TSTP Solution File: SYO566^7 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO566^7 : 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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:06:15 EDT 2024
% Result : Theorem 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO566^7 : TPTP v8.2.0. Released v5.5.0.
% 0.07/0.14 % 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
% 0.15/0.35 % Computer : n026.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 20 08:44:08 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 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
% 0.15/0.39 % (17521)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.39 % (17519)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.39 % (17523)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.15/0.39 % (17521)Instruction limit reached!
% 0.15/0.39 % (17521)------------------------------
% 0.15/0.39 % (17521)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (17521)Termination reason: Unknown
% 0.15/0.39 % (17521)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (17521)Memory used [KB]: 1023
% 0.15/0.39 % (17521)Time elapsed: 0.004 s
% 0.15/0.39 % (17521)Instructions burned: 3 (million)
% 0.15/0.39 % (17521)------------------------------
% 0.15/0.39 % (17521)------------------------------
% 0.15/0.39 % (17520)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.15/0.39 % (17518)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.39 % (17519)Instruction limit reached!
% 0.15/0.39 % (17519)------------------------------
% 0.15/0.39 % (17519)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (17519)Termination reason: Unknown
% 0.15/0.39 % (17519)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (17522)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.39 % (17519)Memory used [KB]: 1023
% 0.15/0.39 % (17519)Time elapsed: 0.005 s
% 0.15/0.39 % (17519)Instructions burned: 4 (million)
% 0.15/0.39 % (17519)------------------------------
% 0.15/0.39 % (17519)------------------------------
% 0.15/0.39 % (17524)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.39 % (17525)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.39 % (17522)Instruction limit reached!
% 0.15/0.39 % (17522)------------------------------
% 0.15/0.39 % (17522)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (17522)Termination reason: Unknown
% 0.15/0.39 % (17522)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (17522)Memory used [KB]: 1023
% 0.15/0.39 % (17522)Time elapsed: 0.004 s
% 0.15/0.39 % (17522)Instructions burned: 2 (million)
% 0.15/0.39 % (17522)------------------------------
% 0.15/0.39 % (17522)------------------------------
% 0.15/0.40 % (17525)Instruction limit reached!
% 0.15/0.40 % (17525)------------------------------
% 0.15/0.40 % (17525)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (17525)Termination reason: Unknown
% 0.15/0.40 % (17525)Termination phase: shuffling
% 0.15/0.40
% 0.15/0.40 % (17525)Memory used [KB]: 1023
% 0.15/0.40 % (17525)Time elapsed: 0.005 s
% 0.15/0.40 % (17525)Instructions burned: 3 (million)
% 0.15/0.40 % (17525)------------------------------
% 0.15/0.40 % (17525)------------------------------
% 0.15/0.40 % (17523)Refutation not found, incomplete strategy
% 0.15/0.40 % (17523)------------------------------
% 0.15/0.40 % (17523)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (17523)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.40
% 0.15/0.40
% 0.15/0.40 % (17523)Memory used [KB]: 5628
% 0.15/0.40 % (17523)Time elapsed: 0.015 s
% 0.15/0.40 % (17523)Instructions burned: 13 (million)
% 0.15/0.40 % (17523)------------------------------
% 0.15/0.40 % (17523)------------------------------
% 0.15/0.41 % (17518)First to succeed.
% 0.15/0.41 % (17524)Instruction limit reached!
% 0.15/0.41 % (17524)------------------------------
% 0.15/0.41 % (17524)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (17524)Termination reason: Unknown
% 0.15/0.41 % (17524)Termination phase: Saturation
% 0.15/0.41
% 0.15/0.41 % (17524)Memory used [KB]: 5756
% 0.15/0.41 % (17524)Time elapsed: 0.020 s
% 0.15/0.41 % (17524)Instructions burned: 18 (million)
% 0.15/0.41 % (17524)------------------------------
% 0.15/0.41 % (17524)------------------------------
% 0.21/0.41 % (17520)Also succeeded, but the first one will report.
% 0.21/0.41 % (17527)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)
% 0.21/0.42 % (17518)Refutation found. Thanks to Tanya!
