TSTP Solution File: SET673^3 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET673^3 : 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 : n008.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 03:12:47 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET673^3 : TPTP v8.2.0. Released v3.6.0.
% 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
% 0.14/0.35 % Computer : n008.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 11:45:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37 % (4748)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (4755)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.37 % (4755)Instruction limit reached!
% 0.14/0.37 % (4755)------------------------------
% 0.14/0.37 % (4755)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (4755)Termination reason: Unknown
% 0.14/0.37 % (4755)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (4755)Memory used [KB]: 1023
% 0.14/0.37 % (4755)Time elapsed: 0.004 s
% 0.14/0.37 % (4755)Instructions burned: 3 (million)
% 0.14/0.37 % (4755)------------------------------
% 0.14/0.37 % (4755)------------------------------
% 0.14/0.37 % (4749)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.37 % (4748)First to succeed.
% 0.14/0.38 % (4749)Instruction limit reached!
% 0.14/0.38 % (4749)------------------------------
% 0.14/0.38 % (4749)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (4749)Termination reason: Unknown
% 0.14/0.38 % (4749)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (4749)Memory used [KB]: 1023
% 0.14/0.38 % (4749)Time elapsed: 0.005 s
% 0.14/0.38 % (4749)Instructions burned: 5 (million)
% 0.14/0.38 % (4749)------------------------------
% 0.14/0.38 % (4749)------------------------------
% 0.14/0.38 % (4750)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.38 % (4748)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% 0.14/0.38 thf(func_def_0, type, in: $i > ($i > $o) > $o).
% 0.14/0.38 thf(func_def_2, type, is_a: $i > ($i > $o) > $o).
% 0.14/0.38 thf(func_def_3, type, emptyset: $i > $o).
% 0.14/0.38 thf(func_def_4, type, unord_pair: $i > $i > $i > $o).
% 0.14/0.38 thf(func_def_5, type, singleton: $i > $i > $o).
% 0.14/0.38 thf(func_def_6, type, union: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_7, type, excl_union: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_8, type, intersection: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_9, type, setminus: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_10, type, complement: ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_11, type, disjoint: ($i > $o) > ($i > $o) > $o).
% 0.14/0.38 thf(func_def_12, type, subset: ($i > $o) > ($i > $o) > $o).
% 0.14/0.38 thf(func_def_13, type, meets: ($i > $o) > ($i > $o) > $o).
% 0.14/0.38 thf(func_def_14, type, misses: ($i > $o) > ($i > $o) > $o).
% 0.14/0.38 thf(func_def_15, type, cartesian_product: ($i > $o) > ($i > $o) > $i > $i > $o).
% 0.14/0.38 thf(func_def_16, type, pair_rel: $i > $i > $i > $i > $o).
% 0.14/0.38 thf(func_def_17, type, id_rel: ($i > $o) > $i > $i > $o).
% 0.14/0.38 thf(func_def_18, type, sub_rel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_19, type, is_rel_on: ($i > $i > $o) > ($i > $o) > ($i > $o) > $o).
% 0.14/0.38 thf(func_def_20, type, restrict_rel_domain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.14/0.38 thf(func_def_21, type, rel_diagonal: $i > $i > $o).
% 0.14/0.38 thf(func_def_22, type, rel_composition: ($i > $i > $o) > ($i > $i > $o) > $i > $i > $o).
% 0.14/0.38 thf(func_def_23, type, reflexive: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_24, type, irreflexive: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_25, type, symmetric: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_26, type, transitive: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_27, type, equiv_rel: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_28, type, rel_codomain: ($i > $i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_29, type, rel_domain: ($i > $i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_30, type, rel_inverse: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.38 thf(func_def_31, type, equiv_classes: ($i > $i > $o) > ($i > $o) > $o).
% 0.14/0.38 thf(func_def_32, type, restrict_rel_codomain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.14/0.38 thf(func_def_33, type, rel_field: ($i > $i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_34, type, well_founded: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_35, type, upwards_well_founded: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_52, type, sK0: $i > $o).
% 0.14/0.38 thf(func_def_53, type, sK1: $i > $o).
% 0.14/0.38 thf(func_def_54, type, sK2: $i > $i > $o).
