TSTP Solution File: SET669^3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET669^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:12:44 EDT 2024
% Result : Theorem 0.11s 0.34s
% Output : Refutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SET669^3 : TPTP v8.2.0. Released v3.6.0.
% 0.09/0.11 % 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
% 0.11/0.32 % Computer : n019.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon May 20 11:09:08 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 This is a TH0_THM_EQU_NAR problem
% 0.11/0.32 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
% 0.11/0.34 % (24628)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)
% 0.11/0.34 % (24627)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.34 % (24631)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)
% 0.11/0.34 % (24632)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)
% 0.11/0.34 % (24628)Instruction limit reached!
% 0.11/0.34 % (24628)------------------------------
% 0.11/0.34 % (24628)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34 % (24628)Termination reason: Unknown
% 0.11/0.34 % (24628)Termination phase: Property scanning
% 0.11/0.34
% 0.11/0.34 % (24628)Memory used [KB]: 1023
% 0.11/0.34 % (24628)Time elapsed: 0.003 s
% 0.11/0.34 % (24628)Instructions burned: 4 (million)
% 0.11/0.34 % (24628)------------------------------
% 0.11/0.34 % (24628)------------------------------
% 0.11/0.34 % (24631)Instruction limit reached!
% 0.11/0.34 % (24631)------------------------------
% 0.11/0.34 % (24631)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34 % (24631)Termination reason: Unknown
% 0.11/0.34 % (24631)Termination phase: shuffling
% 0.11/0.34
% 0.11/0.34 % (24631)Memory used [KB]: 1023
% 0.11/0.34 % (24631)Time elapsed: 0.003 s
% 0.11/0.34 % (24631)Instructions burned: 3 (million)
% 0.11/0.34 % (24631)------------------------------
% 0.11/0.34 % (24631)------------------------------
% 0.11/0.34 % (24627)First to succeed.
% 0.11/0.34 % (24629)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)
% 0.11/0.34 % (24632)Also succeeded, but the first one will report.
% 0.11/0.34 % (24633)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.11/0.34 % (24627)Refutation found. Thanks to Tanya!
% 0.11/0.34 % SZS status Theorem for theBenchmark
% 0.11/0.34 % SZS output start Proof for theBenchmark
% 0.11/0.34 thf(func_def_0, type, in: $i > ($i > $o) > $o).
% 0.11/0.34 thf(func_def_2, type, is_a: $i > ($i > $o) > $o).
% 0.11/0.34 thf(func_def_3, type, emptyset: $i > $o).
% 0.11/0.34 thf(func_def_4, type, unord_pair: $i > $i > $i > $o).
% 0.11/0.34 thf(func_def_5, type, singleton: $i > $i > $o).
% 0.11/0.34 thf(func_def_6, type, union: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.34 thf(func_def_7, type, excl_union: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.34 thf(func_def_8, type, intersection: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.34 thf(func_def_9, type, setminus: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.34 thf(func_def_10, type, complement: ($i > $o) > $i > $o).
% 0.11/0.34 thf(func_def_11, type, disjoint: ($i > $o) > ($i > $o) > $o).
% 0.11/0.34 thf(func_def_12, type, subset: ($i > $o) > ($i > $o) > $o).
% 0.11/0.34 thf(func_def_13, type, meets: ($i > $o) > ($i > $o) > $o).
% 0.11/0.34 thf(func_def_14, type, misses: ($i > $o) > ($i > $o) > $o).
% 0.11/0.34 thf(func_def_15, type, cartesian_product: ($i > $o) > ($i > $o) > $i > $i > $o).
% 0.11/0.34 thf(func_def_16, type, pair_rel: $i > $i > $i > $i > $o).
% 0.11/0.34 thf(func_def_17, type, id_rel: ($i > $o) > $i > $i > $o).
% 0.11/0.34 thf(func_def_18, type, sub_rel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.11/0.34 thf(func_def_19, type, is_rel_on: ($i > $i > $o) > ($i > $o) > ($i > $o) > $o).