% 0.21/0.42 % SZS status Theorem for theBenchmark
% 0.21/0.42 % SZS output start Proof for theBenchmark
% 0.21/0.42 thf(type_def_5, type, mu: $tType).
% 0.21/0.42 thf(func_def_0, type, mu: $tType).
% 0.21/0.42 thf(func_def_1, type, qmltpeq: mu > mu > $i > $o).
% 0.21/0.42 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_8, type, mtrue: $i > $o).
% 0.21/0.42 thf(func_def_9, type, mfalse: $i > $o).
% 0.21/0.42 thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_16, type, exists_in_world: mu > $i > $o).
% 0.21/0.42 thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_22, type, mserial: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_30, type, mvalid: ($i > $o) > $o).
% 0.21/0.42 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.21/0.42 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.21/0.42 thf(func_def_33, type, minvalid: ($i > $o) > $o).
% 0.21/0.42 thf(func_def_34, type, rel_s4: $i > $i > $o).
% 0.21/0.42 thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_37, type, g: mu > $i > $o).
% 0.21/0.42 thf(func_def_38, type, f: mu > $i > $o).
% 0.21/0.42 thf(func_def_54, type, sK0: $i > mu).
% 0.21/0.42 thf(func_def_57, type, sK3: mu).
% 0.21/0.42 thf(f249,plain,(
% 0.21/0.42 $false),
% 0.21/0.42 inference(avatar_sat_refutation,[],[f222,f228,f238,f247])).
% 0.21/0.42 thf(f247,plain,(
% 0.21/0.42 ~spl1_1),
% 0.21/0.42 inference(avatar_contradiction_clause,[],[f246])).
% 0.21/0.42 thf(f246,plain,(
% 0.21/0.42 $false | ~spl1_1),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f239])).
% 0.21/0.42 thf(f239,plain,(
% 0.21/0.42 ($true = $false) | ~spl1_1),
% 0.21/0.42 inference(superposition,[],[f212,f168])).
% 0.21/0.42 thf(f168,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (rel_s4 @ X1 @ X1))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f167])).
% 0.21/0.42 thf(f167,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1))) )),
% 0.21/0.42 inference(pi_clausification,[],[f166])).
% 0.21/0.42 thf(f166,plain,(
% 0.21/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))),
% 0.21/0.42 inference(beta_eta_normalization,[],[f164])).
% 0.21/0.42 thf(f164,plain,(
% 0.21/0.42 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4))),
% 0.21/0.42 inference(definition_unfolding,[],[f130,f116])).
% 0.21/0.42 thf(f116,plain,(
% 0.21/0.42 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.21/0.42 inference(cnf_transformation,[],[f41])).
% 0.21/0.42 thf(f41,plain,(
% 0.21/0.42 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.21/0.42 inference(fool_elimination,[],[f40])).
% 0.21/0.42 thf(f40,plain,(
% 0.21/0.42 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))))),
% 0.21/0.42 inference(rectify,[],[f18])).
% 0.21/0.42 thf(f18,axiom,(
% 0.21/0.42 (mreflexive = (^[X5 : $i > $i > $o] : (! [X8] : (X5 @ X8 @ X8))))),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
% 0.21/0.42 thf(f130,plain,(
% 0.21/0.42 ((mreflexive @ rel_s4) = $true)),
% 0.21/0.42 inference(cnf_transformation,[],[f90])).
% 0.21/0.42 thf(f90,plain,(
% 0.21/0.42 ((mreflexive @ rel_s4) = $true)),
% 0.21/0.42 inference(fool_elimination,[],[f89])).
% 0.21/0.42 thf(f89,plain,(
% 0.21/0.42 (mreflexive @ rel_s4)),
% 0.21/0.42 inference(rectify,[],[f34])).
% 0.21/0.42 thf(f34,axiom,(
% 0.21/0.42 (mreflexive @ rel_s4)),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 0.21/0.42 thf(f212,plain,(
% 0.21/0.42 ((rel_s4 @ sK2 @ sK2) = $false) | ~spl1_1),
% 0.21/0.42 inference(avatar_component_clause,[],[f210])).
