TSTP Solution File: SET647^3 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SET647^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% 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 : Mon Jun 24 14:53:02 EDT 2024
% Result : Theorem 0.13s 0.40s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET647^3 : TPTP v8.2.0. Released v3.6.0.
% 0.07/0.13 % Command : run_vampire %s %d THM
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Jun 23 14:47:39 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 This is a TH0_THM_EQU_NAR problem
% 0.13/0.37 Running higher-order theorem proving
% 0.13/0.37 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.13/0.39 % (26432)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.39 % (26437)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)
% 0.13/0.39 % (26434)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)
% 0.13/0.39 % (26438)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.39 % (26436)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)
% 0.13/0.39 % (26435)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.39 % (26433)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)
% 0.13/0.39 % (26435)Instruction limit reached!
% 0.13/0.39 % (26435)------------------------------
% 0.13/0.39 % (26435)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.39 % (26435)Termination reason: Unknown
% 0.13/0.39 % (26436)Instruction limit reached!
% 0.13/0.39 % (26436)------------------------------
% 0.13/0.39 % (26436)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.39 % (26435)Termination phase: shuffling
% 0.13/0.39
% 0.13/0.39 % (26435)Memory used [KB]: 1023
% 0.13/0.39 % (26435)Time elapsed: 0.004 s
% 0.13/0.39 % (26435)Instructions burned: 2 (million)
% 0.13/0.39 % (26435)------------------------------
% 0.13/0.39 % (26435)------------------------------
% 0.13/0.39 % (26436)Termination reason: Unknown
% 0.13/0.39 % (26436)Termination phase: shuffling
% 0.13/0.39
% 0.13/0.39 % (26436)Memory used [KB]: 1023
% 0.13/0.39 % (26436)Time elapsed: 0.004 s
% 0.13/0.39 % (26436)Instructions burned: 2 (million)
% 0.13/0.39 % (26436)------------------------------
% 0.13/0.39 % (26436)------------------------------
% 0.13/0.39 % (26433)Instruction limit reached!
% 0.13/0.39 % (26433)------------------------------
% 0.13/0.39 % (26433)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.39 % (26433)Termination reason: Unknown
% 0.13/0.39 % (26433)Termination phase: shuffling
% 0.13/0.39
% 0.13/0.39 % (26433)Memory used [KB]: 1023
% 0.13/0.39 % (26433)Time elapsed: 0.004 s
% 0.13/0.39 % (26433)Instructions burned: 4 (million)
% 0.13/0.39 % (26433)------------------------------
% 0.13/0.39 % (26433)------------------------------
% 0.13/0.40 % (26437)First to succeed.
% 0.13/0.40 % (26438)Also succeeded, but the first one will report.
% 0.13/0.40 % (26432)Also succeeded, but the first one will report.
% 0.13/0.40 % (26437)Refutation found. Thanks to Tanya!
% 0.13/0.40 % SZS status Theorem for theBenchmark
% 0.13/0.40 % SZS output start Proof for theBenchmark
% 0.13/0.40 thf(func_def_0, type, in: $i > ($i > $o) > $o).
% 0.13/0.40 thf(func_def_2, type, is_a: $i > ($i > $o) > $o).
% 0.13/0.40 thf(func_def_3, type, emptyset: $i > $o).
% 0.13/0.40 thf(func_def_4, type, unord_pair: $i > $i > $i > $o).
% 0.13/0.40 thf(func_def_5, type, singleton: $i > $i > $o).
% 0.13/0.40 thf(func_def_6, type, union: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.40 thf(func_def_7, type, excl_union: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.40 thf(func_def_8, type, intersection: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.40 thf(func_def_9, type, setminus: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.40 thf(func_def_10, type, complement: ($i > $o) > $i > $o).
% 0.13/0.40 thf(func_def_11, type, disjoint: ($i > $o) > ($i > $o) > $o).
% 0.13/0.40 thf(func_def_12, type, subset: ($i > $o) > ($i > $o) > $o).
% 0.13/0.40 thf(func_def_13, type, meets: ($i > $o) > ($i > $o) > $o).
% 0.13/0.40 thf(func_def_14, type, misses: ($i > $o) > ($i > $o) > $o).
% 0.13/0.40 thf(func_def_15, type, cartesian_product: ($i > $o) > ($i > $o) > $i > $i > $o).
% 0.13/0.40 thf(func_def_16, type, pair_rel: $i > $i > $i > $i > $o).
% 0.13/0.40 thf(func_def_17, type, id_rel: ($i > $o) > $i > $i > $o).