% 0.11/0.34 thf(func_def_20, type, restrict_rel_domain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.11/0.34 thf(func_def_21, type, rel_diagonal: $i > $i > $o).
% 0.11/0.34 thf(func_def_22, type, rel_composition: ($i > $i > $o) > ($i > $i > $o) > $i > $i > $o).
% 0.11/0.34 thf(func_def_23, type, reflexive: ($i > $i > $o) > $o).
% 0.11/0.34 thf(func_def_24, type, irreflexive: ($i > $i > $o) > $o).
% 0.11/0.34 thf(func_def_25, type, symmetric: ($i > $i > $o) > $o).
% 0.11/0.34 thf(func_def_26, type, transitive: ($i > $i > $o) > $o).
% 0.11/0.34 thf(func_def_27, type, equiv_rel: ($i > $i > $o) > $o).
% 0.11/0.34 thf(func_def_28, type, rel_codomain: ($i > $i > $o) > $i > $o).
% 0.11/0.34 thf(func_def_29, type, rel_domain: ($i > $i > $o) > $i > $o).
% 0.11/0.34 thf(func_def_30, type, rel_inverse: ($i > $i > $o) > $i > $i > $o).
% 0.11/0.34 thf(func_def_31, type, equiv_classes: ($i > $i > $o) > ($i > $o) > $o).
% 0.11/0.34 thf(func_def_32, type, restrict_rel_codomain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.11/0.34 thf(func_def_33, type, rel_field: ($i > $i > $o) > $i > $o).
% 0.11/0.34 thf(func_def_34, type, well_founded: ($i > $i > $o) > $o).
% 0.11/0.34 thf(func_def_35, type, upwards_well_founded: ($i > $i > $o) > $o).
% 0.11/0.34 thf(func_def_52, type, sK0: $i > $i > $o).
% 0.11/0.34 thf(func_def_55, type, ph3: !>[X0: $tType]:(X0)).
% 0.11/0.34 thf(f190,plain,(
% 0.11/0.34 $false),
% 0.11/0.34 inference(avatar_sat_refutation,[],[f173,f183,f189])).
% 0.11/0.34 thf(f189,plain,(
% 0.11/0.34 ~spl1_2),
% 0.11/0.34 inference(avatar_contradiction_clause,[],[f188])).
% 0.11/0.34 thf(f188,plain,(
% 0.11/0.34 $false | ~spl1_2),
% 0.11/0.34 inference(equality_resolution,[],[f187])).
% 0.11/0.34 thf(f187,plain,(
% 0.11/0.34 ( ! [X0 : $i] : ((sK2 != X0)) ) | ~spl1_2),
% 0.11/0.34 inference(trivial_inequality_removal,[],[f184])).
% 0.11/0.34 thf(f184,plain,(
% 0.11/0.34 ( ! [X0 : $i] : ((sK2 != X0) | ($false = $true)) ) | ~spl1_2),
% 0.11/0.34 inference(superposition,[],[f172,f160])).
% 0.11/0.34 thf(f160,plain,(
% 0.11/0.34 ( ! [X2 : $i,X1 : $i] : (((sK0 @ X1 @ X2) = $true) | (X1 != X2)) )),
% 0.11/0.34 inference(equality_proxy_clausification,[],[f159])).
% 0.11/0.34 thf(f159,plain,(
% 0.11/0.34 ( ! [X2 : $i,X1 : $i] : (((sK0 @ X1 @ X2) = $true) | ($false = (X1 = X2))) )),
% 0.11/0.34 inference(binary_proxy_clausification,[],[f158])).
% 0.11/0.34 thf(f158,plain,(
% 0.11/0.34 ( ! [X2 : $i,X1 : $i] : ((((X1 = X2) => (sK0 @ X1 @ X2)) = $true)) )),
% 0.11/0.34 inference(beta_eta_normalization,[],[f157])).
