TSTP Solution File: SET649^3 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET649^3 : 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 : n032.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 03:12:39 EDT 2024
% Result : Theorem 0.15s 0.32s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SET649^3 : TPTP v8.2.0. Released v3.6.0.
% 0.05/0.11 % 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
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon May 20 11:34:37 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.30 This is a TH0_THM_EQU_NAR problem
% 0.10/0.30 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
% 0.15/0.31 % (28438)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)
% 0.15/0.31 % (28440)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.31 % (28435)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)
% 0.15/0.31 % (28438)Instruction limit reached!
% 0.15/0.31 % (28438)------------------------------
% 0.15/0.31 % (28438)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.31 % (28438)Termination reason: Unknown
% 0.15/0.31 % (28438)Termination phase: shuffling
% 0.15/0.31
% 0.15/0.31 % (28438)Memory used [KB]: 1023
% 0.15/0.31 % (28438)Time elapsed: 0.002 s
% 0.15/0.31 % (28438)Instructions burned: 3 (million)
% 0.15/0.31 % (28438)------------------------------
% 0.15/0.31 % (28438)------------------------------
% 0.15/0.31 % (28435)Instruction limit reached!
% 0.15/0.31 % (28435)------------------------------
% 0.15/0.31 % (28435)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.31 % (28435)Termination reason: Unknown
% 0.15/0.31 % (28435)Termination phase: Property scanning
% 0.15/0.31
% 0.15/0.31 % (28435)Memory used [KB]: 1023
% 0.15/0.31 % (28435)Time elapsed: 0.003 s
% 0.15/0.31 % (28435)Instructions burned: 5 (million)
% 0.15/0.31 % (28435)------------------------------
% 0.15/0.31 % (28435)------------------------------
% 0.15/0.31 % (28439)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)
% 0.15/0.31 % (28441)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)
% 0.15/0.31 % (28441)Instruction limit reached!
% 0.15/0.31 % (28441)------------------------------
% 0.15/0.31 % (28441)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.31 % (28441)Termination reason: Unknown
% 0.15/0.31 % (28441)Termination phase: shuffling
% 0.15/0.31
% 0.15/0.31 % (28441)Memory used [KB]: 1023
% 0.15/0.31 % (28441)Time elapsed: 0.003 s
% 0.15/0.31 % (28441)Instructions burned: 3 (million)
% 0.15/0.31 % (28441)------------------------------
% 0.15/0.31 % (28441)------------------------------
% 0.15/0.31 % (28440)First to succeed.
% 0.15/0.31 % (28437)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.32 % (28434)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.32 % (28439)Also succeeded, but the first one will report.
% 0.15/0.32 % (28437)Instruction limit reached!
% 0.15/0.32 % (28437)------------------------------
% 0.15/0.32 % (28437)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (28437)Termination reason: Unknown
% 0.15/0.32 % (28437)Termination phase: shuffling
% 0.15/0.32
% 0.15/0.32 % (28437)Memory used [KB]: 1023
% 0.15/0.32 % (28437)Time elapsed: 0.003 s
% 0.15/0.32 % (28437)Instructions burned: 3 (million)
% 0.15/0.32 % (28437)------------------------------
% 0.15/0.32 % (28437)------------------------------
% 0.15/0.32 % (28440)Refutation found. Thanks to Tanya!
% 0.15/0.32 % SZS status Theorem for theBenchmark
% 0.15/0.32 % SZS output start Proof for theBenchmark
% 0.15/0.32 thf(func_def_0, type, in: $i > ($i > $o) > $o).
% 0.15/0.32 thf(func_def_2, type, is_a: $i > ($i > $o) > $o).
% 0.15/0.32 thf(func_def_3, type, emptyset: $i > $o).
% 0.15/0.32 thf(func_def_4, type, unord_pair: $i > $i > $i > $o).
% 0.15/0.32 thf(func_def_5, type, singleton: $i > $i > $o).
% 0.15/0.32 thf(func_def_6, type, union: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_7, type, excl_union: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_8, type, intersection: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_9, type, setminus: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_10, type, complement: ($i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_11, type, disjoint: ($i > $o) > ($i > $o) > $o).
% 0.15/0.32 thf(func_def_12, type, subset: ($i > $o) > ($i > $o) > $o).
% 0.15/0.32 thf(func_def_13, type, meets: ($i > $o) > ($i > $o) > $o).
% 0.15/0.32 thf(func_def_14, type, misses: ($i > $o) > ($i > $o) > $o).
