TSTP Solution File: SYO568^7 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO568^7 : TPTP v8.2.0. Released v5.5.0.
% 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 : n012.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 09:06:16 EDT 2024
% Result : Theorem 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO568^7 : TPTP v8.2.0. Released v5.5.0.
% 0.03/0.14 % 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 : n012.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 10:38:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 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
% 0.20/0.38 % (22353)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.38 % (22355)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)
% 0.20/0.38 % (22354)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)
% 0.20/0.38 % (22356)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.38 % (22358)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)
% 0.20/0.38 % (22359)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.38 % (22356)Instruction limit reached!
% 0.20/0.38 % (22356)------------------------------
% 0.20/0.38 % (22356)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (22356)Termination reason: Unknown
% 0.20/0.38 % (22356)Termination phase: shuffling
% 0.20/0.38
% 0.20/0.38 % (22356)Memory used [KB]: 1023
% 0.20/0.38 % (22356)Time elapsed: 0.004 s
% 0.20/0.38 % (22356)Instructions burned: 3 (million)
% 0.20/0.38 % (22356)------------------------------
% 0.20/0.38 % (22356)------------------------------
% 0.20/0.38 % (22354)Instruction limit reached!
% 0.20/0.38 % (22354)------------------------------
% 0.20/0.38 % (22354)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (22354)Termination reason: Unknown
% 0.20/0.38 % (22354)Termination phase: Property scanning
% 0.20/0.38
% 0.20/0.38 % (22354)Memory used [KB]: 1023
% 0.20/0.38 % (22354)Time elapsed: 0.005 s
% 0.20/0.38 % (22354)Instructions burned: 5 (million)
% 0.20/0.38 % (22354)------------------------------
% 0.20/0.38 % (22354)------------------------------
% 0.20/0.38 % (22357)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)
% 0.20/0.38 % (22357)Instruction limit reached!
% 0.20/0.38 % (22357)------------------------------
% 0.20/0.38 % (22357)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (22357)Termination reason: Unknown
% 0.20/0.38 % (22357)Termination phase: shuffling
% 0.20/0.38
% 0.20/0.38 % (22357)Memory used [KB]: 1023
% 0.20/0.38 % (22357)Time elapsed: 0.003 s
% 0.20/0.38 % (22357)Instructions burned: 2 (million)
% 0.20/0.38 % (22357)------------------------------
% 0.20/0.38 % (22357)------------------------------
% 0.20/0.39 % (22358)Refutation not found, incomplete strategy
% 0.20/0.39 % (22358)------------------------------
% 0.20/0.39 % (22358)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (22358)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.39
% 0.20/0.39
% 0.20/0.39 % (22358)Memory used [KB]: 5628
% 0.20/0.39 % (22358)Time elapsed: 0.009 s
% 0.20/0.39 % (22358)Instructions burned: 11 (million)
% 0.20/0.39 % (22358)------------------------------
% 0.20/0.39 % (22358)------------------------------
% 0.20/0.39 % (22359)Instruction limit reached!
% 0.20/0.39 % (22359)------------------------------
% 0.20/0.39 % (22359)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (22359)Termination reason: Unknown
% 0.20/0.39 % (22359)Termination phase: Saturation
% 0.20/0.39
% 0.20/0.39 % (22359)Memory used [KB]: 5756
% 0.20/0.39 % (22359)Time elapsed: 0.013 s
% 0.20/0.39 % (22359)Instructions burned: 19 (million)
% 0.20/0.39 % (22359)------------------------------
% 0.20/0.39 % (22359)------------------------------
% 0.20/0.39 % (22360)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)
% 0.20/0.39 % (22360)Instruction limit reached!
% 0.20/0.39 % (22360)------------------------------
% 0.20/0.39 % (22360)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (22360)Termination reason: Unknown
% 0.20/0.39 % (22360)Termination phase: shuffling
% 0.20/0.39
% 0.20/0.39 % (22360)Memory used [KB]: 1023
% 0.20/0.39 % (22360)Time elapsed: 0.003 s
% 0.20/0.39 % (22360)Instructions burned: 3 (million)
% 0.20/0.39 % (22360)------------------------------
% 0.20/0.39 % (22360)------------------------------
% 0.20/0.40 % (22355)Instruction limit reached!
% 0.20/0.40 % (22355)------------------------------
% 0.20/0.40 % (22355)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (22355)Termination reason: Unknown
% 0.20/0.40 % (22355)Termination phase: Saturation
% 0.20/0.40
% 0.20/0.40 % (22355)Memory used [KB]: 5756
% 0.20/0.40 % (22355)Time elapsed: 0.019 s
% 0.20/0.40 % (22355)Instructions burned: 27 (million)
% 0.20/0.40 % (22355)------------------------------
% 0.20/0.40 % (22355)------------------------------
% 0.20/0.40 % (22353)First to succeed.
% 0.20/0.40 % (22368)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)
% 0.20/0.40 % (22367)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)
% 0.20/0.40 % (22370)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)
% 0.20/0.40 % (22370)Instruction limit reached!
% 0.20/0.40 % (22370)------------------------------
% 0.20/0.40 % (22370)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (22370)Termination reason: Unknown
% 0.20/0.40 % (22370)Termination phase: shuffling
% 0.20/0.40
% 0.20/0.40 % (22370)Memory used [KB]: 1023
% 0.20/0.40 % (22370)Time elapsed: 0.005 s
% 0.20/0.40 % (22370)Instructions burned: 3 (million)
% 0.20/0.40 % (22370)------------------------------
% 0.20/0.40 % (22370)------------------------------
% 0.20/0.41 % (22353)Refutation found. Thanks to Tanya!
% 0.20/0.41 % SZS status Theorem for theBenchmark
% 0.20/0.41 % SZS output start Proof for theBenchmark
% 0.20/0.41 thf(type_def_5, type, mu: $tType).
% 0.20/0.41 thf(func_def_0, type, mu: $tType).
% 0.20/0.41 thf(func_def_1, type, qmltpeq: mu > mu > $i > $o).
% 0.20/0.41 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_8, type, mtrue: $i > $o).
% 0.20/0.41 thf(func_def_9, type, mfalse: $i > $o).
% 0.20/0.41 thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_16, type, exists_in_world: mu > $i > $o).