% 0.14/0.38 thf(func_def_55, type, sK3: $i > $o).
% 0.14/0.38 thf(func_def_57, type, ph5: !>[X0: $tType]:(X0)).
% 0.14/0.38 thf(f218,plain,(
% 0.14/0.38 $false),
% 0.14/0.38 inference(avatar_sat_refutation,[],[f188,f199,f217])).
% 0.14/0.38 thf(f217,plain,(
% 0.14/0.38 ~spl4_1),
% 0.14/0.38 inference(avatar_contradiction_clause,[],[f216])).
% 0.14/0.38 thf(f216,plain,(
% 0.14/0.38 $false | ~spl4_1),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f213])).
% 0.14/0.38 thf(f213,plain,(
% 0.14/0.38 ($false = $true) | ~spl4_1),
% 0.14/0.38 inference(superposition,[],[f183,f211])).
% 0.14/0.38 thf(f211,plain,(
% 0.14/0.38 ((sK1 @ sK7) = $true)),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f208])).
% 0.14/0.38 thf(f208,plain,(
% 0.14/0.38 ((sK1 @ sK7) = $true) | ($false = $true)),
% 0.14/0.38 inference(superposition,[],[f202,f160])).
% 0.14/0.38 thf(f160,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($false = (sK3 @ X1)) | ((sK1 @ X1) = $true)) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f159])).
% 0.14/0.38 thf(f159,plain,(
% 0.14/0.38 ( ! [X1 : $i] : ((((sK3 @ X1) => (sK1 @ X1)) = $true)) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f158])).
% 0.14/0.38 thf(f158,plain,(
% 0.14/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK3 @ Y0) => (sK1 @ Y0))) @ X1) = $true)) )),
% 0.14/0.38 inference(pi_clausification,[],[f157])).
% 0.14/0.38 thf(f157,plain,(
% 0.14/0.38 ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (sK1 @ Y0)))) = $true)),
% 0.14/0.38 inference(beta_eta_normalization,[],[f153])).
% 0.14/0.38 thf(f153,plain,(
% 0.14/0.38 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ sK3 @ sK1) = $true)),
% 0.14/0.38 inference(definition_unfolding,[],[f125,f135])).
% 0.14/0.38 thf(f135,plain,(
% 0.14/0.38 (subset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f107])).
% 0.14/0.38 thf(f107,plain,(
% 0.14/0.38 (subset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f106])).
% 0.14/0.38 thf(f106,plain,(
% 0.14/0.38 ((^[X0 : $i > $o, X1 : $i > $o] : (! [X2] : ((X0 @ X2) => (X1 @ X2)))) = subset)),
% 0.14/0.38 inference(rectify,[],[f12])).
% 0.14/0.38 thf(f12,axiom,(
% 0.14/0.38 ((^[X0 : $i > $o, X2 : $i > $o] : (! [X3] : ((X0 @ X3) => (X2 @ X3)))) = subset)),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset)).
% 0.14/0.38 thf(f125,plain,(
% 0.14/0.38 ((subset @ sK3 @ sK1) = $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f111])).
% 0.14/0.38 thf(f111,plain,(
% 0.14/0.38 ((subset @ sK3 @ sK1) = $true) & ((restrict_rel_codomain @ sK2 @ sK1) != sK2) & ((is_rel_on @ sK2 @ sK0 @ sK3) = $true)),
% 0.14/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f109,f110])).
% 0.14/0.38 thf(f110,plain,(
% 0.14/0.38 ? [X0 : $i > $o,X1 : $i > $o,X2 : $i > $i > $o,X3 : $i > $o] : (((subset @ X3 @ X1) = $true) & ((restrict_rel_codomain @ X2 @ X1) != X2) & ((is_rel_on @ X2 @ X0 @ X3) = $true)) => (((subset @ sK3 @ sK1) = $true) & ((restrict_rel_codomain @ sK2 @ sK1) != sK2) & ((is_rel_on @ sK2 @ sK0 @ sK3) = $true))),
% 0.14/0.38 introduced(choice_axiom,[])).
