 thf(f236,plain,(
% 0.24/0.42 ($false = (rel_b @ sK1 @ sK4)) | ~spl0_2),
% 0.24/0.42 inference(avatar_component_clause,[],[f234])).
% 0.24/0.42 % SZS output end Proof for theBenchmark
% 0.24/0.42 % (23823)------------------------------
% 0.24/0.42 % (23823)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.42 % (23823)Termination reason: Refutation
% 0.24/0.42
% 0.24/0.42 % (23823)Memory used [KB]: 5884
% 0.24/0.42 % (23823)Time elapsed: 0.026 s
% 0.24/0.42 % (23823)Instructions burned: 31 (million)
% 0.24/0.42 % (23823)------------------------------
% 0.24/0.42 % (23823)------------------------------
% 0.24/0.42 % (23822)Success in time 0.038 s
% 0.24/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------