% 0.20/0.41 thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o).
% 0.20/0.41 thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o).
% 0.20/0.41 thf(func_def_22, type, mserial: ($i > $i > $o) > $o).
% 0.20/0.41 thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o).
% 0.20/0.41 thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o).
% 0.20/0.41 thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.20/0.41 thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o).
% 0.20/0.41 thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.20/0.41 thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.20/0.41 thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.20/0.41 thf(func_def_30, type, mvalid: ($i > $o) > $o).
% 0.20/0.41 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.20/0.41 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.20/0.41 thf(func_def_33, type, minvalid: ($i > $o) > $o).
% 0.20/0.41 thf(func_def_34, type, rel_s4: $i > $i > $o).
% 0.20/0.41 thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o).
% 0.20/0.41 thf(func_def_37, type, f: mu > $i > $o).
% 0.20/0.41 thf(func_def_38, type, a: mu).
% 0.20/0.41 thf(func_def_54, type, sK0: $i > mu).
% 0.20/0.41 thf(f399,plain,(
% 0.20/0.41 $false),
% 0.20/0.41 inference(avatar_sat_refutation,[],[f248,f253,f259,f265,f286,f296,f324,f345,f364,f378,f398])).
% 0.20/0.41 thf(f398,plain,(
% 0.20/0.41 ~spl1_1 | ~spl1_3),
% 0.20/0.41 inference(avatar_contradiction_clause,[],[f397])).
% 0.20/0.41 thf(f397,plain,(
% 0.20/0.41 $false | (~spl1_1 | ~spl1_3)),
% 0.20/0.41 inference(trivial_inequality_removal,[],[f391])).
% 0.20/0.41 thf(f391,plain,(
% 0.20/0.41 ($true = $false) | (~spl1_1 | ~spl1_3)),
% 0.20/0.41 inference(superposition,[],[f240,f388])).
% 0.20/0.41 thf(f388,plain,(
% 0.20/0.41 ((rel_s4 @ sK3 @ sK3) = $false) | (~spl1_1 | ~spl1_3)),
% 0.20/0.41 inference(trivial_inequality_removal,[],[f383])).
% 0.20/0.41 thf(f383,plain,(
% 0.20/0.41 ((rel_s4 @ sK3 @ sK3) = $false) | ($true = $false) | (~spl1_1 | ~spl1_3)),
% 0.20/0.41 inference(superposition,[],[f243,f252])).
% 0.20/0.41 thf(f252,plain,(
% 0.20/0.41 ((f @ a @ sK3) = $false) | ~spl1_3),
% 0.20/0.41 inference(avatar_component_clause,[],[f250])).
% 0.20/0.41 thf(f250,plain,(
% 0.20/0.41 spl1_3 <=> ((f @ a @ sK3) = $false)),
% 0.20/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_3])])).
% 0.20/0.41 thf(f243,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = (f @ a @ X1)) | ($false = (rel_s4 @ sK3 @ X1))) ) | ~spl1_1),
% 0.20/0.41 inference(avatar_component_clause,[],[f242])).
% 0.20/0.41 thf(f242,plain,(
% 0.20/0.41 spl1_1 <=> ! [X1] : (($true = (f @ a @ X1)) | ($false = (rel_s4 @ sK3 @ X1)))),
% 0.20/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.20/0.41 thf(f240,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = (rel_s4 @ X1 @ X1))) )),
% 0.20/0.41 inference(beta_eta_normalization,[],[f239])).
% 0.20/0.41 thf(f239,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1))) )),
% 0.20/0.41 inference(pi_clausification,[],[f238])).
% 0.20/0.41 thf(f238,plain,(
% 0.20/0.41 ($true = (!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))),
% 0.20/0.41 inference(beta_eta_normalization,[],[f167])).
% 0.20/0.41 thf(f167,plain,(
% 0.20/0.41 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4) = $true)),
% 0.20/0.41 inference(definition_unfolding,[],[f130,f147])).
% 0.20/0.41 thf(f147,plain,(
% 0.20/0.41 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.20/0.41 inference(cnf_transformation,[],[f85])).
% 0.20/0.41 thf(f85,plain,(
% 0.20/0.41 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.20/0.41 inference(fool_elimination,[],[f84])).
% 0.20/0.41 thf(f84,plain,(
% 0.20/0.41 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))))),
% 0.20/0.41 inference(rectify,[],[f18])).
% 0.20/0.41 thf(f18,axiom,(
% 0.20/0.41 (mreflexive = (^[X5 : $i > $i > $o] : (! [X8] : (X5 @ X8 @ X8))))),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
% 0.20/0.41 thf(f130,plain,(
% 0.20/0.41 ((mreflexive @ rel_s4) = $true)),
% 0.20/0.41 inference(cnf_transformation,[],[f50])).
% 0.20/0.41 thf(f50,plain,(
% 0.20/0.41 ((mreflexive @ rel_s4) = $true)),
% 0.20/0.41 inference(fool_elimination,[],[f49])).
% 0.20/0.41 thf(f49,plain,(
% 0.20/0.41 (mreflexive @ rel_s4)),
% 0.20/0.41 inference(rectify,[],[f34])).
% 0.20/0.41 thf(f34,axiom,(
% 0.20/0.41 (mreflexive @ rel_s4)),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 0.20/0.41 thf(f378,plain,(
% 0.20/0.41 ~spl1_9),
% 0.20/0.41 inference(avatar_contradiction_clause,[],[f377])).
% 0.20/0.41 thf(f377,plain,(
% 0.20/0.41 $false | ~spl1_9),
% 0.20/0.41 inference(trivial_inequality_removal,[],[f369])).
% 0.20/0.41 thf(f369,plain,(
% 0.20/0.41 ($true = $false) | ~spl1_9),
% 0.20/0.41 inference(superposition,[],[f361,f179])).
% 0.20/0.41 thf(f179,plain,(
% 0.20/0.41 ($true = (rel_s4 @ sK2 @ sK3))),
% 0.20/0.41 inference(not_proxy_clausification,[],[f178])).
% 0.20/0.41 thf(f178,plain,(
% 0.20/0.41 ($false = (~ (rel_s4 @ sK2 @ sK3)))),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f176])).