% 0.14/0.38 thf(f109,plain,(
% 0.14/0.38 ? [X0 : $i > $o,X1 : $i > $o,X2 : $i > $i > $o,X3 : $i > $o] : (((subset @ X3 @ X1) = $true) & ((restrict_rel_codomain @ X2 @ X1) != X2) & ((is_rel_on @ X2 @ X0 @ X3) = $true))),
% 0.14/0.38 inference(flattening,[],[f108])).
% 0.14/0.38 thf(f108,plain,(
% 0.14/0.38 ? [X0 : $i > $o,X1 : $i > $o,X2 : $i > $i > $o,X3 : $i > $o] : (((restrict_rel_codomain @ X2 @ X1) != X2) & (((subset @ X3 @ X1) = $true) & ((is_rel_on @ X2 @ X0 @ X3) = $true)))),
% 0.14/0.38 inference(ennf_transformation,[],[f51])).
% 0.14/0.38 thf(f51,plain,(
% 0.14/0.38 ~! [X0 : $i > $o,X1 : $i > $o,X2 : $i > $i > $o,X3 : $i > $o] : ((((subset @ X3 @ X1) = $true) & ((is_rel_on @ X2 @ X0 @ X3) = $true)) => ((restrict_rel_codomain @ X2 @ X1) = X2))),
% 0.14/0.38 inference(fool_elimination,[],[f50])).
% 0.14/0.38 thf(f50,plain,(
% 0.14/0.38 ~! [X0 : $i > $o,X1 : $i > $o,X2 : $i > $i > $o,X3 : $i > $o] : (((subset @ X3 @ X1) & (is_rel_on @ X2 @ X0 @ X3)) => ((restrict_rel_codomain @ X2 @ X1) = X2))),
% 0.14/0.38 inference(rectify,[],[f37])).
% 0.14/0.38 thf(f37,negated_conjecture,(
% 0.14/0.38 ~! [X0 : $i > $o,X11 : $i > $o,X8 : $i > $i > $o,X2 : $i > $o] : (((subset @ X2 @ X11) & (is_rel_on @ X8 @ X0 @ X2)) => ((restrict_rel_codomain @ X8 @ X11) = X8))),
% 0.14/0.38 inference(negated_conjecture,[],[f36])).
% 0.14/0.38 thf(f36,conjecture,(
% 0.14/0.38 ! [X0 : $i > $o,X11 : $i > $o,X8 : $i > $i > $o,X2 : $i > $o] : (((subset @ X2 @ X11) & (is_rel_on @ X8 @ X0 @ X2)) => ((restrict_rel_codomain @ X8 @ X11) = X8))),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm)).
% 0.14/0.38 thf(f202,plain,(
% 0.14/0.38 ((sK3 @ sK7) = $true)),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f194])).
% 0.14/0.38 thf(f194,plain,(
% 0.14/0.38 ($false = $true) | ((sK3 @ sK7) = $true)),
% 0.14/0.38 inference(superposition,[],[f167,f179])).
% 0.14/0.38 thf(f179,plain,(
% 0.14/0.38 ((sK2 @ sK6 @ sK7) = $true)),
% 0.14/0.38 inference(duplicate_literal_removal,[],[f177])).
% 0.14/0.38 thf(f177,plain,(
% 0.14/0.38 ((sK2 @ sK6 @ sK7) = $true) | ((sK2 @ sK6 @ sK7) = $true)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f173])).
% 0.14/0.38 thf(f173,plain,(
% 0.14/0.38 ((sK2 @ sK6 @ sK7) = $true) | ($true = ((sK1 @ sK7) & (sK2 @ sK6 @ sK7)))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f172])).
% 0.14/0.38 thf(f172,plain,(
% 0.14/0.38 ((sK2 @ sK6 @ sK7) != ((sK1 @ sK7) & (sK2 @ sK6 @ sK7)))),
% 0.14/0.38 inference(beta_eta_normalization,[],[f171])).
% 0.14/0.38 thf(f171,plain,(
% 0.14/0.38 (((^[Y0 : $i]: ((sK1 @ Y0) & (sK2 @ sK6 @ Y0))) @ sK7) != (sK2 @ sK6 @ sK7))),
% 0.14/0.38 inference(negative_extensionality,[],[f170])).