% 0.15/0.32 thf(func_def_15, type, cartesian_product: ($i > $o) > ($i > $o) > $i > $i > $o).
% 0.15/0.32 thf(func_def_16, type, pair_rel: $i > $i > $i > $i > $o).
% 0.15/0.32 thf(func_def_17, type, id_rel: ($i > $o) > $i > $i > $o).
% 0.15/0.32 thf(func_def_18, type, sub_rel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.15/0.32 thf(func_def_19, type, is_rel_on: ($i > $i > $o) > ($i > $o) > ($i > $o) > $o).
% 0.15/0.32 thf(func_def_20, type, restrict_rel_domain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.15/0.32 thf(func_def_21, type, rel_diagonal: $i > $i > $o).
% 0.15/0.32 thf(func_def_22, type, rel_composition: ($i > $i > $o) > ($i > $i > $o) > $i > $i > $o).
% 0.15/0.32 thf(func_def_23, type, reflexive: ($i > $i > $o) > $o).
% 0.15/0.32 thf(func_def_24, type, irreflexive: ($i > $i > $o) > $o).
% 0.15/0.32 thf(func_def_25, type, symmetric: ($i > $i > $o) > $o).
% 0.15/0.32 thf(func_def_26, type, transitive: ($i > $i > $o) > $o).
% 0.15/0.32 thf(func_def_27, type, equiv_rel: ($i > $i > $o) > $o).
% 0.15/0.32 thf(func_def_28, type, rel_codomain: ($i > $i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_29, type, rel_domain: ($i > $i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_30, type, rel_inverse: ($i > $i > $o) > $i > $i > $o).
% 0.15/0.32 thf(func_def_31, type, equiv_classes: ($i > $i > $o) > ($i > $o) > $o).
% 0.15/0.32 thf(func_def_32, type, restrict_rel_codomain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.15/0.32 thf(func_def_33, type, rel_field: ($i > $i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_34, type, well_founded: ($i > $i > $o) > $o).
% 0.15/0.32 thf(func_def_35, type, upwards_well_founded: ($i > $i > $o) > $o).
% 0.15/0.32 thf(func_def_52, type, sK0: $i > $o).
% 0.15/0.32 thf(func_def_53, type, sK1: $i > $i > $o).
% 0.15/0.32 thf(func_def_54, type, sK2: $i > $o).
% 0.15/0.32 thf(f198,plain,(
% 0.15/0.32 $false),
% 0.15/0.32 inference(avatar_sat_refutation,[],[f183,f190,f197])).
% 0.15/0.32 thf(f197,plain,(
% 0.15/0.32 ~spl3_1),
% 0.15/0.32 inference(avatar_contradiction_clause,[],[f196])).
% 0.15/0.32 thf(f196,plain,(
% 0.15/0.32 $false | ~spl3_1),
% 0.15/0.32 inference(trivial_inequality_removal,[],[f195])).
% 0.15/0.32 thf(f195,plain,(
% 0.15/0.32 ($false = $true) | ~spl3_1),
% 0.15/0.32 inference(backward_demodulation,[],[f173,f194])).
% 0.15/0.32 thf(f194,plain,(
% 0.15/0.32 ( ! [X0 : $i] : (($false = (sK1 @ X0 @ sK4))) ) | ~spl3_1),
% 0.15/0.32 inference(trivial_inequality_removal,[],[f192])).
% 0.15/0.32 thf(f192,plain,(
% 0.15/0.32 ( ! [X0 : $i] : (($false = (sK1 @ X0 @ sK4)) | ($false = $true)) ) | ~spl3_1),
% 0.15/0.32 inference(superposition,[],[f161,f178])).
% 0.15/0.32 thf(f178,plain,(
% 0.15/0.32 ((sK0 @ sK4) = $false) | ~spl3_1),
% 0.15/0.32 inference(avatar_component_clause,[],[f176])).
% 0.15/0.32 thf(f176,plain,(
% 0.15/0.32 spl3_1 <=> ((sK0 @ sK4) = $false)),
% 0.15/0.32 introduced(avatar_definition,[new_symbols(naming,[spl3_1])])).
% 0.15/0.32 thf(f161,plain,(
% 0.15/0.32 ( ! [X2 : $i,X1 : $i] : (((sK0 @ X1) = $true) | ((sK1 @ X2 @ X1) = $false)) )),
% 0.15/0.32 inference(beta_eta_normalization,[],[f160])).