% 0.20/0.41 thf(f176,plain,(
% 0.20/0.41 ($false = ((~ (rel_s4 @ sK2 @ sK3)) | (~ ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0)))) | (~ (f @ a @ sK3)))) | (~ ((f @ a @ sK3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0)))))))))))),
% 0.20/0.41 inference(beta_eta_normalization,[],[f175])).
% 0.20/0.41 thf(f175,plain,(
% 0.20/0.41 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (f @ a @ Y1)))) | (~ (f @ a @ Y0)))) | (~ ((f @ a @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (f @ a @ Y1))))))))))) @ sK3))),
% 0.20/0.41 inference(sigma_clausification,[],[f174])).
% 0.20/0.41 thf(f174,plain,(
% 0.20/0.41 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (f @ a @ Y1)))) | (~ (f @ a @ Y0)))) | (~ ((f @ a @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (f @ a @ Y1)))))))))))) = $false)),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f172])).
% 0.20/0.41 thf(f172,plain,(
% 0.20/0.41 (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (f @ a @ Y1)))) | (~ (f @ a @ Y0)))) | (~ ((f @ a @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (f @ a @ Y1)))))))))))) | (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK2 @ Y1)) | (~ (f @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK2 @ Y1)) | (f @ Y0 @ Y1)))))))))) = $false)),
% 0.20/0.41 inference(beta_eta_normalization,[],[f171])).
% 0.20/0.41 thf(f171,plain,(
% 0.20/0.41 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ ((~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (f @ a @ Y2)))) | (~ (f @ a @ Y1)))) | (~ ((f @ a @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (f @ a @ Y2)))))))))))) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (~ (f @ Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (f @ Y1 @ Y2))))))))))) @ sK2))),
% 0.20/0.41 inference(sigma_clausification,[],[f170])).
% 0.20/0.41 thf(f170,plain,(
% 0.20/0.41 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ ((~ ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (f @ a @ Y2)))) | (~ (f @ a @ Y1)))) | (~ ((f @ a @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (f @ a @ Y2)))))))))))) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (~ (f @ Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (f @ Y1 @ Y2)))))))))))) != $true)),
% 0.20/0.41 inference(beta_eta_normalization,[],[f168])).
% 0.20/0.41 thf(f168,plain,(
% 0.20/0.41 ($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 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((Y2 @ Y3) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ (f @ Y0)) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ (f @ Y0)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ (f @ a)) @ (f @ a))))))),
% 0.20/0.41 inference(definition_unfolding,[],[f137,f153,f159,f129,f120,f152,f152,f142,f152,f161,f152])).
% 0.20/0.41 thf(f161,plain,(
% 0.20/0.41 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.20/0.41 inference(definition_unfolding,[],[f122,f158,f159,f159])).
% 0.20/0.41 thf(f158,plain,(
% 0.20/0.41 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.20/0.41 inference(definition_unfolding,[],[f150,f142,f120,f142,f142])).
% 0.20/0.41 thf(f150,plain,(
% 0.20/0.41 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.41 inference(cnf_transformation,[],[f101])).
% 0.20/0.41 thf(f101,plain,(
% 0.20/0.41 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.41 inference(fool_elimination,[],[f100])).
% 0.20/0.41 thf(f100,plain,(
% 0.20/0.41 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.20/0.41 inference(rectify,[],[f8])).
% 0.20/0.41 thf(f8,axiom,(
% 0.20/0.41 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.20/0.41 thf(f122,plain,(
% 0.20/0.41 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.20/0.41 inference(cnf_transformation,[],[f109])).
% 0.20/0.41 thf(f109,plain,(
% 0.20/0.41 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.20/0.41 inference(fool_elimination,[],[f108])).
% 0.20/0.41 thf(f108,plain,(
% 0.20/0.41 ((^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))) = mequiv)),
% 0.20/0.41 inference(rectify,[],[f11])).
% 0.20/0.41 thf(f11,axiom,(
% 0.20/0.41 ((^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))) = mequiv)),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
% 0.20/0.41 thf(f142,plain,(
% 0.20/0.41 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.41 inference(cnf_transformation,[],[f66])).
% 0.20/0.41 thf(f66,plain,(
% 0.20/0.41 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.41 inference(fool_elimination,[],[f65])).
% 0.20/0.41 thf(f65,plain,(
% 0.20/0.41 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.20/0.41 inference(rectify,[],[f2])).
% 0.20/0.41 thf(f2,axiom,(
% 0.20/0.41 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.20/0.41 thf(f152,plain,(
% 0.20/0.41 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.41 inference(cnf_transformation,[],[f64])).
% 0.20/0.41 thf(f64,plain,(
% 0.20/0.41 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.41 inference(fool_elimination,[],[f63])).
% 0.20/0.41 thf(f63,plain,(
% 0.20/0.41 (mbox_s4 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s4 @ X1 @ X2)))))),
% 0.20/0.41 inference(rectify,[],[f32])).
% 0.20/0.41 thf(f32,axiom,(
% 0.20/0.41 (mbox_s4 = (^[X3 : $i > $o, X2 : $i] : (! [X6] : ((X3 @ X6) | ~(rel_s4 @ X2 @ X6)))))),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4)).
% 0.20/0.41 thf(f120,plain,(
% 0.20/0.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.20/0.41 inference(cnf_transformation,[],[f68])).
% 0.20/0.41 thf(f68,plain,(
% 0.20/0.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.20/0.41 inference(fool_elimination,[],[f67])).
% 0.20/0.41 thf(f67,plain,(
% 0.20/0.41 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.20/0.41 inference(rectify,[],[f3])).
% 0.20/0.41 thf(f3,axiom,(
% 0.20/0.41 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.20/0.41 thf(f129,plain,(
% 0.20/0.41 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.20/0.41 inference(cnf_transformation,[],[f48])).
% 0.20/0.41 thf(f48,plain,(
% 0.20/0.41 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.20/0.41 inference(fool_elimination,[],[f47])).
% 0.20/0.41 thf(f47,plain,(
% 0.20/0.41 (mforall_ind = (^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : ((exists_in_world @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 0.20/0.41 inference(rectify,[],[f15])).
% 0.20/0.41 thf(f15,axiom,(
% 0.20/0.41 (mforall_ind = (^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : ((exists_in_world @ X0 @ X2) => (X3 @ X0 @ X2)))))),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)).
