TSTP Solution File: SET672^3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET672^3 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n009.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 03:12:46 EDT 2024
% Result : Theorem 0.21s 0.39s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET672^3 : TPTP v8.2.0. Released v3.6.0.
% 0.03/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n009.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 12:16:08 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/sandbox/benchmark/theBenchmark.p
% 0.21/0.38 % (6090)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)
% 0.21/0.38 % (6089)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)
% 0.21/0.38 % (6088)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.38 % (6091)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38 % (6092)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)
% 0.21/0.38 % (6093)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)
% 0.21/0.38 % (6094)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.38 % (6091)Instruction limit reached!
% 0.21/0.38 % (6091)------------------------------
% 0.21/0.38 % (6091)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (6091)Termination reason: Unknown
% 0.21/0.38 % (6091)Termination phase: shuffling
% 0.21/0.38 % (6092)Instruction limit reached!
% 0.21/0.38 % (6092)------------------------------
% 0.21/0.38 % (6092)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38
% 0.21/0.38 % (6091)Memory used [KB]: 1023
% 0.21/0.38 % (6091)Time elapsed: 0.003 s
% 0.21/0.38 % (6091)Instructions burned: 2 (million)
% 0.21/0.38 % (6091)------------------------------
% 0.21/0.38 % (6091)------------------------------
% 0.21/0.38 % (6092)Termination reason: Unknown
% 0.21/0.38 % (6092)Termination phase: shuffling
% 0.21/0.38
% 0.21/0.38 % (6092)Memory used [KB]: 1023
% 0.21/0.38 % (6092)Time elapsed: 0.003 s
% 0.21/0.38 % (6092)Instructions burned: 2 (million)
% 0.21/0.38 % (6092)------------------------------
% 0.21/0.38 % (6092)------------------------------
% 0.21/0.38 % (6089)Instruction limit reached!
% 0.21/0.38 % (6089)------------------------------
% 0.21/0.38 % (6089)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (6089)Termination reason: Unknown
% 0.21/0.38 % (6089)Termination phase: shuffling
% 0.21/0.38
% 0.21/0.38 % (6089)Memory used [KB]: 1023
% 0.21/0.38 % (6089)Time elapsed: 0.004 s
% 0.21/0.38 % (6089)Instructions burned: 4 (million)
% 0.21/0.38 % (6089)------------------------------
% 0.21/0.38 % (6089)------------------------------
% 0.21/0.38 % (6095)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)
% 0.21/0.38 % (6095)Instruction limit reached!
% 0.21/0.38 % (6095)------------------------------
% 0.21/0.38 % (6095)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (6095)Termination reason: Unknown
% 0.21/0.38 % (6095)Termination phase: shuffling
% 0.21/0.38
% 0.21/0.38 % (6095)Memory used [KB]: 1023
% 0.21/0.38 % (6095)Time elapsed: 0.003 s
% 0.21/0.38 % (6095)Instructions burned: 3 (million)
% 0.21/0.38 % (6095)------------------------------
% 0.21/0.38 % (6095)------------------------------
% 0.21/0.39 % (6093)First to succeed.
% 0.21/0.39 % (6094)Also succeeded, but the first one will report.
% 0.21/0.39 % (6088)Also succeeded, but the first one will report.
% 0.21/0.39 % (6093)Refutation found. Thanks to Tanya!
% 0.21/0.39 % SZS status Theorem for theBenchmark
% 0.21/0.39 % SZS output start Proof for theBenchmark
% 0.21/0.39 thf(func_def_0, type, in: $i > ($i > $o) > $o).
% 0.21/0.39 thf(func_def_2, type, is_a: $i > ($i > $o) > $o).
% 0.21/0.39 thf(func_def_3, type, emptyset: $i > $o).
% 0.21/0.39 thf(func_def_4, type, unord_pair: $i > $i > $i > $o).