% 0.13/0.40 thf(func_def_18, type, sub_rel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.13/0.40 thf(func_def_19, type, is_rel_on: ($i > $i > $o) > ($i > $o) > ($i > $o) > $o).
% 0.13/0.40 thf(func_def_20, type, restrict_rel_domain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.13/0.40 thf(func_def_21, type, rel_diagonal: $i > $i > $o).
% 0.13/0.40 thf(func_def_22, type, rel_composition: ($i > $i > $o) > ($i > $i > $o) > $i > $i > $o).
% 0.13/0.40 thf(func_def_23, type, reflexive: ($i > $i > $o) > $o).
% 0.13/0.40 thf(func_def_24, type, irreflexive: ($i > $i > $o) > $o).
% 0.13/0.40 thf(func_def_25, type, symmetric: ($i > $i > $o) > $o).
% 0.13/0.40 thf(func_def_26, type, transitive: ($i > $i > $o) > $o).
% 0.13/0.40 thf(func_def_27, type, equiv_rel: ($i > $i > $o) > $o).
% 0.13/0.40 thf(func_def_28, type, rel_codomain: ($i > $i > $o) > $i > $o).
% 0.13/0.40 thf(func_def_29, type, rel_domain: ($i > $i > $o) > $i > $o).
% 0.13/0.40 thf(func_def_30, type, rel_inverse: ($i > $i > $o) > $i > $i > $o).
% 0.13/0.40 thf(func_def_31, type, equiv_classes: ($i > $i > $o) > ($i > $o) > $o).
% 0.13/0.40 thf(func_def_32, type, restrict_rel_codomain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.13/0.40 thf(func_def_33, type, rel_field: ($i > $i > $o) > $i > $o).
% 0.13/0.40 thf(func_def_34, type, well_founded: ($i > $i > $o) > $o).
% 0.13/0.40 thf(func_def_35, type, upwards_well_founded: ($i > $i > $o) > $o).
% 0.13/0.40 thf(func_def_52, type, sK0: $i > $o).
% 0.13/0.40 thf(func_def_53, type, sK1: $i > $i > $o).
% 0.13/0.40 thf(f161,plain,(
% 0.13/0.40 $false),
% 0.13/0.40 inference(avatar_sat_refutation,[],[f143,f153,f160])).
% 0.13/0.40 thf(f160,plain,(
% 0.13/0.40 ~spl2_1),
% 0.13/0.40 inference(avatar_contradiction_clause,[],[f159])).
% 0.13/0.40 thf(f159,plain,(
% 0.13/0.40 $false | ~spl2_1),
% 0.13/0.40 inference(trivial_inequality_removal,[],[f156])).
% 0.13/0.40 thf(f156,plain,(
% 0.13/0.40 ($false = $true) | ~spl2_1),
% 0.13/0.40 inference(superposition,[],[f132,f138])).
% 0.13/0.40 thf(f138,plain,(
% 0.13/0.40 ( ! [X1 : $i] : (($false = (sK1 @ X1 @ sK4))) ) | ~spl2_1),
% 0.13/0.40 inference(avatar_component_clause,[],[f137])).
% 0.13/0.40 thf(f137,plain,(
% 0.13/0.40 spl2_1 <=> ! [X1] : ($false = (sK1 @ X1 @ sK4))),
% 0.13/0.40 introduced(avatar_definition,[new_symbols(naming,[spl2_1])])).
% 0.13/0.40 thf(f132,plain,(
% 0.13/0.40 ((sK1 @ sK3 @ sK4) = $true)),
% 0.13/0.40 inference(binary_proxy_clausification,[],[f130])).
% 0.13/0.40 thf(f130,plain,(
% 0.13/0.40 ($false = ((sK1 @ sK3 @ sK4) => ((sK0 @ sK3) & (?? @ $i @ (^[Y0 : $i]: (sK1 @ Y0 @ sK4))))))),
% 0.13/0.40 inference(beta_eta_normalization,[],[f129])).
% 0.13/0.40 thf(f129,plain,(
% 0.13/0.40 (((^[Y0 : $i]: ((sK1 @ sK3 @ Y0) => ((sK0 @ sK3) & (?? @ $i @ (^[Y1 : $i]: (sK1 @ Y1 @ Y0)))))) @ sK4) = $false)),
% 0.13/0.40 inference(sigma_clausification,[],[f128])).
% 0.13/0.40 thf(f128,plain,(
% 0.13/0.40 ($false = (!! @ $i @ (^[Y0 : $i]: ((sK1 @ sK3 @ Y0) => ((sK0 @ sK3) & (?? @ $i @ (^[Y1 : $i]: (sK1 @ Y1 @ Y0))))))))),
% 0.13/0.40 inference(beta_eta_normalization,[],[f127])).