% 0.20/0.41 thf(f159,plain,(
% 0.20/0.41 (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)))))),
% 0.20/0.41 inference(definition_unfolding,[],[f146,f120,f142])).
% 0.20/0.41 thf(f146,plain,(
% 0.20/0.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.41 inference(cnf_transformation,[],[f60])).
% 0.20/0.41 thf(f60,plain,(
% 0.20/0.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.41 inference(fool_elimination,[],[f59])).
% 0.20/0.41 thf(f59,plain,(
% 0.20/0.41 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.20/0.41 inference(rectify,[],[f9])).
% 0.20/0.41 thf(f9,axiom,(
% 0.20/0.41 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.20/0.41 thf(f153,plain,(
% 0.20/0.41 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.41 inference(cnf_transformation,[],[f113])).
% 0.20/0.41 thf(f113,plain,(
% 0.20/0.41 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.41 inference(fool_elimination,[],[f112])).
% 0.20/0.41 thf(f112,plain,(
% 0.20/0.41 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.20/0.41 inference(rectify,[],[f28])).
% 0.20/0.41 thf(f28,axiom,(
% 0.20/0.41 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.20/0.41 thf(f137,plain,(
% 0.20/0.41 ($true != (mvalid @ (mimplies @ (mforall_ind @ (^[Y0 : mu]: (mor @ (mbox_s4 @ (f @ Y0)) @ (mbox_s4 @ (mnot @ (f @ Y0)))))) @ (mbox_s4 @ (mequiv @ (mbox_s4 @ (f @ a)) @ (f @ a))))))),
% 0.20/0.41 inference(cnf_transformation,[],[f114])).
% 0.20/0.41 thf(f114,plain,(
% 0.20/0.41 ($true != (mvalid @ (mimplies @ (mforall_ind @ (^[Y0 : mu]: (mor @ (mbox_s4 @ (f @ Y0)) @ (mbox_s4 @ (mnot @ (f @ Y0)))))) @ (mbox_s4 @ (mequiv @ (mbox_s4 @ (f @ a)) @ (f @ a))))))),
% 0.20/0.41 inference(flattening,[],[f58])).
% 0.20/0.41 thf(f58,plain,(
% 0.20/0.41 ~($true = (mvalid @ (mimplies @ (mforall_ind @ (^[Y0 : mu]: (mor @ (mbox_s4 @ (f @ Y0)) @ (mbox_s4 @ (mnot @ (f @ Y0)))))) @ (mbox_s4 @ (mequiv @ (mbox_s4 @ (f @ a)) @ (f @ a))))))),
% 0.20/0.41 inference(fool_elimination,[],[f57])).
% 0.20/0.41 thf(f57,plain,(
% 0.20/0.41 ~(mvalid @ (mimplies @ (mforall_ind @ (^[X0 : mu] : (mor @ (mbox_s4 @ (f @ X0)) @ (mbox_s4 @ (mnot @ (f @ X0)))))) @ (mbox_s4 @ (mequiv @ (mbox_s4 @ (f @ a)) @ (f @ a)))))),
% 0.20/0.41 inference(rectify,[],[f39])).
% 0.20/0.41 thf(f39,negated_conjecture,(
% 0.20/0.41 ~(mvalid @ (mimplies @ (mforall_ind @ (^[X0 : mu] : (mor @ (mbox_s4 @ (f @ X0)) @ (mbox_s4 @ (mnot @ (f @ X0)))))) @ (mbox_s4 @ (mequiv @ (mbox_s4 @ (f @ a)) @ (f @ a)))))),
% 0.20/0.41 inference(negated_conjecture,[],[f38])).
% 0.20/0.41 thf(f38,conjecture,(
% 0.20/0.41 (mvalid @ (mimplies @ (mforall_ind @ (^[X0 : mu] : (mor @ (mbox_s4 @ (f @ X0)) @ (mbox_s4 @ (mnot @ (f @ X0)))))) @ (mbox_s4 @ (mequiv @ (mbox_s4 @ (f @ a)) @ (f @ a)))))),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 0.20/0.41 thf(f361,plain,(
% 0.20/0.41 ($false = (rel_s4 @ sK2 @ sK3)) | ~spl1_9),
% 0.20/0.41 inference(avatar_component_clause,[],[f359])).
% 0.20/0.41 thf(f359,plain,(
% 0.20/0.41 spl1_9 <=> ($false = (rel_s4 @ sK2 @ sK3))),
% 0.20/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_9])])).
% 0.20/0.41 thf(f364,plain,(
% 0.20/0.41 spl1_9 | spl1_8 | ~spl1_3 | spl1_6),
% 0.20/0.41 inference(avatar_split_clause,[],[f363,f275,f250,f283,f359])).
% 0.20/0.41 thf(f283,plain,(
% 0.20/0.41 spl1_8 <=> ! [X0] : (($false = (f @ a @ X0)) | ((rel_s4 @ sK2 @ X0) = $false))),
% 0.20/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_8])])).
% 0.20/0.41 thf(f275,plain,(
% 0.20/0.41 spl1_6 <=> ($false = (exists_in_world @ a @ sK2))),
% 0.20/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_6])])).
% 0.20/0.41 thf(f363,plain,(
% 0.20/0.41 ( ! [X0 : $i] : (($false = (rel_s4 @ sK2 @ sK3)) | ($false = (f @ a @ X0)) | ((rel_s4 @ sK2 @ X0) = $false)) ) | (~spl1_3 | spl1_6)),
% 0.20/0.41 inference(subsumption_resolution,[],[f355,f276])).
% 0.20/0.41 thf(f276,plain,(
% 0.20/0.41 ($false != (exists_in_world @ a @ sK2)) | spl1_6),
% 0.20/0.41 inference(avatar_component_clause,[],[f275])).
% 0.20/0.41 thf(f355,plain,(
% 0.20/0.41 ( ! [X0 : $i] : (($false = (rel_s4 @ sK2 @ sK3)) | ($false = (f @ a @ X0)) | ($false = (exists_in_world @ a @ sK2)) | ((rel_s4 @ sK2 @ X0) = $false)) ) | ~spl1_3),
% 0.20/0.41 inference(trivial_inequality_removal,[],[f350])).