% 0.11/0.34 thf(f157,plain,(
% 0.11/0.34 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((X1 = Y0) => (sK0 @ X1 @ Y0))) @ X2))) )),
% 0.11/0.34 inference(pi_clausification,[],[f156])).
% 0.11/0.34 thf(f156,plain,(
% 0.11/0.34 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((X1 = Y0) => (sK0 @ X1 @ Y0)))) = $true)) )),
% 0.11/0.34 inference(beta_eta_normalization,[],[f155])).
% 0.11/0.34 thf(f155,plain,(
% 0.11/0.34 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y0 = Y1) => (sK0 @ Y0 @ Y1))))) @ X1) = $true)) )),
% 0.11/0.34 inference(pi_clausification,[],[f154])).
% 0.11/0.34 thf(f154,plain,(
% 0.11/0.34 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y0 = Y1) => (sK0 @ Y0 @ Y1)))))) = $true)),
% 0.11/0.34 inference(boolean_simplification,[],[f153])).
% 0.11/0.34 thf(f153,plain,(
% 0.11/0.34 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((Y0 = Y1) & $true) => (sK0 @ Y0 @ Y1)))))) = $true)),
% 0.11/0.34 inference(beta_eta_normalization,[],[f152])).
% 0.11/0.34 thf(f152,plain,(
% 0.11/0.34 (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) & (Y0 @ Y1))))))) @ (^[Y0 : $i]: ($true))) @ sK0) = $true)),
% 0.11/0.34 inference(definition_unfolding,[],[f131,f129,f116])).
% 0.11/0.34 thf(f116,plain,(
% 0.11/0.34 (id_rel = (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) & (Y0 @ Y1))))))))),
% 0.11/0.34 inference(cnf_transformation,[],[f101])).
% 0.11/0.34 thf(f101,plain,(
% 0.11/0.34 (id_rel = (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) & (Y0 @ Y1))))))))),
% 0.11/0.34 inference(fool_elimination,[],[f100])).
% 0.11/0.34 thf(f100,plain,(
% 0.11/0.34 (id_rel = (^[X0 : $i > $o, X1 : $i, X2 : $i] : ((X0 @ X1) & (X1 = X2))))),
% 0.11/0.34 inference(rectify,[],[f17])).
% 0.11/0.34 thf(f17,axiom,(
% 0.11/0.34 (id_rel = (^[X5 : $i > $o, X0 : $i, X2 : $i] : ((X5 @ X0) & (X0 = X2))))),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_rel)).
% 0.11/0.34 thf(f129,plain,(
% 0.11/0.34 (sub_rel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 0.11/0.34 inference(cnf_transformation,[],[f60])).
% 0.11/0.34 thf(f60,plain,(
% 0.11/0.34 (sub_rel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 0.11/0.34 inference(fool_elimination,[],[f59])).
% 0.11/0.34 thf(f59,plain,(
% 0.11/0.34 ((^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X3 @ X2) => (X1 @ X3 @ X2)))) = sub_rel)),
% 0.11/0.34 inference(rectify,[],[f18])).
% 0.11/0.34 thf(f18,axiom,(
% 0.11/0.34 ((^[X6 : $i > $i > $o, X7 : $i > $i > $o] : (! [X2,X0] : ((X6 @ X0 @ X2) => (X7 @ X0 @ X2)))) = sub_rel)),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sub_rel)).
% 0.11/0.34 thf(f131,plain,(
% 0.11/0.34 ((sub_rel @ (id_rel @ (^[Y0 : $i]: ($true))) @ sK0) = $true)),
% 0.11/0.34 inference(cnf_transformation,[],[f110])).
% 0.11/0.34 thf(f110,plain,(
% 0.11/0.34 (((subset @ (^[Y0 : $i]: ($true)) @ (rel_domain @ sK0)) != $true) | ((^[Y0 : $i]: ($true)) != (rel_codomain @ sK0))) & ((sub_rel @ (id_rel @ (^[Y0 : $i]: ($true))) @ sK0) = $true)),
% 0.11/0.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f108,f109])).