% 0.14/0.38 thf(f170,plain,(
% 0.14/0.38 ((^[Y0 : $i]: ((sK1 @ Y0) & (sK2 @ sK6 @ Y0))) != (sK2 @ sK6))),
% 0.14/0.38 inference(beta_eta_normalization,[],[f169])).
% 0.14/0.38 thf(f169,plain,(
% 0.14/0.38 (((^[Y0 : $i]: ((^[Y1 : $i]: ((sK1 @ Y1) & (sK2 @ Y0 @ Y1))))) @ sK6) != (sK2 @ sK6))),
% 0.14/0.38 inference(negative_extensionality,[],[f156])).
% 0.14/0.38 thf(f156,plain,(
% 0.14/0.38 ((^[Y0 : $i]: ((^[Y1 : $i]: ((sK1 @ Y1) & (sK2 @ Y0 @ Y1))))) != sK2)),
% 0.14/0.38 inference(beta_eta_normalization,[],[f154])).
% 0.14/0.38 thf(f154,plain,(
% 0.14/0.38 (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 @ Y3) & (Y0 @ Y2 @ Y3))))))))) @ sK2 @ sK1) != sK2)),
% 0.14/0.38 inference(definition_unfolding,[],[f124,f132])).
% 0.14/0.38 thf(f132,plain,(
% 0.14/0.38 (restrict_rel_codomain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 @ Y3) & (Y0 @ Y2 @ Y3))))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f49])).
% 0.14/0.38 thf(f49,plain,(
% 0.14/0.38 (restrict_rel_codomain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 @ Y3) & (Y0 @ Y2 @ Y3))))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f48])).
% 0.14/0.38 thf(f48,plain,(
% 0.14/0.38 (restrict_rel_codomain = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i, X3 : $i] : ((X0 @ X2 @ X3) & (X1 @ X3))))),
% 0.14/0.38 inference(rectify,[],[f32])).
% 0.14/0.38 thf(f32,axiom,(
% 0.14/0.38 (restrict_rel_codomain = (^[X8 : $i > $i > $o, X5 : $i > $o, X0 : $i, X2 : $i] : ((X8 @ X0 @ X2) & (X5 @ X2))))),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_rel_codomain)).
% 0.14/0.38 thf(f124,plain,(
% 0.14/0.38 ((restrict_rel_codomain @ sK2 @ sK1) != sK2)),
% 0.14/0.38 inference(cnf_transformation,[],[f111])).
% 0.14/0.38 thf(f167,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : (($false = (sK2 @ X1 @ X2)) | ((sK3 @ X2) = $true)) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f166])).
% 0.14/0.38 thf(f166,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : ((((sK0 @ X1) & (sK3 @ X2)) = $true) | ($false = (sK2 @ X1 @ X2))) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f165])).
% 0.14/0.38 thf(f165,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : ((((sK2 @ X1 @ X2) => ((sK0 @ X1) & (sK3 @ X2))) = $true)) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f164])).
% 0.14/0.38 thf(f164,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((sK2 @ X1 @ Y0) => ((sK0 @ X1) & (sK3 @ Y0)))) @ X2) = $true)) )),
% 0.14/0.38 inference(pi_clausification,[],[f163])).
% 0.14/0.38 thf(f163,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ X1 @ Y0) => ((sK0 @ X1) & (sK3 @ Y0))))) = $true)) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f162])).
% 0.14/0.38 thf(f162,plain,(
% 0.14/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => ((sK0 @ Y0) & (sK3 @ Y1)))))) @ X1) = $true)) )),
% 0.14/0.38 inference(pi_clausification,[],[f161])).
% 0.14/0.38 thf(f161,plain,(
% 0.14/0.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => ((sK0 @ Y0) & (sK3 @ Y1))))))) = $true)),
% 0.14/0.38 inference(beta_eta_normalization,[],[f155])).
% 0.14/0.38 thf(f155,plain,(
% 0.14/0.38 (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => ((Y1 @ Y3) & (Y2 @ Y4)))))))))))) @ sK2 @ sK0 @ sK3) = $true)),
% 0.14/0.38 inference(definition_unfolding,[],[f123,f142])).