% 0.20/0.41 thf(f350,plain,(
% 0.20/0.41 ( ! [X0 : $i] : (($false = (rel_s4 @ sK2 @ sK3)) | ((rel_s4 @ sK2 @ X0) = $false) | ($false = (f @ a @ X0)) | ($true = $false) | ($false = (exists_in_world @ a @ sK2))) ) | ~spl1_3),
% 0.20/0.41 inference(superposition,[],[f228,f252])).
% 0.20/0.41 thf(f228,plain,(
% 0.20/0.41 ( ! [X2 : $i,X3 : $i,X1 : mu] : (($true = (f @ X1 @ X3)) | ((exists_in_world @ X1 @ sK2) = $false) | ($false = (rel_s4 @ sK2 @ X3)) | ($false = (f @ X1 @ X2)) | ($false = (rel_s4 @ sK2 @ X2))) )),
% 0.20/0.41 inference(not_proxy_clausification,[],[f227])).
% 0.20/0.41 thf(f227,plain,(
% 0.20/0.41 ( ! [X2 : $i,X3 : $i,X1 : mu] : (($false = (rel_s4 @ sK2 @ X2)) | ($false = (f @ X1 @ X2)) | ($true = (f @ X1 @ X3)) | ((~ (rel_s4 @ sK2 @ X3)) = $true) | ((exists_in_world @ X1 @ sK2) = $false)) )),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f226])).
% 0.20/0.41 thf(f226,plain,(
% 0.20/0.41 ( ! [X2 : $i,X3 : $i,X1 : mu] : (($true = ((~ (rel_s4 @ sK2 @ X3)) | (f @ X1 @ X3))) | ((exists_in_world @ X1 @ sK2) = $false) | ($false = (f @ X1 @ X2)) | ($false = (rel_s4 @ sK2 @ X2))) )),
% 0.20/0.41 inference(beta_eta_normalization,[],[f225])).
% 0.20/0.41 thf(f225,plain,(
% 0.20/0.41 ( ! [X2 : $i,X3 : $i,X1 : mu] : (($false = (rel_s4 @ sK2 @ X2)) | ($true = ((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (f @ X1 @ Y0))) @ X3)) | ($false = (f @ X1 @ X2)) | ((exists_in_world @ X1 @ sK2) = $false)) )),
% 0.20/0.41 inference(pi_clausification,[],[f224])).
% 0.20/0.41 thf(f224,plain,(
% 0.20/0.41 ( ! [X2 : $i,X1 : mu] : (($false = (rel_s4 @ sK2 @ X2)) | ((exists_in_world @ X1 @ sK2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (f @ X1 @ Y0))))) | ($false = (f @ X1 @ X2))) )),
% 0.20/0.41 inference(not_proxy_clausification,[],[f223])).
% 0.20/0.41 thf(f223,plain,(
% 0.20/0.41 ( ! [X2 : $i,X1 : mu] : (((~ (f @ X1 @ X2)) = $true) | ((exists_in_world @ X1 @ sK2) = $false) | ($false = (rel_s4 @ sK2 @ X2)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (f @ X1 @ Y0)))))) )),
% 0.20/0.41 inference(not_proxy_clausification,[],[f222])).
% 0.20/0.41 thf(f222,plain,(
% 0.20/0.41 ( ! [X2 : $i,X1 : mu] : (((exists_in_world @ X1 @ sK2) = $false) | ($true = (~ (rel_s4 @ sK2 @ X2))) | ((~ (f @ X1 @ X2)) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (f @ X1 @ Y0)))))) )),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f221])).
% 0.20/0.41 thf(f221,plain,(
% 0.20/0.41 ( ! [X2 : $i,X1 : mu] : (((exists_in_world @ X1 @ sK2) = $false) | (((~ (rel_s4 @ sK2 @ X2)) | (~ (f @ X1 @ X2))) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (f @ X1 @ Y0)))))) )),
% 0.20/0.41 inference(beta_eta_normalization,[],[f220])).
% 0.20/0.41 thf(f220,plain,(
% 0.20/0.41 ( ! [X2 : $i,X1 : mu] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (f @ X1 @ Y0))))) | (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ (f @ X1 @ Y0)))) @ X2) = $true) | ((exists_in_world @ X1 @ sK2) = $false)) )),
% 0.20/0.41 inference(pi_clausification,[],[f219])).
% 0.20/0.41 thf(f219,plain,(
% 0.20/0.41 ( ! [X1 : mu] : (((exists_in_world @ X1 @ sK2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ (f @ X1 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (f @ X1 @ Y0)))))) )),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f218])).
% 0.20/0.41 thf(f218,plain,(
% 0.20/0.41 ( ! [X1 : mu] : ((((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ (f @ X1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (f @ X1 @ Y0))))) = $true) | ((exists_in_world @ X1 @ sK2) = $false)) )),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f217])).
% 0.20/0.41 thf(f217,plain,(
% 0.20/0.41 ( ! [X1 : mu] : ((((exists_in_world @ X1 @ sK2) => ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ (f @ X1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (f @ X1 @ Y0)))))) = $true)) )),
% 0.20/0.41 inference(beta_eta_normalization,[],[f216])).
% 0.20/0.41 thf(f216,plain,(
% 0.20/0.41 ( ! [X1 : mu] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK2 @ Y1)) | (~ (f @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK2 @ Y1)) | (f @ Y0 @ Y1))))))) @ X1) = $true)) )),
% 0.20/0.41 inference(pi_clausification,[],[f215])).
% 0.20/0.41 thf(f215,plain,(
% 0.20/0.41 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK2 @ Y1)) | (~ (f @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK2 @ Y1)) | (f @ Y0 @ Y1)))))))) = $true)),
% 0.20/0.41 inference(not_proxy_clausification,[],[f173])).
% 0.20/0.41 thf(f173,plain,(
% 0.20/0.41 ((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK2 @ Y1)) | (~ (f @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK2 @ Y1)) | (f @ Y0 @ Y1))))))))) = $false)),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f172])).
% 0.20/0.41 thf(f345,plain,(
% 0.20/0.41 ~spl1_2 | ~spl1_8),
% 0.20/0.41 inference(avatar_contradiction_clause,[],[f344])).