% 0.21/0.42 thf(f210,plain,(
% 0.21/0.42 spl1_1 <=> ((rel_s4 @ sK2 @ sK2) = $false)),
% 0.21/0.42 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.21/0.42 thf(f238,plain,(
% 0.21/0.42 ~spl1_3),
% 0.21/0.42 inference(avatar_contradiction_clause,[],[f237])).
% 0.21/0.42 thf(f237,plain,(
% 0.21/0.42 $false | ~spl1_3),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f229])).
% 0.21/0.42 thf(f229,plain,(
% 0.21/0.42 ($true = $false) | ~spl1_3),
% 0.21/0.42 inference(superposition,[],[f220,f202])).
% 0.21/0.42 thf(f202,plain,(
% 0.21/0.42 ($true = (exists_in_world @ sK3 @ sK2))),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f200])).
% 0.21/0.42 thf(f200,plain,(
% 0.21/0.42 ($false = ((exists_in_world @ sK3 @ sK2) => (g @ sK3 @ sK2)))),
% 0.21/0.42 inference(beta_eta_normalization,[],[f199])).
% 0.21/0.42 thf(f199,plain,(
% 0.21/0.42 (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (g @ Y0 @ sK2))) @ sK3) = $false)),
% 0.21/0.42 inference(sigma_clausification,[],[f193])).
% 0.21/0.42 thf(f193,plain,(
% 0.21/0.42 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (g @ Y0 @ sK2)))) = $false)),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f181])).
% 0.21/0.42 thf(f181,plain,(
% 0.21/0.42 (((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (f @ Y0 @ sK2))))) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (g @ Y0 @ sK2))))) = $false)),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f180])).
% 0.21/0.42 thf(f180,plain,(
% 0.21/0.42 (((~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (f @ Y1 @ Y0)) | (g @ Y1 @ Y0))))) | (~ (rel_s4 @ sK2 @ Y0)))))) | ((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (f @ Y0 @ sK2))))) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (g @ Y0 @ sK2)))))) = $false)),
% 0.21/0.42 inference(beta_eta_normalization,[],[f179])).
% 0.21/0.42 thf(f179,plain,(
% 0.21/0.42 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (f @ Y2 @ Y1)) | (g @ Y2 @ Y1))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | ((~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (f @ Y1 @ Y0))))) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (g @ Y1 @ Y0))))))) @ sK2) = $false)),
% 0.21/0.42 inference(sigma_clausification,[],[f178])).
% 0.21/0.42 thf(f178,plain,(
% 0.21/0.42 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ (f @ Y2 @ Y1)) | (g @ Y2 @ Y1))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | ((~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (f @ Y1 @ Y0))))) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (g @ Y1 @ Y0)))))))))),
% 0.21/0.42 inference(beta_eta_normalization,[],[f165])).
% 0.21/0.42 thf(f165,plain,(
% 0.21/0.42 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[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 > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) | (Y4 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ (f @ Y0) @ (g @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ 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]: (f @ Y0))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: (g @ Y0)))))))),
% 0.21/0.42 inference(definition_unfolding,[],[f135,f143,f155,f136,f134,f155,f155,f134,f134])).
% 0.21/0.42 thf(f134,plain,(
% 0.21/0.42 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f45])).
% 0.21/0.42 thf(f45,plain,(
% 0.21/0.42 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.21/0.42 inference(fool_elimination,[],[f44])).
% 0.21/0.42 thf(f44,plain,(
% 0.21/0.42 (mforall_ind = (^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : ((exists_in_world @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 0.21/0.42 inference(rectify,[],[f15])).
% 0.21/0.42 thf(f15,axiom,(
% 0.21/0.42 (mforall_ind = (^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : ((exists_in_world @ X0 @ X2) => (X3 @ X0 @ X2)))))),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)).
% 0.21/0.42 thf(f136,plain,(
% 0.21/0.42 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f96])).