% 0.21/0.39 thf(func_def_5, type, singleton: $i > $i > $o).
% 0.21/0.39 thf(func_def_6, type, union: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_7, type, excl_union: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_8, type, intersection: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_9, type, setminus: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_10, type, complement: ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_11, type, disjoint: ($i > $o) > ($i > $o) > $o).
% 0.21/0.39 thf(func_def_12, type, subset: ($i > $o) > ($i > $o) > $o).
% 0.21/0.39 thf(func_def_13, type, meets: ($i > $o) > ($i > $o) > $o).
% 0.21/0.39 thf(func_def_14, type, misses: ($i > $o) > ($i > $o) > $o).
% 0.21/0.39 thf(func_def_15, type, cartesian_product: ($i > $o) > ($i > $o) > $i > $i > $o).
% 0.21/0.39 thf(func_def_16, type, pair_rel: $i > $i > $i > $i > $o).
% 0.21/0.39 thf(func_def_17, type, id_rel: ($i > $o) > $i > $i > $o).
% 0.21/0.39 thf(func_def_18, type, sub_rel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_19, type, is_rel_on: ($i > $i > $o) > ($i > $o) > ($i > $o) > $o).
% 0.21/0.39 thf(func_def_20, type, restrict_rel_domain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.21/0.39 thf(func_def_21, type, rel_diagonal: $i > $i > $o).
% 0.21/0.39 thf(func_def_22, type, rel_composition: ($i > $i > $o) > ($i > $i > $o) > $i > $i > $o).
% 0.21/0.39 thf(func_def_23, type, reflexive: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_24, type, irreflexive: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_25, type, symmetric: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_26, type, transitive: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_27, type, equiv_rel: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_28, type, rel_codomain: ($i > $i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_29, type, rel_domain: ($i > $i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_30, type, rel_inverse: ($i > $i > $o) > $i > $i > $o).
% 0.21/0.39 thf(func_def_31, type, equiv_classes: ($i > $i > $o) > ($i > $o) > $o).
% 0.21/0.39 thf(func_def_32, type, restrict_rel_codomain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.21/0.39 thf(func_def_33, type, rel_field: ($i > $i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_34, type, well_founded: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_35, type, upwards_well_founded: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_52, type, sK0: $i > $i > $o).
% 0.21/0.39 thf(func_def_53, type, sK1: $i > $o).
% 0.21/0.39 thf(func_def_54, type, sK2: $i > $o).
% 0.21/0.39 thf(func_def_55, type, sK3: $i > $o).
% 0.21/0.39 thf(f166,plain,(
% 0.21/0.39 $false),
% 0.21/0.39 inference(avatar_sat_refutation,[],[f144,f150,f165])).
% 0.21/0.39 thf(f165,plain,(
% 0.21/0.39 ~spl4_1),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f164])).
% 0.21/0.39 thf(f164,plain,(
% 0.21/0.39 $false | ~spl4_1),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f163])).
% 0.21/0.39 thf(f163,plain,(
% 0.21/0.39 ($false = $true) | ~spl4_1),
% 0.21/0.39 inference(forward_demodulation,[],[f157,f139])).
% 0.21/0.39 thf(f139,plain,(
% 0.21/0.39 ((sK1 @ sK6) = $false) | ~spl4_1),
% 0.21/0.39 inference(avatar_component_clause,[],[f137])).
% 0.21/0.39 thf(f137,plain,(
% 0.21/0.39 spl4_1 <=> ((sK1 @ sK6) = $false)),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl4_1])])).
% 0.21/0.39 thf(f157,plain,(
% 0.21/0.39 ((sK1 @ sK6) = $true)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f155])).
% 0.21/0.39 thf(f155,plain,(
% 0.21/0.39 ((sK1 @ sK6) = $true) | ($false = $true)),
% 0.21/0.39 inference(superposition,[],[f124,f134])).