% 0.15/0.32 thf(f160,plain,(
% 0.15/0.32 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (sK1 @ Y0 @ X1)) @ X2) = $false) | ((sK0 @ X1) = $true)) )),
% 0.15/0.32 inference(pi_clausification,[],[f159])).
% 0.15/0.32 thf(f159,plain,(
% 0.15/0.32 ( ! [X1 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: (sK1 @ Y0 @ X1)))) | ((sK0 @ X1) = $true)) )),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f158])).
% 0.15/0.32 thf(f158,plain,(
% 0.15/0.32 ( ! [X1 : $i] : ((((?? @ $i @ (^[Y0 : $i]: (sK1 @ Y0 @ X1))) => (sK0 @ X1)) = $true)) )),
% 0.15/0.32 inference(beta_eta_normalization,[],[f157])).
% 0.15/0.32 thf(f157,plain,(
% 0.15/0.32 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (sK1 @ Y1 @ Y0))) => (sK0 @ Y0))) @ X1))) )),
% 0.15/0.32 inference(pi_clausification,[],[f156])).
% 0.15/0.32 thf(f156,plain,(
% 0.15/0.32 ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (sK1 @ Y1 @ Y0))) => (sK0 @ Y0)))) = $true)),
% 0.15/0.32 inference(beta_eta_normalization,[],[f153])).
% 0.15/0.32 thf(f153,plain,(
% 0.15/0.32 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ sK1) @ sK0) = $true)),
% 0.15/0.32 inference(definition_unfolding,[],[f121,f139,f115])).
% 0.15/0.32 thf(f115,plain,(
% 0.15/0.32 (rel_codomain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.15/0.32 inference(cnf_transformation,[],[f103])).
% 0.15/0.32 thf(f103,plain,(
% 0.15/0.32 (rel_codomain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.15/0.32 inference(fool_elimination,[],[f102])).
% 0.15/0.32 thf(f102,plain,(
% 0.15/0.32 (rel_codomain = (^[X0 : $i > $i > $o, X1 : $i] : (? [X2] : (X0 @ X2 @ X1))))),
% 0.15/0.32 inference(rectify,[],[f28])).
% 0.15/0.32 thf(f28,axiom,(
% 0.15/0.32 (rel_codomain = (^[X8 : $i > $i > $o, X2 : $i] : (? [X0] : (X8 @ X0 @ X2))))),
% 0.15/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',rel_codomain)).
% 0.15/0.32 thf(f139,plain,(
% 0.15/0.32 (subset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.15/0.32 inference(cnf_transformation,[],[f97])).
% 0.15/0.32 thf(f97,plain,(
% 0.15/0.32 (subset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.15/0.32 inference(fool_elimination,[],[f96])).
% 0.15/0.32 thf(f96,plain,(
% 0.15/0.32 (subset = (^[X0 : $i > $o, X1 : $i > $o] : (! [X2] : ((X0 @ X2) => (X1 @ X2)))))),
% 0.15/0.32 inference(rectify,[],[f12])).
% 0.15/0.32 thf(f12,axiom,(
% 0.15/0.32 (subset = (^[X0 : $i > $o, X2 : $i > $o] : (! [X3] : ((X0 @ X3) => (X2 @ X3)))))),
% 0.15/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset)).
% 0.15/0.32 thf(f121,plain,(
% 0.15/0.32 ((subset @ (rel_codomain @ sK1) @ sK0) = $true)),
% 0.15/0.32 inference(cnf_transformation,[],[f111])).
% 0.15/0.32 thf(f111,plain,(
% 0.15/0.32 ((subset @ (rel_codomain @ sK1) @ sK0) = $true) & ($true != (sub_rel @ sK1 @ (cartesian_product @ sK2 @ sK0))) & ($true = (subset @ (rel_domain @ sK1) @ sK2))),
% 0.15/0.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f109,f110])).
% 0.15/0.32 thf(f110,plain,(
% 0.15/0.32 ? [X0 : $i > $o,X1 : $i > $i > $o,X2 : $i > $o] : (((subset @ (rel_codomain @ X1) @ X0) = $true) & ((sub_rel @ X1 @ (cartesian_product @ X2 @ X0)) != $true) & ((subset @ (rel_domain @ X1) @ X2) = $true)) => (((subset @ (rel_codomain @ sK1) @ sK0) = $true) & ($true != (sub_rel @ sK1 @ (cartesian_product @ sK2 @ sK0))) & ($true = (subset @ (rel_domain @ sK1) @ sK2)))),
% 0.15/0.32 introduced(choice_axiom,[])).