% 0.21/0.42 thf(f96,plain,(
% 0.21/0.42 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.21/0.42 inference(fool_elimination,[],[f95])).
% 0.21/0.42 thf(f95,plain,(
% 0.21/0.42 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s4 @ X1 @ X2) | (X0 @ X2)))) = mbox_s4)),
% 0.21/0.42 inference(rectify,[],[f32])).
% 0.21/0.42 thf(f32,axiom,(
% 0.21/0.42 ((^[X3 : $i > $o, X2 : $i] : (! [X6] : (~(rel_s4 @ X2 @ X6) | (X3 @ X6)))) = mbox_s4)),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4)).
% 0.21/0.42 thf(f155,plain,(
% 0.21/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.21/0.42 inference(definition_unfolding,[],[f146,f145,f132])).
% 0.21/0.42 thf(f132,plain,(
% 0.21/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f84])).
% 0.21/0.42 thf(f84,plain,(
% 0.21/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.42 inference(fool_elimination,[],[f83])).
% 0.21/0.42 thf(f83,plain,(
% 0.21/0.42 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.21/0.42 inference(rectify,[],[f2])).
% 0.21/0.42 thf(f2,axiom,(
% 0.21/0.42 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.21/0.42 thf(f145,plain,(
% 0.21/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f71])).
% 0.21/0.42 thf(f71,plain,(
% 0.21/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.42 inference(fool_elimination,[],[f70])).
% 0.21/0.42 thf(f70,plain,(
% 0.21/0.42 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.21/0.42 inference(rectify,[],[f3])).
% 0.21/0.42 thf(f3,axiom,(
% 0.21/0.42 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.21/0.42 thf(f146,plain,(
% 0.21/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.42 inference(cnf_transformation,[],[f77])).
% 0.21/0.42 thf(f77,plain,(
% 0.21/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.42 inference(fool_elimination,[],[f76])).
% 0.21/0.42 thf(f76,plain,(
% 0.21/0.42 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.21/0.42 inference(rectify,[],[f9])).
% 0.21/0.42 thf(f9,axiom,(
% 0.21/0.42 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.21/0.42 thf(f143,plain,(
% 0.21/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.42 inference(cnf_transformation,[],[f86])).
% 0.21/0.42 thf(f86,plain,(
% 0.21/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.42 inference(fool_elimination,[],[f85])).
% 0.21/0.42 thf(f85,plain,(
% 0.21/0.42 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.21/0.42 inference(rectify,[],[f28])).
% 0.21/0.42 thf(f28,axiom,(
% 0.21/0.42 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.21/0.42 thf(f135,plain,(
% 0.21/0.42 ($true != (mvalid @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mimplies @ (f @ Y0) @ (g @ Y0))))) @ (mimplies @ (mforall_ind @ (^[Y0 : mu]: (f @ Y0))) @ (mforall_ind @ (^[Y0 : mu]: (g @ Y0)))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f111])).
% 0.21/0.42 thf(f111,plain,(
% 0.21/0.42 ($true != (mvalid @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mimplies @ (f @ Y0) @ (g @ Y0))))) @ (mimplies @ (mforall_ind @ (^[Y0 : mu]: (f @ Y0))) @ (mforall_ind @ (^[Y0 : mu]: (g @ Y0)))))))),
% 0.21/0.42 inference(flattening,[],[f43])).
% 0.21/0.42 thf(f43,plain,(
% 0.21/0.42 ~($true = (mvalid @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mimplies @ (f @ Y0) @ (g @ Y0))))) @ (mimplies @ (mforall_ind @ (^[Y0 : mu]: (f @ Y0))) @ (mforall_ind @ (^[Y0 : mu]: (g @ Y0)))))))),
% 0.21/0.42 inference(fool_elimination,[],[f42])).
% 0.21/0.42 thf(f42,plain,(
% 0.21/0.42 ~(mvalid @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mimplies @ (f @ X0) @ (g @ X0))))) @ (mimplies @ (mforall_ind @ (^[X1 : mu] : (f @ X1))) @ (mforall_ind @ (^[X2 : mu] : (g @ X2))))))),
% 0.21/0.42 inference(rectify,[],[f38])).