% 0.21/0.39 thf(f134,plain,(
% 0.21/0.39 ((sK0 @ sK6 @ sK5) = $true)),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f132])).
% 0.21/0.39 thf(f132,plain,(
% 0.21/0.39 ($true = ((sK0 @ sK6 @ sK5) & (sK3 @ sK5)))),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f130])).
% 0.21/0.39 thf(f130,plain,(
% 0.21/0.39 ((((sK0 @ sK6 @ sK5) & (sK3 @ sK5)) => ((sK3 @ sK5) & (sK1 @ sK6))) = $false)),
% 0.21/0.39 inference(beta_eta_normalization,[],[f129])).
% 0.21/0.39 thf(f129,plain,(
% 0.21/0.39 (((^[Y0 : $i]: (((sK0 @ Y0 @ sK5) & (sK3 @ sK5)) => ((sK3 @ sK5) & (sK1 @ Y0)))) @ sK6) = $false)),
% 0.21/0.39 inference(sigma_clausification,[],[f128])).
% 0.21/0.39 thf(f128,plain,(
% 0.21/0.39 ((!! @ $i @ (^[Y0 : $i]: (((sK0 @ Y0 @ sK5) & (sK3 @ sK5)) => ((sK3 @ sK5) & (sK1 @ Y0))))) = $false)),
% 0.21/0.39 inference(beta_eta_normalization,[],[f127])).
% 0.21/0.39 thf(f127,plain,(
% 0.21/0.39 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y1 @ Y0) & (sK3 @ Y0)) => ((sK3 @ Y0) & (sK1 @ Y1)))))) @ sK5) = $false)),
% 0.21/0.39 inference(sigma_clausification,[],[f126])).
% 0.21/0.39 thf(f126,plain,(
% 0.21/0.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y1 @ Y0) & (sK3 @ Y0)) => ((sK3 @ Y0) & (sK1 @ Y1))))))) != $true)),
% 0.21/0.39 inference(beta_eta_normalization,[],[f117])).
% 0.21/0.39 thf(f117,plain,(
% 0.21/0.39 (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) => ((Y2 @ Y3) & (Y1 @ Y4)))))))))))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))) @ sK0 @ sK3) @ sK1 @ sK3) != $true)),
% 0.21/0.39 inference(definition_unfolding,[],[f112,f115,f111])).
% 0.21/0.39 thf(f111,plain,(
% 0.21/0.39 (restrict_rel_codomain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f86])).
% 0.21/0.39 thf(f86,plain,(
% 0.21/0.39 (restrict_rel_codomain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))))),
% 0.21/0.39 inference(fool_elimination,[],[f85])).
% 0.21/0.39 thf(f85,plain,(
% 0.21/0.39 (restrict_rel_codomain = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i, X3 : $i] : ((X1 @ X3) & (X0 @ X2 @ X3))))),
% 0.21/0.39 inference(rectify,[],[f32])).
% 0.21/0.39 thf(f32,axiom,(
% 0.21/0.39 (restrict_rel_codomain = (^[X8 : $i > $i > $o, X5 : $i > $o, X0 : $i, X2 : $i] : ((X5 @ X2) & (X8 @ X0 @ X2))))),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',restrict_rel_codomain)).
% 0.21/0.39 thf(f115,plain,(
% 0.21/0.39 (is_rel_on = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) => ((Y2 @ Y3) & (Y1 @ Y4)))))))))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f62])).
% 0.21/0.39 thf(f62,plain,(
% 0.21/0.39 (is_rel_on = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) => ((Y2 @ Y3) & (Y1 @ Y4)))))))))))))),
% 0.21/0.39 inference(fool_elimination,[],[f61])).
% 0.21/0.39 thf(f61,plain,(
% 0.21/0.39 (is_rel_on = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i > $o] : (! [X3,X4] : ((X0 @ X3 @ X4) => ((X1 @ X3) & (X2 @ X4))))))),
% 0.21/0.39 inference(rectify,[],[f19])).