% 0.13/0.40 thf(f127,plain,(
% 0.13/0.40 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y0 @ Y1) => ((sK0 @ Y0) & (?? @ $i @ (^[Y2 : $i]: (sK1 @ Y2 @ Y1)))))))) @ sK3) = $false)),
% 0.13/0.40 inference(sigma_clausification,[],[f126])).
% 0.13/0.40 thf(f126,plain,(
% 0.13/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y0 @ Y1) => ((sK0 @ Y0) & (?? @ $i @ (^[Y2 : $i]: (sK1 @ Y2 @ Y1))))))))) != $true)),
% 0.13/0.40 inference(beta_eta_normalization,[],[f120])).
% 0.13/0.40 thf(f120,plain,(
% 0.13/0.40 (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))) @ sK1 @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y0 @ Y2) & (Y1 @ Y3))))))))) @ sK0 @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ sK1))) != $true)),
% 0.13/0.40 inference(definition_unfolding,[],[f113,f115,f112,f118])).
% 0.13/0.40 thf(f118,plain,(
% 0.13/0.40 (rel_codomain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.13/0.40 inference(cnf_transformation,[],[f42])).
% 0.13/0.40 thf(f42,plain,(
% 0.13/0.40 (rel_codomain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.13/0.40 inference(fool_elimination,[],[f41])).
% 0.13/0.40 thf(f41,plain,(
% 0.13/0.40 ((^[X0 : $i > $i > $o, X1 : $i] : (? [X2] : (X0 @ X2 @ X1))) = rel_codomain)),
% 0.13/0.40 inference(rectify,[],[f28])).
% 0.13/0.40 thf(f28,axiom,(
% 0.13/0.40 ((^[X8 : $i > $i > $o, X2 : $i] : (? [X0] : (X8 @ X0 @ X2))) = rel_codomain)),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',rel_codomain)).
% 0.13/0.40 thf(f112,plain,(
% 0.13/0.40 (cartesian_product = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y0 @ Y2) & (Y1 @ Y3))))))))))),
% 0.13/0.40 inference(cnf_transformation,[],[f68])).
% 0.13/0.40 thf(f68,plain,(
% 0.13/0.40 (cartesian_product = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y0 @ Y2) & (Y1 @ Y3))))))))))),
% 0.13/0.40 inference(fool_elimination,[],[f67])).
% 0.13/0.40 thf(f67,plain,(
% 0.13/0.40 (cartesian_product = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i, X3 : $i] : ((X1 @ X3) & (X0 @ X2))))),
% 0.13/0.40 inference(rectify,[],[f15])).
% 0.13/0.40 thf(f15,axiom,(
% 0.13/0.40 (cartesian_product = (^[X0 : $i > $o, X2 : $i > $o, X3 : $i, X4 : $i] : ((X2 @ X4) & (X0 @ X3))))),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product)).
% 0.13/0.40 thf(f115,plain,(
% 0.13/0.40 (sub_rel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 0.13/0.40 inference(cnf_transformation,[],[f72])).
% 0.13/0.40 thf(f72,plain,(
% 0.13/0.40 (sub_rel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 0.13/0.40 inference(fool_elimination,[],[f71])).
% 0.13/0.40 thf(f71,plain,(
% 0.13/0.40 (sub_rel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X3 @ X2) => (X1 @ X3 @ X2)))))),
% 0.13/0.40 inference(rectify,[],[f18])).
% 0.13/0.40 thf(f18,axiom,(
% 0.13/0.40 (sub_rel = (^[X6 : $i > $i > $o, X7 : $i > $i > $o] : (! [X2,X0] : ((X6 @ X0 @ X2) => (X7 @ X0 @ X2)))))),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',sub_rel)).
% 0.13/0.40 thf(f113,plain,(
% 0.13/0.40 ((sub_rel @ sK1 @ (cartesian_product @ sK0 @ (rel_codomain @ sK1))) != $true)),
% 0.13/0.40 inference(cnf_transformation,[],[f110])).
% 0.13/0.40 thf(f110,plain,(
% 0.13/0.40 ($true = (subset @ (rel_domain @ sK1) @ sK0)) & ((sub_rel @ sK1 @ (cartesian_product @ sK0 @ (rel_codomain @ sK1))) != $true)),
% 0.13/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f108,f109])).