% 0.20/0.41 thf(f344,plain,(
% 0.20/0.41 $false | (~spl1_2 | ~spl1_8)),
% 0.20/0.41 inference(trivial_inequality_removal,[],[f337])).
% 0.20/0.41 thf(f337,plain,(
% 0.20/0.41 ($true = $false) | (~spl1_2 | ~spl1_8)),
% 0.20/0.41 inference(superposition,[],[f334,f179])).
% 0.20/0.41 thf(f334,plain,(
% 0.20/0.41 ($false = (rel_s4 @ sK2 @ sK3)) | (~spl1_2 | ~spl1_8)),
% 0.20/0.41 inference(trivial_inequality_removal,[],[f328])).
% 0.20/0.41 thf(f328,plain,(
% 0.20/0.41 ($true = $false) | ($false = (rel_s4 @ sK2 @ sK3)) | (~spl1_2 | ~spl1_8)),
% 0.20/0.41 inference(superposition,[],[f284,f247])).
% 0.20/0.41 thf(f247,plain,(
% 0.20/0.41 ($true = (f @ a @ sK3)) | ~spl1_2),
% 0.20/0.41 inference(avatar_component_clause,[],[f245])).
% 0.20/0.41 thf(f245,plain,(
% 0.20/0.41 spl1_2 <=> ($true = (f @ a @ sK3))),
% 0.20/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.20/0.41 thf(f284,plain,(
% 0.20/0.41 ( ! [X0 : $i] : (($false = (f @ a @ X0)) | ((rel_s4 @ sK2 @ X0) = $false)) ) | ~spl1_8),
% 0.20/0.41 inference(avatar_component_clause,[],[f283])).
% 0.20/0.41 thf(f324,plain,(
% 0.20/0.41 ~spl1_5 | ~spl1_7),
% 0.20/0.41 inference(avatar_contradiction_clause,[],[f323])).
% 0.20/0.41 thf(f323,plain,(
% 0.20/0.41 $false | (~spl1_5 | ~spl1_7)),
% 0.20/0.41 inference(trivial_inequality_removal,[],[f318])).
% 0.20/0.41 thf(f318,plain,(
% 0.20/0.41 ($true = $false) | (~spl1_5 | ~spl1_7)),
% 0.20/0.41 inference(superposition,[],[f263,f314])).
% 0.20/0.41 thf(f314,plain,(
% 0.20/0.41 ($false = (rel_s4 @ sK3 @ sK4)) | ~spl1_7),
% 0.20/0.41 inference(trivial_inequality_removal,[],[f309])).
% 0.20/0.41 thf(f309,plain,(
% 0.20/0.41 ($false = (rel_s4 @ sK3 @ sK4)) | ($true = $false) | ~spl1_7),
% 0.20/0.41 inference(superposition,[],[f179,f303])).
% 0.20/0.41 thf(f303,plain,(
% 0.20/0.41 ( ! [X0 : $i] : (((rel_s4 @ sK2 @ X0) = $false) | ((rel_s4 @ X0 @ sK4) = $false)) ) | ~spl1_7),
% 0.20/0.41 inference(trivial_inequality_removal,[],[f300])).
% 0.20/0.41 thf(f300,plain,(
% 0.20/0.41 ( ! [X0 : $i] : (((rel_s4 @ sK2 @ X0) = $false) | ($true = $false) | ((rel_s4 @ X0 @ sK4) = $false)) ) | ~spl1_7),
% 0.20/0.41 inference(superposition,[],[f281,f237])).
% 0.20/0.41 thf(f237,plain,(
% 0.20/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (rel_s4 @ X1 @ X2)) | ($false = (rel_s4 @ X1 @ X3)) | ((rel_s4 @ X3 @ X2) = $false)) )),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f236])).
% 0.20/0.41 thf(f236,plain,(
% 0.20/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (rel_s4 @ X1 @ X2)) | ($false = ((rel_s4 @ X3 @ X2) & (rel_s4 @ X1 @ X3)))) )),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f235])).
% 0.20/0.41 thf(f235,plain,(
% 0.20/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((rel_s4 @ X3 @ X2) & (rel_s4 @ X1 @ X3)) => (rel_s4 @ X1 @ X2)))) )),
% 0.20/0.41 inference(beta_eta_normalization,[],[f234])).
% 0.20/0.41 thf(f234,plain,(
% 0.20/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((rel_s4 @ Y0 @ X2) & (rel_s4 @ X1 @ Y0)) => (rel_s4 @ X1 @ X2))) @ X3))) )),
% 0.20/0.41 inference(pi_clausification,[],[f233])).
% 0.20/0.41 thf(f233,plain,(
% 0.20/0.41 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s4 @ Y0 @ X2) & (rel_s4 @ X1 @ Y0)) => (rel_s4 @ X1 @ X2)))))) )),
% 0.20/0.41 inference(beta_eta_normalization,[],[f232])).
% 0.20/0.41 thf(f232,plain,(
% 0.20/0.41 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ Y1 @ Y0) & (rel_s4 @ X1 @ Y1)) => (rel_s4 @ X1 @ Y0))))) @ X2))) )),
% 0.20/0.41 inference(pi_clausification,[],[f231])).
% 0.20/0.41 thf(f231,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ Y1 @ Y0) & (rel_s4 @ X1 @ Y1)) => (rel_s4 @ X1 @ Y0)))))))) )),
% 0.20/0.41 inference(beta_eta_normalization,[],[f230])).
% 0.20/0.41 thf(f230,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y2 @ Y1) & (rel_s4 @ Y0 @ Y2)) => (rel_s4 @ Y0 @ Y1))))))) @ X1))) )),
% 0.20/0.41 inference(pi_clausification,[],[f229])).
% 0.20/0.41 thf(f229,plain,(
% 0.20/0.41 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y2 @ Y1) & (rel_s4 @ Y0 @ Y2)) => (rel_s4 @ Y0 @ Y1)))))))))),
% 0.20/0.41 inference(beta_eta_normalization,[],[f169])).
% 0.20/0.41 thf(f169,plain,(
% 0.20/0.41 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) @ rel_s4) = $true)),
% 0.20/0.41 inference(definition_unfolding,[],[f154,f128])).