% 0.21/0.39 thf(f19,axiom,(
% 0.21/0.39 (is_rel_on = (^[X8 : $i > $i > $o, X9 : $i > $o, X10 : $i > $o] : (! [X0,X2] : ((X8 @ X0 @ X2) => ((X9 @ X0) & (X10 @ X2))))))),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',is_rel_on)).
% 0.21/0.39 thf(f112,plain,(
% 0.21/0.39 ((is_rel_on @ (restrict_rel_codomain @ sK0 @ sK3) @ sK1 @ sK3) != $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f110])).
% 0.21/0.39 thf(f110,plain,(
% 0.21/0.39 ((is_rel_on @ sK0 @ sK1 @ sK2) = $true) & ((is_rel_on @ (restrict_rel_codomain @ sK0 @ sK3) @ sK1 @ sK3) != $true)),
% 0.21/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f108,f109])).
% 0.21/0.39 thf(f109,plain,(
% 0.21/0.39 ? [X0 : $i > $i > $o,X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((is_rel_on @ X0 @ X1 @ X2) = $true) & ((is_rel_on @ (restrict_rel_codomain @ X0 @ X3) @ X1 @ X3) != $true)) => (((is_rel_on @ sK0 @ sK1 @ sK2) = $true) & ((is_rel_on @ (restrict_rel_codomain @ sK0 @ sK3) @ sK1 @ sK3) != $true))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f108,plain,(
% 0.21/0.39 ? [X0 : $i > $i > $o,X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((is_rel_on @ X0 @ X1 @ X2) = $true) & ((is_rel_on @ (restrict_rel_codomain @ X0 @ X3) @ X1 @ X3) != $true))),
% 0.21/0.39 inference(ennf_transformation,[],[f66])).
% 0.21/0.39 thf(f66,plain,(
% 0.21/0.39 ~! [X0 : $i > $i > $o,X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((is_rel_on @ X0 @ X1 @ X2) = $true) => ((is_rel_on @ (restrict_rel_codomain @ X0 @ X3) @ X1 @ X3) = $true))),
% 0.21/0.39 inference(fool_elimination,[],[f65])).
% 0.21/0.39 thf(f65,plain,(
% 0.21/0.39 ~! [X0 : $i > $i > $o,X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : ((is_rel_on @ X0 @ X1 @ X2) => (is_rel_on @ (restrict_rel_codomain @ X0 @ X3) @ X1 @ X3))),
% 0.21/0.39 inference(rectify,[],[f37])).
% 0.21/0.39 thf(f37,negated_conjecture,(
% 0.21/0.39 ~! [X8 : $i > $i > $o,X0 : $i > $o,X2 : $i > $o,X11 : $i > $o] : ((is_rel_on @ X8 @ X0 @ X2) => (is_rel_on @ (restrict_rel_codomain @ X8 @ X11) @ X0 @ X11))),
% 0.21/0.39 inference(negated_conjecture,[],[f36])).
% 0.21/0.39 thf(f36,conjecture,(
% 0.21/0.39 ! [X8 : $i > $i > $o,X0 : $i > $o,X2 : $i > $o,X11 : $i > $o] : ((is_rel_on @ X8 @ X0 @ X2) => (is_rel_on @ (restrict_rel_codomain @ X8 @ X11) @ X0 @ X11))),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm)).
% 0.21/0.39 thf(f124,plain,(
% 0.21/0.39 ( ! [X2 : $i,X1 : $i] : (((sK0 @ X2 @ X1) = $false) | ((sK1 @ X2) = $true)) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f123])).
% 0.21/0.39 thf(f123,plain,(
% 0.21/0.39 ( ! [X2 : $i,X1 : $i] : (((sK0 @ X2 @ X1) = $false) | (((sK2 @ X1) & (sK1 @ X2)) = $true)) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f122])).