% 0.15/0.32 thf(f109,plain,(
% 0.15/0.32 ? [X0 : $i > $o,X1 : $i > $i > $o,X2 : $i > $o] : (((subset @ (rel_codomain @ X1) @ X0) = $true) & ((sub_rel @ X1 @ (cartesian_product @ X2 @ X0)) != $true) & ((subset @ (rel_domain @ X1) @ X2) = $true))),
% 0.15/0.32 inference(flattening,[],[f108])).
% 0.15/0.32 thf(f108,plain,(
% 0.15/0.32 ? [X0 : $i > $o,X1 : $i > $i > $o,X2 : $i > $o] : (((sub_rel @ X1 @ (cartesian_product @ X2 @ X0)) != $true) & (((subset @ (rel_codomain @ X1) @ X0) = $true) & ((subset @ (rel_domain @ X1) @ X2) = $true)))),
% 0.15/0.32 inference(ennf_transformation,[],[f42])).
% 0.15/0.32 thf(f42,plain,(
% 0.15/0.32 ~! [X0 : $i > $o,X1 : $i > $i > $o,X2 : $i > $o] : ((((subset @ (rel_codomain @ X1) @ X0) = $true) & ((subset @ (rel_domain @ X1) @ X2) = $true)) => ((sub_rel @ X1 @ (cartesian_product @ X2 @ X0)) = $true))),
% 0.15/0.32 inference(fool_elimination,[],[f41])).
% 0.15/0.32 thf(f41,plain,(
% 0.15/0.32 ~! [X0 : $i > $o,X1 : $i > $i > $o,X2 : $i > $o] : (((subset @ (rel_codomain @ X1) @ X0) & (subset @ (rel_domain @ X1) @ X2)) => (sub_rel @ X1 @ (cartesian_product @ X2 @ X0)))),
% 0.15/0.32 inference(rectify,[],[f37])).
% 0.15/0.32 thf(f37,negated_conjecture,(
% 0.15/0.32 ~! [X2 : $i > $o,X8 : $i > $i > $o,X0 : $i > $o] : (((subset @ (rel_codomain @ X8) @ X2) & (subset @ (rel_domain @ X8) @ X0)) => (sub_rel @ X8 @ (cartesian_product @ X0 @ X2)))),
% 0.15/0.32 inference(negated_conjecture,[],[f36])).
% 0.15/0.32 thf(f36,conjecture,(
% 0.15/0.32 ! [X2 : $i > $o,X8 : $i > $i > $o,X0 : $i > $o] : (((subset @ (rel_codomain @ X8) @ X2) & (subset @ (rel_domain @ X8) @ X0)) => (sub_rel @ X8 @ (cartesian_product @ X0 @ X2)))),
% 0.15/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm)).
% 0.15/0.32 thf(f173,plain,(
% 0.15/0.32 ((sK1 @ sK5 @ sK4) = $true)),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f171])).
% 0.15/0.32 thf(f171,plain,(
% 0.15/0.32 (((sK1 @ sK5 @ sK4) => ((sK2 @ sK5) & (sK0 @ sK4))) = $false)),
% 0.15/0.32 inference(beta_eta_normalization,[],[f170])).
% 0.15/0.32 thf(f170,plain,(
% 0.15/0.32 (((^[Y0 : $i]: ((sK1 @ Y0 @ sK4) => ((sK2 @ Y0) & (sK0 @ sK4)))) @ sK5) = $false)),
% 0.15/0.32 inference(sigma_clausification,[],[f169])).
% 0.15/0.32 thf(f169,plain,(
% 0.15/0.32 ($false = (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0 @ sK4) => ((sK2 @ Y0) & (sK0 @ sK4))))))),
% 0.15/0.32 inference(beta_eta_normalization,[],[f168])).
% 0.15/0.32 thf(f168,plain,(
% 0.15/0.32 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1 @ Y0) => ((sK2 @ Y1) & (sK0 @ Y0)))))) @ sK4))),
% 0.15/0.32 inference(sigma_clausification,[],[f167])).
% 0.15/0.32 thf(f167,plain,(
% 0.15/0.32 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1 @ Y0) => ((sK2 @ Y1) & (sK0 @ Y0))))))) != $true)),
% 0.15/0.32 inference(beta_eta_normalization,[],[f154])).
% 0.15/0.32 thf(f154,plain,(
% 0.15/0.32 (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))) @ sK1 @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y0 @ Y2) & (Y1 @ Y3))))))))) @ sK2 @ sK0)) != $true)),
% 0.15/0.32 inference(definition_unfolding,[],[f120,f130,f134])).