% 0.20/0.41 thf(f128,plain,(
% 0.20/0.41 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.20/0.41 inference(cnf_transformation,[],[f89])).
% 0.20/0.41 thf(f89,plain,(
% 0.20/0.41 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.20/0.41 inference(fool_elimination,[],[f88])).
% 0.20/0.41 thf(f88,plain,(
% 0.20/0.41 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X3 @ X1) & (X0 @ X1 @ X2)) => (X0 @ X3 @ X2)))) = mtransitive)),
% 0.20/0.41 inference(rectify,[],[f21])).
% 0.20/0.41 thf(f21,axiom,(
% 0.20/0.41 ((^[X5 : $i > $i > $o] : (! [X9,X10,X8] : (((X5 @ X8 @ X9) & (X5 @ X9 @ X10)) => (X5 @ X8 @ X10)))) = mtransitive)),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive)).
% 0.20/0.41 thf(f154,plain,(
% 0.20/0.41 ((mtransitive @ rel_s4) = $true)),
% 0.20/0.41 inference(cnf_transformation,[],[f46])).
% 0.20/0.41 thf(f46,plain,(
% 0.20/0.41 ((mtransitive @ rel_s4) = $true)),
% 0.20/0.41 inference(fool_elimination,[],[f45])).
% 0.20/0.41 thf(f45,plain,(
% 0.20/0.41 (mtransitive @ rel_s4)),
% 0.20/0.41 inference(rectify,[],[f35])).
% 0.20/0.41 thf(f35,axiom,(
% 0.20/0.41 (mtransitive @ rel_s4)),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 0.20/0.41 thf(f281,plain,(
% 0.20/0.41 ($false = (rel_s4 @ sK2 @ sK4)) | ~spl1_7),
% 0.20/0.41 inference(avatar_component_clause,[],[f279])).
% 0.20/0.41 thf(f279,plain,(
% 0.20/0.41 spl1_7 <=> ($false = (rel_s4 @ sK2 @ sK4))),
% 0.20/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_7])])).
% 0.20/0.41 thf(f263,plain,(
% 0.20/0.41 ($true = (rel_s4 @ sK3 @ sK4)) | ~spl1_5),
% 0.20/0.41 inference(avatar_component_clause,[],[f261])).
% 0.20/0.41 thf(f261,plain,(
% 0.20/0.41 spl1_5 <=> ($true = (rel_s4 @ sK3 @ sK4))),
% 0.20/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_5])])).
% 0.20/0.41 thf(f296,plain,(
% 0.20/0.41 ~spl1_6),
% 0.20/0.41 inference(avatar_contradiction_clause,[],[f295])).
% 0.20/0.41 thf(f295,plain,(
% 0.20/0.41 $false | ~spl1_6),
% 0.20/0.41 inference(trivial_inequality_removal,[],[f287])).
% 0.20/0.41 thf(f287,plain,(
% 0.20/0.41 ($true = $false) | ~spl1_6),
% 0.20/0.41 inference(superposition,[],[f277,f140])).
% 0.20/0.41 thf(f140,plain,(
% 0.20/0.41 ( ! [X0 : $i] : (((exists_in_world @ a @ X0) = $true)) )),
% 0.20/0.41 inference(cnf_transformation,[],[f42])).
% 0.20/0.41 thf(f42,plain,(
% 0.20/0.41 ! [X0] : ((exists_in_world @ a @ X0) = $true)),
% 0.20/0.41 inference(fool_elimination,[],[f41])).
% 0.20/0.41 thf(f41,plain,(
% 0.20/0.41 ! [X0] : (exists_in_world @ a @ X0)),
% 0.20/0.41 inference(rectify,[],[f37])).
% 0.20/0.41 thf(f37,axiom,(
% 0.20/0.41 ! [X6] : (exists_in_world @ a @ X6)),
% 0.20/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_a_ax)).
% 0.20/0.41 thf(f277,plain,(
% 0.20/0.41 ($false = (exists_in_world @ a @ sK2)) | ~spl1_6),
% 0.20/0.41 inference(avatar_component_clause,[],[f275])).
% 0.20/0.41 thf(f286,plain,(
% 0.20/0.41 spl1_6 | spl1_8 | spl1_7 | ~spl1_4),
% 0.20/0.41 inference(avatar_split_clause,[],[f272,f255,f279,f283,f275])).
% 0.20/0.41 thf(f255,plain,(
% 0.20/0.41 spl1_4 <=> ($false = (f @ a @ sK4))),
% 0.20/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_4])])).
% 0.20/0.41 thf(f272,plain,(
% 0.20/0.41 ( ! [X0 : $i] : (((rel_s4 @ sK2 @ X0) = $false) | ($false = (exists_in_world @ a @ sK2)) | ($false = (rel_s4 @ sK2 @ sK4)) | ($false = (f @ a @ X0))) ) | ~spl1_4),
% 0.20/0.41 inference(trivial_inequality_removal,[],[f269])).
% 0.20/0.41 thf(f269,plain,(
% 0.20/0.41 ( ! [X0 : $i] : (($false = (f @ a @ X0)) | ($false = (rel_s4 @ sK2 @ sK4)) | ($false = (exists_in_world @ a @ sK2)) | ((rel_s4 @ sK2 @ X0) = $false) | ($true = $false)) ) | ~spl1_4),
% 0.20/0.41 inference(superposition,[],[f257,f228])).
% 0.20/0.41 thf(f257,plain,(
% 0.20/0.41 ($false = (f @ a @ sK4)) | ~spl1_4),
% 0.20/0.41 inference(avatar_component_clause,[],[f255])).
% 0.20/0.41 thf(f265,plain,(
% 0.20/0.41 spl1_3 | spl1_5),
% 0.20/0.41 inference(avatar_split_clause,[],[f192,f261,f250])).
% 0.20/0.41 thf(f192,plain,(
% 0.20/0.41 ((f @ a @ sK3) = $false) | ($true = (rel_s4 @ sK3 @ sK4))),
% 0.20/0.41 inference(not_proxy_clausification,[],[f191])).
% 0.20/0.41 thf(f191,plain,(
% 0.20/0.41 ((f @ a @ sK3) = $false) | ($false = (~ (rel_s4 @ sK3 @ sK4)))),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f189])).