% 0.21/0.39 thf(f122,plain,(
% 0.21/0.39 ( ! [X2 : $i,X1 : $i] : (($true = ((sK0 @ X2 @ X1) => ((sK2 @ X1) & (sK1 @ X2))))) )),
% 0.21/0.39 inference(beta_eta_normalization,[],[f121])).
% 0.21/0.39 thf(f121,plain,(
% 0.21/0.39 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((sK0 @ Y0 @ X1) => ((sK2 @ X1) & (sK1 @ Y0)))) @ X2))) )),
% 0.21/0.39 inference(pi_clausification,[],[f120])).
% 0.21/0.39 thf(f120,plain,(
% 0.21/0.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0 @ X1) => ((sK2 @ X1) & (sK1 @ Y0))))) = $true)) )),
% 0.21/0.39 inference(beta_eta_normalization,[],[f119])).
% 0.21/0.39 thf(f119,plain,(
% 0.21/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ Y0) => ((sK2 @ Y0) & (sK1 @ Y1)))))) @ X1) = $true)) )),
% 0.21/0.39 inference(pi_clausification,[],[f118])).
% 0.21/0.39 thf(f118,plain,(
% 0.21/0.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ Y0) => ((sK2 @ Y0) & (sK1 @ Y1))))))) = $true)),
% 0.21/0.39 inference(beta_eta_normalization,[],[f116])).
% 0.21/0.39 thf(f116,plain,(
% 0.21/0.39 (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) => ((Y2 @ Y3) & (Y1 @ Y4)))))))))))) @ sK0 @ sK1 @ sK2) = $true)),
% 0.21/0.39 inference(definition_unfolding,[],[f113,f115])).
% 0.21/0.39 thf(f113,plain,(
% 0.21/0.39 ((is_rel_on @ sK0 @ sK1 @ sK2) = $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f110])).
% 0.21/0.39 thf(f150,plain,(
% 0.21/0.39 ~spl4_2),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f149])).
% 0.21/0.39 thf(f149,plain,(
% 0.21/0.39 $false | ~spl4_2),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f146])).
% 0.21/0.39 thf(f146,plain,(
% 0.21/0.39 ($false = $true) | ~spl4_2),
% 0.21/0.39 inference(superposition,[],[f143,f133])).
% 0.21/0.39 thf(f133,plain,(
% 0.21/0.39 ((sK3 @ sK5) = $true)),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f132])).
% 0.21/0.39 thf(f143,plain,(
% 0.21/0.39 ((sK3 @ sK5) = $false) | ~spl4_2),
% 0.21/0.39 inference(avatar_component_clause,[],[f141])).
% 0.21/0.39 thf(f141,plain,(
% 0.21/0.39 spl4_2 <=> ((sK3 @ sK5) = $false)),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl4_2])])).
% 0.21/0.39 thf(f144,plain,(
% 0.21/0.39 spl4_1 | spl4_2),
% 0.21/0.39 inference(avatar_split_clause,[],[f135,f141,f137])).
% 0.21/0.39 thf(f135,plain,(
% 0.21/0.39 ((sK3 @ sK5) = $false) | ((sK1 @ sK6) = $false)),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f131])).
% 0.21/0.39 thf(f131,plain,(
% 0.21/0.39 (((sK3 @ sK5) & (sK1 @ sK6)) = $false)),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f130])).
% 0.21/0.39 % SZS output end Proof for theBenchmark
% 0.21/0.39 % (6093)------------------------------
% 0.21/0.39 % (6093)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (6093)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (6093)Memory used [KB]: 5628
% 0.21/0.39 % (6093)Time elapsed: 0.009 s
% 0.21/0.39 % (6093)Instructions burned: 9 (million)
% 0.21/0.39 % (6093)------------------------------
% 0.21/0.39 % (6093)------------------------------
% 0.21/0.39 % (6087)Success in time 0.012 s
% 0.21/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------