% 0.14/0.38 thf(f142,plain,(
% 0.14/0.38 (is_rel_on = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => ((Y1 @ Y3) & (Y2 @ Y4)))))))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f94])).
% 0.14/0.38 thf(f94,plain,(
% 0.14/0.38 (is_rel_on = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y3 @ Y4) => ((Y1 @ Y3) & (Y2 @ Y4)))))))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f93])).
% 0.14/0.38 thf(f93,plain,(
% 0.14/0.38 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i > $o] : (! [X3,X4] : ((X0 @ X4 @ X3) => ((X2 @ X3) & (X1 @ X4))))) = is_rel_on)),
% 0.14/0.38 inference(rectify,[],[f19])).
% 0.14/0.38 thf(f19,axiom,(
% 0.14/0.38 ((^[X8 : $i > $i > $o, X9 : $i > $o, X10 : $i > $o] : (! [X2,X0] : ((X8 @ X0 @ X2) => ((X10 @ X2) & (X9 @ X0))))) = is_rel_on)),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',is_rel_on)).
% 0.14/0.38 thf(f123,plain,(
% 0.14/0.38 ((is_rel_on @ sK2 @ sK0 @ sK3) = $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f111])).
% 0.14/0.38 thf(f183,plain,(
% 0.14/0.38 ($false = (sK1 @ sK7)) | ~spl4_1),
% 0.14/0.38 inference(avatar_component_clause,[],[f181])).
% 0.14/0.38 thf(f181,plain,(
% 0.14/0.38 spl4_1 <=> ($false = (sK1 @ sK7))),
% 0.14/0.38 introduced(avatar_definition,[new_symbols(naming,[spl4_1])])).
% 0.14/0.38 thf(f199,plain,(
% 0.14/0.38 ~spl4_2),
% 0.14/0.38 inference(avatar_contradiction_clause,[],[f198])).
% 0.14/0.38 thf(f198,plain,(
% 0.14/0.38 $false | ~spl4_2),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f192])).
% 0.14/0.38 thf(f192,plain,(
% 0.14/0.38 ($false = $true) | ~spl4_2),
% 0.14/0.38 inference(superposition,[],[f187,f179])).
% 0.14/0.38 thf(f187,plain,(
% 0.14/0.38 ($false = (sK2 @ sK6 @ sK7)) | ~spl4_2),
% 0.14/0.38 inference(avatar_component_clause,[],[f185])).
% 0.14/0.38 thf(f185,plain,(
% 0.14/0.38 spl4_2 <=> ($false = (sK2 @ sK6 @ sK7))),
% 0.14/0.38 introduced(avatar_definition,[new_symbols(naming,[spl4_2])])).
% 0.14/0.38 thf(f188,plain,(
% 0.14/0.38 spl4_1 | spl4_2),
% 0.14/0.38 inference(avatar_split_clause,[],[f176,f185,f181])).
% 0.14/0.38 thf(f176,plain,(
% 0.14/0.38 ($false = (sK1 @ sK7)) | ($false = (sK2 @ sK6 @ sK7))),
% 0.14/0.38 inference(duplicate_literal_removal,[],[f175])).
% 0.14/0.38 thf(f175,plain,(
% 0.14/0.38 ($false = (sK2 @ sK6 @ sK7)) | ($false = (sK1 @ sK7)) | ($false = (sK2 @ sK6 @ sK7))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f174])).
% 0.14/0.38 thf(f174,plain,(
% 0.14/0.38 ($false = ((sK1 @ sK7) & (sK2 @ sK6 @ sK7))) | ($false = (sK2 @ sK6 @ sK7))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f172])).
% 0.14/0.38 % SZS output end Proof for theBenchmark
% 0.14/0.38 % (4748)------------------------------
% 0.14/0.38 % (4748)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (4748)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (4748)Memory used [KB]: 5628
% 0.14/0.38 % (4748)Time elapsed: 0.011 s
% 0.14/0.38 % (4748)Instructions burned: 11 (million)
% 0.14/0.38 % (4748)------------------------------
% 0.14/0.38 % (4748)------------------------------
% 0.14/0.38 % (4747)Success in time 0.022 s
% 0.14/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------