% 0.20/0.41 thf(f189,plain,(
% 0.20/0.41 ($false = ((f @ a @ sK3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0))))))) | ($false = (~ (rel_s4 @ sK3 @ sK4)))),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f187])).
% 0.20/0.41 thf(f187,plain,(
% 0.20/0.41 ($false = ((~ (rel_s4 @ sK3 @ sK4)) | (f @ a @ sK4))) | ($false = ((f @ a @ sK3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0)))))))),
% 0.20/0.41 inference(not_proxy_clausification,[],[f186])).
% 0.20/0.41 thf(f186,plain,(
% 0.20/0.41 ((~ ((f @ a @ sK3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0))))))) = $true) | ($false = ((~ (rel_s4 @ sK3 @ sK4)) | (f @ a @ sK4)))),
% 0.20/0.41 inference(beta_eta_normalization,[],[f185])).
% 0.20/0.41 thf(f185,plain,(
% 0.20/0.41 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0))) @ sK4)) | ((~ ((f @ a @ sK3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0))))))) = $true)),
% 0.20/0.41 inference(sigma_clausification,[],[f184])).
% 0.20/0.41 thf(f184,plain,(
% 0.20/0.41 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0))))) | ((~ ((f @ a @ sK3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0))))))) = $true)),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f182])).
% 0.20/0.41 thf(f182,plain,(
% 0.20/0.41 (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0)))) | (~ (f @ a @ sK3))) = $false) | ((~ ((f @ a @ sK3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0))))))) = $true)),
% 0.20/0.41 inference(not_proxy_clausification,[],[f181])).
% 0.20/0.41 thf(f181,plain,(
% 0.20/0.41 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0)))) | (~ (f @ a @ sK3))))) | ((~ ((f @ a @ sK3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0))))))) = $true)),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f180])).
% 0.20/0.41 thf(f180,plain,(
% 0.20/0.41 (((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0)))) | (~ (f @ a @ sK3)))) | (~ ((f @ a @ sK3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0)))))))) = $true)),
% 0.20/0.41 inference(not_proxy_clausification,[],[f177])).
% 0.20/0.41 thf(f177,plain,(
% 0.20/0.41 ((~ ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0)))) | (~ (f @ a @ sK3)))) | (~ ((f @ a @ sK3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0))))))))) = $false)),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f176])).
% 0.20/0.41 thf(f259,plain,(
% 0.20/0.41 spl1_4 | spl1_3),
% 0.20/0.41 inference(avatar_split_clause,[],[f200,f250,f255])).
% 0.20/0.41 thf(f200,plain,(
% 0.20/0.41 ($false = (f @ a @ sK4)) | ((f @ a @ sK3) = $false)),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f188])).
% 0.20/0.41 thf(f188,plain,(
% 0.20/0.41 ($false = (f @ a @ sK4)) | ($false = ((f @ a @ sK3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0)))))))),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f187])).
% 0.20/0.41 thf(f253,plain,(
% 0.20/0.41 spl1_3 | spl1_2),
% 0.20/0.41 inference(avatar_split_clause,[],[f209,f245,f250])).
% 0.20/0.41 thf(f209,plain,(
% 0.20/0.41 ((f @ a @ sK3) = $false) | ($true = (f @ a @ sK3))),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f207])).
% 0.20/0.41 thf(f207,plain,(
% 0.20/0.41 ($true = (f @ a @ sK3)) | ($false = ((f @ a @ sK3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0)))))))),
% 0.20/0.41 inference(not_proxy_clausification,[],[f206])).
% 0.20/0.41 thf(f206,plain,(
% 0.20/0.41 ($true = (f @ a @ sK3)) | ((~ ((f @ a @ sK3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0))))))) = $true)),
% 0.20/0.41 inference(not_proxy_clausification,[],[f183])).
% 0.20/0.41 thf(f183,plain,(
% 0.20/0.41 ($false = (~ (f @ a @ sK3))) | ((~ ((f @ a @ sK3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0))))))) = $true)),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f182])).
% 0.20/0.41 thf(f248,plain,(
% 0.20/0.41 spl1_1 | spl1_2),
% 0.20/0.41 inference(avatar_split_clause,[],[f214,f245,f242])).
% 0.20/0.41 thf(f214,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = (f @ a @ X1)) | ($false = (rel_s4 @ sK3 @ X1)) | ($true = (f @ a @ sK3))) )),
% 0.20/0.41 inference(not_proxy_clausification,[],[f213])).
% 0.20/0.41 thf(f213,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (((~ (rel_s4 @ sK3 @ X1)) = $true) | ($true = (f @ a @ X1)) | ($true = (f @ a @ sK3))) )),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f212])).
% 0.20/0.41 thf(f212,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = (f @ a @ sK3)) | (((~ (rel_s4 @ sK3 @ X1)) | (f @ a @ X1)) = $true)) )),
% 0.20/0.41 inference(beta_eta_normalization,[],[f211])).
% 0.20/0.41 thf(f211,plain,(
% 0.20/0.41 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0))) @ X1)) | ($true = (f @ a @ sK3))) )),
% 0.20/0.41 inference(pi_clausification,[],[f210])).
% 0.20/0.41 thf(f210,plain,(
% 0.20/0.41 ($true = (f @ a @ sK3)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0)))))),
% 0.20/0.41 inference(not_proxy_clausification,[],[f208])).
% 0.20/0.41 thf(f208,plain,(
% 0.20/0.41 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (f @ a @ Y0)))))) | ($true = (f @ a @ sK3))),
% 0.20/0.41 inference(binary_proxy_clausification,[],[f207])).
% 0.20/0.41 % SZS output end Proof for theBenchmark
% 0.20/0.41 % (22353)------------------------------
% 0.20/0.41 % (22353)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (22353)Termination reason: Refutation
% 0.20/0.41
% 0.20/0.41 % (22353)Memory used [KB]: 5884
% 0.20/0.41 % (22353)Time elapsed: 0.026 s
% 0.20/0.41 % (22353)Instructions burned: 28 (million)
% 0.20/0.41 % (22353)------------------------------
% 0.20/0.41 % (22353)------------------------------
% 0.20/0.41 % (22350)Success in time 0.03 s
% 0.20/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------