% 0.21/0.42 thf(f38,negated_conjecture,(
% 0.21/0.42 ~(mvalid @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mimplies @ (f @ X0) @ (g @ X0))))) @ (mimplies @ (mforall_ind @ (^[X0 : mu] : (f @ X0))) @ (mforall_ind @ (^[X0 : mu] : (g @ X0))))))),
% 0.21/0.42 inference(negated_conjecture,[],[f37])).
% 0.21/0.42 thf(f37,conjecture,(
% 0.21/0.42 (mvalid @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mimplies @ (f @ X0) @ (g @ X0))))) @ (mimplies @ (mforall_ind @ (^[X0 : mu] : (f @ X0))) @ (mforall_ind @ (^[X0 : mu] : (g @ X0))))))),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 0.21/0.42 thf(f220,plain,(
% 0.21/0.42 ((exists_in_world @ sK3 @ sK2) = $false) | ~spl1_3),
% 0.21/0.42 inference(avatar_component_clause,[],[f218])).
% 0.21/0.42 thf(f218,plain,(
% 0.21/0.42 spl1_3 <=> ((exists_in_world @ sK3 @ sK2) = $false)),
% 0.21/0.42 introduced(avatar_definition,[new_symbols(naming,[spl1_3])])).
% 0.21/0.42 thf(f228,plain,(
% 0.21/0.42 spl1_3 | ~spl1_2),
% 0.21/0.42 inference(avatar_split_clause,[],[f225,f214,f218])).
% 0.21/0.42 thf(f214,plain,(
% 0.21/0.42 spl1_2 <=> ($false = (f @ sK3 @ sK2))),
% 0.21/0.42 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.21/0.42 thf(f225,plain,(
% 0.21/0.42 ((exists_in_world @ sK3 @ sK2) = $false) | ~spl1_2),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f224])).
% 0.21/0.42 thf(f224,plain,(
% 0.21/0.42 ((exists_in_world @ sK3 @ sK2) = $false) | ($true = $false) | ~spl1_2),
% 0.21/0.42 inference(superposition,[],[f198,f216])).
% 0.21/0.42 thf(f216,plain,(
% 0.21/0.42 ($false = (f @ sK3 @ sK2)) | ~spl1_2),
% 0.21/0.42 inference(avatar_component_clause,[],[f214])).
% 0.21/0.42 thf(f198,plain,(
% 0.21/0.42 ( ! [X1 : mu] : (((f @ X1 @ sK2) = $true) | ((exists_in_world @ X1 @ sK2) = $false)) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f197])).
% 0.21/0.42 thf(f197,plain,(
% 0.21/0.42 ( ! [X1 : mu] : (($true = ((exists_in_world @ X1 @ sK2) => (f @ X1 @ sK2)))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f196])).
% 0.21/0.42 thf(f196,plain,(
% 0.21/0.42 ( ! [X1 : mu] : (($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (f @ Y0 @ sK2))) @ X1))) )),
% 0.21/0.42 inference(pi_clausification,[],[f195])).
% 0.21/0.42 thf(f195,plain,(
% 0.21/0.42 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (f @ Y0 @ sK2)))) = $true)),
% 0.21/0.42 inference(not_proxy_clausification,[],[f194])).
% 0.21/0.42 thf(f194,plain,(
% 0.21/0.42 ((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (f @ Y0 @ sK2))))) = $false)),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f181])).
% 0.21/0.42 thf(f222,plain,(
% 0.21/0.42 spl1_2 | spl1_3 | spl1_1),
% 0.21/0.42 inference(avatar_split_clause,[],[f207,f210,f218,f214])).
% 0.21/0.42 thf(f207,plain,(
% 0.21/0.42 ((exists_in_world @ sK3 @ sK2) = $false) | ($false = (f @ sK3 @ sK2)) | ((rel_s4 @ sK2 @ sK2) = $false)),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f205])).