% 0.11/0.34 thf(f109,plain,(
% 0.11/0.34 ? [X0 : $i > $i > $o] : ((($true != (subset @ (^[Y0 : $i]: ($true)) @ (rel_domain @ X0))) | ((rel_codomain @ X0) != (^[Y0 : $i]: ($true)))) & ((sub_rel @ (id_rel @ (^[Y0 : $i]: ($true))) @ X0) = $true)) => ((((subset @ (^[Y0 : $i]: ($true)) @ (rel_domain @ sK0)) != $true) | ((^[Y0 : $i]: ($true)) != (rel_codomain @ sK0))) & ((sub_rel @ (id_rel @ (^[Y0 : $i]: ($true))) @ sK0) = $true))),
% 0.11/0.34 introduced(choice_axiom,[])).
% 0.11/0.34 thf(f108,plain,(
% 0.11/0.34 ? [X0 : $i > $i > $o] : ((($true != (subset @ (^[Y0 : $i]: ($true)) @ (rel_domain @ X0))) | ((rel_codomain @ X0) != (^[Y0 : $i]: ($true)))) & ((sub_rel @ (id_rel @ (^[Y0 : $i]: ($true))) @ X0) = $true))),
% 0.11/0.34 inference(ennf_transformation,[],[f47])).
% 0.11/0.34 thf(f47,plain,(
% 0.11/0.34 ~! [X0 : $i > $i > $o] : (((sub_rel @ (id_rel @ (^[Y0 : $i]: ($true))) @ X0) = $true) => (($true = (subset @ (^[Y0 : $i]: ($true)) @ (rel_domain @ X0))) & ((rel_codomain @ X0) = (^[Y0 : $i]: ($true)))))),
% 0.11/0.34 inference(fool_elimination,[],[f46])).
% 0.11/0.34 thf(f46,plain,(
% 0.11/0.34 ~! [X0 : $i > $i > $o] : ((sub_rel @ (id_rel @ (^[X1 : $i] : ($true))) @ X0) => (((^[X2 : $i] : ($true)) = (rel_codomain @ X0)) & (subset @ (^[X3 : $i] : ($true)) @ (rel_domain @ X0))))),
% 0.11/0.34 inference(rectify,[],[f37])).
% 0.11/0.34 thf(f37,negated_conjecture,(
% 0.11/0.34 ~! [X8 : $i > $i > $o] : ((sub_rel @ (id_rel @ (^[X0 : $i] : ($true))) @ X8) => (((^[X0 : $i] : ($true)) = (rel_codomain @ X8)) & (subset @ (^[X0 : $i] : ($true)) @ (rel_domain @ X8))))),
% 0.11/0.34 inference(negated_conjecture,[],[f36])).
% 0.11/0.34 thf(f36,conjecture,(
% 0.11/0.34 ! [X8 : $i > $i > $o] : ((sub_rel @ (id_rel @ (^[X0 : $i] : ($true))) @ X8) => (((^[X0 : $i] : ($true)) = (rel_codomain @ X8)) & (subset @ (^[X0 : $i] : ($true)) @ (rel_domain @ X8))))),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm)).
% 0.11/0.34 thf(f172,plain,(
% 0.11/0.34 ( ! [X1 : $i] : (($false = (sK0 @ sK2 @ X1))) ) | ~spl1_2),
% 0.11/0.34 inference(avatar_component_clause,[],[f171])).
% 0.11/0.34 thf(f171,plain,(
% 0.11/0.34 spl1_2 <=> ! [X1] : ($false = (sK0 @ sK2 @ X1))),
% 0.11/0.34 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.11/0.34 thf(f183,plain,(
% 0.11/0.34 spl1_1),
% 0.11/0.34 inference(avatar_contradiction_clause,[],[f182])).
% 0.11/0.34 thf(f182,plain,(
% 0.11/0.34 $false | spl1_1),
% 0.11/0.34 inference(equality_resolution,[],[f181])).