% 0.13/0.40 thf(f109,plain,(
% 0.13/0.40 ? [X0 : $i > $o,X1 : $i > $i > $o] : (((subset @ (rel_domain @ X1) @ X0) = $true) & ($true != (sub_rel @ X1 @ (cartesian_product @ X0 @ (rel_codomain @ X1))))) => (($true = (subset @ (rel_domain @ sK1) @ sK0)) & ((sub_rel @ sK1 @ (cartesian_product @ sK0 @ (rel_codomain @ sK1))) != $true))),
% 0.13/0.40 introduced(choice_axiom,[])).
% 0.13/0.40 thf(f108,plain,(
% 0.13/0.40 ? [X0 : $i > $o,X1 : $i > $i > $o] : (((subset @ (rel_domain @ X1) @ X0) = $true) & ($true != (sub_rel @ X1 @ (cartesian_product @ X0 @ (rel_codomain @ X1)))))),
% 0.13/0.40 inference(ennf_transformation,[],[f50])).
% 0.13/0.40 thf(f50,plain,(
% 0.13/0.40 ~! [X0 : $i > $o,X1 : $i > $i > $o] : (((subset @ (rel_domain @ X1) @ X0) = $true) => ($true = (sub_rel @ X1 @ (cartesian_product @ X0 @ (rel_codomain @ X1)))))),
% 0.13/0.40 inference(fool_elimination,[],[f49])).
% 0.13/0.40 thf(f49,plain,(
% 0.13/0.40 ~! [X0 : $i > $o,X1 : $i > $i > $o] : ((subset @ (rel_domain @ X1) @ X0) => (sub_rel @ X1 @ (cartesian_product @ X0 @ (rel_codomain @ X1))))),
% 0.13/0.40 inference(rectify,[],[f37])).
% 0.13/0.40 thf(f37,negated_conjecture,(
% 0.13/0.40 ~! [X0 : $i > $o,X8 : $i > $i > $o] : ((subset @ (rel_domain @ X8) @ X0) => (sub_rel @ X8 @ (cartesian_product @ X0 @ (rel_codomain @ X8))))),
% 0.13/0.40 inference(negated_conjecture,[],[f36])).
% 0.13/0.40 thf(f36,conjecture,(
% 0.13/0.40 ! [X0 : $i > $o,X8 : $i > $i > $o] : ((subset @ (rel_domain @ X8) @ X0) => (sub_rel @ X8 @ (cartesian_product @ X0 @ (rel_codomain @ X8))))),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm)).
% 0.13/0.40 thf(f153,plain,(
% 0.13/0.40 ~spl2_2),
% 0.13/0.40 inference(avatar_contradiction_clause,[],[f152])).
% 0.13/0.40 thf(f152,plain,(
% 0.13/0.40 $false | ~spl2_2),
% 0.13/0.40 inference(trivial_inequality_removal,[],[f151])).
% 0.13/0.40 thf(f151,plain,(
% 0.13/0.40 ($false = $true) | ~spl2_2),
% 0.13/0.40 inference(forward_demodulation,[],[f146,f142])).
% 0.13/0.40 thf(f142,plain,(
% 0.13/0.40 ($false = (sK0 @ sK3)) | ~spl2_2),
% 0.13/0.40 inference(avatar_component_clause,[],[f140])).
% 0.13/0.40 thf(f140,plain,(
% 0.13/0.40 spl2_2 <=> ($false = (sK0 @ sK3))),
% 0.13/0.40 introduced(avatar_definition,[new_symbols(naming,[spl2_2])])).
% 0.13/0.40 thf(f146,plain,(
% 0.13/0.40 ($true = (sK0 @ sK3))),
% 0.13/0.40 inference(trivial_inequality_removal,[],[f144])).
% 0.13/0.40 thf(f144,plain,(
% 0.13/0.40 ($true = (sK0 @ sK3)) | ($false = $true)),
% 0.13/0.40 inference(superposition,[],[f132,f125])).
% 0.13/0.40 thf(f125,plain,(
% 0.13/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (sK1 @ X1 @ X2)) | ($true = (sK0 @ X1))) )),
% 0.13/0.40 inference(pi_clausification,[],[f124])).
% 0.13/0.40 thf(f124,plain,(
% 0.13/0.40 ( ! [X1 : $i] : (($false = (?? @ $i @ (sK1 @ X1))) | ($true = (sK0 @ X1))) )),
% 0.13/0.40 inference(binary_proxy_clausification,[],[f123])).
% 0.13/0.40 thf(f123,plain,(
% 0.13/0.40 ( ! [X1 : $i] : ((((?? @ $i @ (sK1 @ X1)) => (sK0 @ X1)) = $true)) )),
% 0.13/0.40 inference(beta_eta_normalization,[],[f122])).