% 0.21/0.42 thf(f205,plain,(
% 0.21/0.42 ((rel_s4 @ sK2 @ sK2) = $false) | ($false = (f @ sK3 @ sK2)) | ($true = $false) | ((exists_in_world @ sK3 @ sK2) = $false)),
% 0.21/0.42 inference(superposition,[],[f192,f201])).
% 0.21/0.42 thf(f201,plain,(
% 0.21/0.42 ($false = (g @ sK3 @ sK2))),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f200])).
% 0.21/0.42 thf(f192,plain,(
% 0.21/0.42 ( ! [X2 : mu,X1 : $i] : (($true = (g @ X2 @ X1)) | ($false = (f @ X2 @ X1)) | ((rel_s4 @ sK2 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f191])).
% 0.21/0.42 thf(f191,plain,(
% 0.21/0.42 ( ! [X2 : mu,X1 : $i] : (($true = (~ (f @ X2 @ X1))) | ($true = (g @ X2 @ X1)) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK2 @ X1) = $false)) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f190])).
% 0.21/0.42 thf(f190,plain,(
% 0.21/0.42 ( ! [X2 : mu,X1 : $i] : (((rel_s4 @ sK2 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ($true = ((~ (f @ X2 @ X1)) | (g @ X2 @ X1)))) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f189])).
% 0.21/0.42 thf(f189,plain,(
% 0.21/0.42 ( ! [X2 : mu,X1 : $i] : (((rel_s4 @ sK2 @ X1) = $false) | ($true = ((exists_in_world @ X2 @ X1) => ((~ (f @ X2 @ X1)) | (g @ X2 @ X1))))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f188])).
% 0.21/0.42 thf(f188,plain,(
% 0.21/0.42 ( ! [X2 : mu,X1 : $i] : (((rel_s4 @ sK2 @ X1) = $false) | ($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((~ (f @ Y0 @ X1)) | (g @ Y0 @ X1)))) @ X2))) )),
% 0.21/0.42 inference(pi_clausification,[],[f187])).
% 0.21/0.42 thf(f187,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (((rel_s4 @ sK2 @ X1) = $false) | ($true = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((~ (f @ Y0 @ X1)) | (g @ Y0 @ X1))))))) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f186])).
% 0.21/0.42 thf(f186,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (((~ (rel_s4 @ sK2 @ X1)) = $true) | ($true = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((~ (f @ Y0 @ X1)) | (g @ Y0 @ X1))))))) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f185])).
% 0.21/0.42 thf(f185,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((~ (f @ Y0 @ X1)) | (g @ Y0 @ X1))))) | (~ (rel_s4 @ sK2 @ X1))))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f184])).
% 0.21/0.42 thf(f184,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (f @ Y1 @ Y0)) | (g @ Y1 @ Y0))))) | (~ (rel_s4 @ sK2 @ Y0)))) @ X1))) )),
% 0.21/0.42 inference(pi_clausification,[],[f183])).
% 0.21/0.42 thf(f183,plain,(
% 0.21/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (f @ Y1 @ Y0)) | (g @ Y1 @ Y0))))) | (~ (rel_s4 @ sK2 @ Y0))))))),
% 0.21/0.42 inference(not_proxy_clausification,[],[f182])).
% 0.21/0.42 thf(f182,plain,(
% 0.21/0.42 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ (f @ Y1 @ Y0)) | (g @ Y1 @ Y0))))) | (~ (rel_s4 @ sK2 @ Y0)))))))),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f180])).
% 0.21/0.42 % SZS output end Proof for theBenchmark
% 0.21/0.42 % (17518)------------------------------
% 0.21/0.42 % (17518)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (17518)Termination reason: Refutation
% 0.21/0.42
% 0.21/0.42 % (17518)Memory used [KB]: 5756
% 0.21/0.42 % (17518)Time elapsed: 0.024 s
% 0.21/0.42 % (17518)Instructions burned: 16 (million)
% 0.21/0.42 % (17518)------------------------------
% 0.21/0.42 % (17518)------------------------------
% 0.21/0.42 % (17517)Success in time 0.048 s
% 0.21/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------