% 0.11/0.34 thf(f181,plain,(
% 0.11/0.34 ( ! [X0 : $i] : ((sK4 != X0)) ) | spl1_1),
% 0.11/0.34 inference(trivial_inequality_removal,[],[f178])).
% 0.11/0.34 thf(f178,plain,(
% 0.11/0.34 ( ! [X0 : $i] : (($false = $true) | (sK4 != X0)) ) | spl1_1),
% 0.11/0.34 inference(superposition,[],[f177,f160])).
% 0.11/0.34 thf(f177,plain,(
% 0.11/0.34 ( ! [X1 : $i] : (($false = (sK0 @ X1 @ sK4))) ) | spl1_1),
% 0.11/0.34 inference(beta_eta_normalization,[],[f176])).
% 0.11/0.34 thf(f176,plain,(
% 0.11/0.34 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: (sK0 @ Y0 @ sK4)) @ X1))) ) | spl1_1),
% 0.11/0.34 inference(pi_clausification,[],[f175])).
% 0.11/0.34 thf(f175,plain,(
% 0.11/0.34 ((?? @ $i @ (^[Y0 : $i]: (sK0 @ Y0 @ sK4))) != $true) | spl1_1),
% 0.11/0.34 inference(beta_eta_normalization,[],[f174])).
% 0.11/0.34 thf(f174,plain,(
% 0.11/0.34 (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (sK0 @ Y1 @ Y0)))) @ sK4) != ((^[Y0 : $i]: ($true)) @ sK4)) | spl1_1),
% 0.11/0.34 inference(negative_extensionality,[],[f169])).
% 0.11/0.34 thf(f169,plain,(
% 0.11/0.34 ((^[Y0 : $i]: ($true)) != (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (sK0 @ Y1 @ Y0))))) | spl1_1),
% 0.11/0.34 inference(avatar_component_clause,[],[f167])).
% 0.11/0.34 thf(f167,plain,(
% 0.11/0.34 spl1_1 <=> ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (sK0 @ Y1 @ Y0)))))),
% 0.11/0.34 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.11/0.34 thf(f173,plain,(
% 0.11/0.34 ~spl1_1 | spl1_2),
% 0.11/0.34 inference(avatar_split_clause,[],[f165,f171,f167])).
% 0.11/0.34 thf(f165,plain,(
% 0.11/0.34 ( ! [X1 : $i] : (($false = (sK0 @ sK2 @ X1)) | ((^[Y0 : $i]: ($true)) != (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (sK0 @ Y1 @ Y0)))))) )),
% 0.11/0.34 inference(pi_clausification,[],[f164])).
% 0.11/0.34 thf(f164,plain,(
% 0.11/0.34 ($false = (?? @ $i @ (sK0 @ sK2))) | ((^[Y0 : $i]: ($true)) != (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (sK0 @ Y1 @ Y0)))))),
% 0.11/0.34 inference(beta_eta_normalization,[],[f163])).
% 0.11/0.34 thf(f163,plain,(
% 0.11/0.34 ($false = ((^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))) @ sK2)) | ((^[Y0 : $i]: ($true)) != (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (sK0 @ Y1 @ Y0)))))),
% 0.11/0.34 inference(sigma_clausification,[],[f162])).
% 0.11/0.34 thf(f162,plain,(
% 0.11/0.34 ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0)))) != $true) | ((^[Y0 : $i]: ($true)) != (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (sK0 @ Y1 @ Y0)))))),
% 0.11/0.34 inference(boolean_simplification,[],[f161])).
% 0.11/0.34 thf(f161,plain,(
% 0.11/0.34 ((^[Y0 : $i]: ($true)) != (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (sK0 @ Y1 @ Y0))))) | ($true != (!! @ $i @ (^[Y0 : $i]: ($true => (?? @ $i @ (sK0 @ Y0))))))),
% 0.11/0.34 inference(beta_eta_normalization,[],[f151])).