% 0.13/0.40 thf(f122,plain,(
% 0.13/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((?? @ $i @ (sK1 @ Y0)) => (sK0 @ Y0))) @ X1))) )),
% 0.13/0.40 inference(pi_clausification,[],[f121])).
% 0.13/0.40 thf(f121,plain,(
% 0.13/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (sK1 @ Y0)) => (sK0 @ Y0)))))),
% 0.13/0.40 inference(beta_eta_normalization,[],[f119])).
% 0.13/0.40 thf(f119,plain,(
% 0.13/0.40 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ sK1) @ sK0))),
% 0.13/0.40 inference(definition_unfolding,[],[f114,f117,f116])).
% 0.13/0.40 thf(f116,plain,(
% 0.13/0.40 (rel_domain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.13/0.40 inference(cnf_transformation,[],[f62])).
% 0.13/0.40 thf(f62,plain,(
% 0.13/0.40 (rel_domain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.13/0.40 inference(fool_elimination,[],[f61])).
% 0.13/0.40 thf(f61,plain,(
% 0.13/0.40 (rel_domain = (^[X0 : $i > $i > $o, X1 : $i] : (? [X2] : (X0 @ X1 @ X2))))),
% 0.13/0.40 inference(rectify,[],[f29])).
% 0.13/0.40 thf(f29,axiom,(
% 0.13/0.40 (rel_domain = (^[X8 : $i > $i > $o, X0 : $i] : (? [X2] : (X8 @ X0 @ X2))))),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',rel_domain)).
% 0.13/0.40 thf(f117,plain,(
% 0.13/0.40 (subset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.13/0.40 inference(cnf_transformation,[],[f46])).
% 0.13/0.40 thf(f46,plain,(
% 0.13/0.40 (subset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.13/0.40 inference(fool_elimination,[],[f45])).
% 0.13/0.40 thf(f45,plain,(
% 0.13/0.40 ((^[X0 : $i > $o, X1 : $i > $o] : (! [X2] : ((X0 @ X2) => (X1 @ X2)))) = subset)),
% 0.13/0.40 inference(rectify,[],[f12])).
% 0.13/0.40 thf(f12,axiom,(
% 0.13/0.40 ((^[X0 : $i > $o, X2 : $i > $o] : (! [X3] : ((X0 @ X3) => (X2 @ X3)))) = subset)),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset)).
% 0.13/0.40 thf(f114,plain,(
% 0.13/0.40 ($true = (subset @ (rel_domain @ sK1) @ sK0))),
% 0.13/0.40 inference(cnf_transformation,[],[f110])).
% 0.13/0.40 thf(f143,plain,(
% 0.13/0.40 spl2_1 | spl2_2),
% 0.13/0.40 inference(avatar_split_clause,[],[f135,f140,f137])).
% 0.13/0.40 thf(f135,plain,(
% 0.13/0.40 ( ! [X1 : $i] : (($false = (sK0 @ sK3)) | ($false = (sK1 @ X1 @ sK4))) )),
% 0.13/0.40 inference(beta_eta_normalization,[],[f134])).
% 0.13/0.40 thf(f134,plain,(
% 0.13/0.40 ( ! [X1 : $i] : (($false = (sK0 @ sK3)) | (((^[Y0 : $i]: (sK1 @ Y0 @ sK4)) @ X1) = $false)) )),
% 0.13/0.40 inference(pi_clausification,[],[f133])).
% 0.13/0.40 thf(f133,plain,(
% 0.13/0.40 ($false = (sK0 @ sK3)) | ($false = (?? @ $i @ (^[Y0 : $i]: (sK1 @ Y0 @ sK4))))),
% 0.13/0.40 inference(binary_proxy_clausification,[],[f131])).
% 0.13/0.40 thf(f131,plain,(
% 0.13/0.40 ($false = ((sK0 @ sK3) & (?? @ $i @ (^[Y0 : $i]: (sK1 @ Y0 @ sK4)))))),
% 0.13/0.40 inference(binary_proxy_clausification,[],[f130])).
% 0.13/0.40 % SZS output end Proof for theBenchmark
% 0.13/0.40 % (26437)------------------------------
% 0.13/0.40 % (26437)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.40 % (26437)Termination reason: Refutation
% 0.13/0.40
% 0.13/0.40 % (26437)Memory used [KB]: 5628
% 0.13/0.40 % (26437)Time elapsed: 0.010 s
% 0.13/0.40 % (26437)Instructions burned: 8 (million)
% 0.13/0.40 % (26437)------------------------------
% 0.13/0.40 % (26437)------------------------------
% 0.13/0.40 % (26431)Success in time 0.017 s
%------------------------------------------------------------------------------