% 0.11/0.34 thf(f151,plain,(
% 0.11/0.34 ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ (^[Y0 : $i]: ($true)) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ sK0))) | (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ sK0) != (^[Y0 : $i]: ($true)))),
% 0.11/0.34 inference(definition_unfolding,[],[f132,f141,f114,f117])).
% 0.11/0.34 thf(f117,plain,(
% 0.11/0.34 (rel_codomain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.11/0.34 inference(cnf_transformation,[],[f80])).
% 0.11/0.34 thf(f80,plain,(
% 0.11/0.34 (rel_codomain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.11/0.34 inference(fool_elimination,[],[f79])).
% 0.11/0.34 thf(f79,plain,(
% 0.11/0.34 (rel_codomain = (^[X0 : $i > $i > $o, X1 : $i] : (? [X2] : (X0 @ X2 @ X1))))),
% 0.11/0.34 inference(rectify,[],[f28])).
% 0.11/0.34 thf(f28,axiom,(
% 0.11/0.34 (rel_codomain = (^[X8 : $i > $i > $o, X2 : $i] : (? [X0] : (X8 @ X0 @ X2))))),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rel_codomain)).
% 0.11/0.34 thf(f114,plain,(
% 0.11/0.34 (rel_domain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.11/0.34 inference(cnf_transformation,[],[f88])).
% 0.11/0.34 thf(f88,plain,(
% 0.11/0.34 (rel_domain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.11/0.34 inference(fool_elimination,[],[f87])).
% 0.11/0.34 thf(f87,plain,(
% 0.11/0.34 ((^[X0 : $i > $i > $o, X1 : $i] : (? [X2] : (X0 @ X1 @ X2))) = rel_domain)),
% 0.11/0.34 inference(rectify,[],[f29])).
% 0.11/0.34 thf(f29,axiom,(
% 0.11/0.34 ((^[X8 : $i > $i > $o, X0 : $i] : (? [X2] : (X8 @ X0 @ X2))) = rel_domain)),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rel_domain)).
% 0.11/0.34 thf(f141,plain,(
% 0.11/0.34 (subset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.11/0.34 inference(cnf_transformation,[],[f103])).
% 0.11/0.34 thf(f103,plain,(
% 0.11/0.34 (subset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.11/0.34 inference(fool_elimination,[],[f102])).
% 0.11/0.34 thf(f102,plain,(
% 0.11/0.34 (subset = (^[X0 : $i > $o, X1 : $i > $o] : (! [X2] : ((X0 @ X2) => (X1 @ X2)))))),
% 0.11/0.34 inference(rectify,[],[f12])).
% 0.11/0.34 thf(f12,axiom,(
% 0.11/0.34 (subset = (^[X0 : $i > $o, X2 : $i > $o] : (! [X3] : ((X0 @ X3) => (X2 @ X3)))))),
% 0.11/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset)).
% 0.11/0.34 thf(f132,plain,(
% 0.11/0.34 ((subset @ (^[Y0 : $i]: ($true)) @ (rel_domain @ sK0)) != $true) | ((^[Y0 : $i]: ($true)) != (rel_codomain @ sK0))),
% 0.11/0.34 inference(cnf_transformation,[],[f110])).
% 0.11/0.34 % SZS output end Proof for theBenchmark
% 0.11/0.34 % (24627)------------------------------
% 0.11/0.34 % (24627)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34 % (24627)Termination reason: Refutation
% 0.11/0.34
% 0.11/0.34 % (24627)Memory used [KB]: 5628
% 0.11/0.34 % (24627)Time elapsed: 0.008 s
% 0.11/0.34 % (24627)Instructions burned: 9 (million)
% 0.11/0.34 % (24627)------------------------------
% 0.11/0.34 % (24627)------------------------------
% 0.11/0.34 % (24626)Success in time 0.021 s
% 0.11/0.35 % Vampire---4.8 exiting
%------------------------------------------------------------------------------