% 0.15/0.32 thf(f134,plain,(
% 0.15/0.32 (cartesian_product = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y0 @ Y2) & (Y1 @ Y3))))))))))),
% 0.15/0.32 inference(cnf_transformation,[],[f59])).
% 0.15/0.32 thf(f59,plain,(
% 0.15/0.32 (cartesian_product = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y0 @ Y2) & (Y1 @ Y3))))))))))),
% 0.15/0.32 inference(fool_elimination,[],[f58])).
% 0.15/0.32 thf(f58,plain,(
% 0.15/0.32 (cartesian_product = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i, X3 : $i] : ((X1 @ X3) & (X0 @ X2))))),
% 0.15/0.32 inference(rectify,[],[f15])).
% 0.15/0.32 thf(f15,axiom,(
% 0.15/0.32 (cartesian_product = (^[X0 : $i > $o, X2 : $i > $o, X3 : $i, X4 : $i] : ((X2 @ X4) & (X0 @ X3))))),
% 0.15/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product)).
% 0.15/0.32 thf(f130,plain,(
% 0.15/0.32 (sub_rel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))))),
% 0.15/0.32 inference(cnf_transformation,[],[f86])).
% 0.15/0.32 thf(f86,plain,(
% 0.15/0.32 (sub_rel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))))),
% 0.15/0.32 inference(fool_elimination,[],[f85])).
% 0.15/0.32 thf(f85,plain,(
% 0.15/0.32 ((^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))) = sub_rel)),
% 0.15/0.32 inference(rectify,[],[f18])).
% 0.15/0.32 thf(f18,axiom,(
% 0.15/0.32 ((^[X6 : $i > $i > $o, X7 : $i > $i > $o] : (! [X0,X2] : ((X6 @ X0 @ X2) => (X7 @ X0 @ X2)))) = sub_rel)),
% 0.15/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',sub_rel)).
% 0.15/0.32 thf(f120,plain,(
% 0.15/0.32 ($true != (sub_rel @ sK1 @ (cartesian_product @ sK2 @ sK0)))),
% 0.15/0.32 inference(cnf_transformation,[],[f111])).
% 0.15/0.32 thf(f190,plain,(
% 0.15/0.32 ~spl3_2),
% 0.15/0.32 inference(avatar_contradiction_clause,[],[f189])).
% 0.15/0.32 thf(f189,plain,(
% 0.15/0.32 $false | ~spl3_2),
% 0.15/0.32 inference(trivial_inequality_removal,[],[f188])).
% 0.15/0.32 thf(f188,plain,(
% 0.15/0.32 ($false = $true) | ~spl3_2),
% 0.15/0.32 inference(backward_demodulation,[],[f173,f187])).
% 0.15/0.32 thf(f187,plain,(
% 0.15/0.32 ( ! [X0 : $i] : (($false = (sK1 @ sK5 @ X0))) ) | ~spl3_2),
% 0.15/0.32 inference(trivial_inequality_removal,[],[f185])).
% 0.15/0.32 thf(f185,plain,(
% 0.15/0.32 ( ! [X0 : $i] : (($false = (sK1 @ sK5 @ X0)) | ($false = $true)) ) | ~spl3_2),
% 0.15/0.32 inference(superposition,[],[f182,f166])).
% 0.15/0.32 thf(f166,plain,(
% 0.15/0.32 ( ! [X2 : $i,X1 : $i] : (($true = (sK2 @ X1)) | ($false = (sK1 @ X1 @ X2))) )),
% 0.15/0.32 inference(pi_clausification,[],[f165])).
% 0.15/0.32 thf(f165,plain,(
% 0.15/0.32 ( ! [X1 : $i] : (($true = (sK2 @ X1)) | ((?? @ $i @ (sK1 @ X1)) = $false)) )),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f164])).
% 0.15/0.32 thf(f164,plain,(
% 0.15/0.32 ( ! [X1 : $i] : ((((?? @ $i @ (sK1 @ X1)) => (sK2 @ X1)) = $true)) )),
% 0.15/0.32 inference(beta_eta_normalization,[],[f163])).
% 0.15/0.32 thf(f163,plain,(
% 0.15/0.32 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((?? @ $i @ (sK1 @ Y0)) => (sK2 @ Y0))) @ X1))) )),
% 0.15/0.32 inference(pi_clausification,[],[f162])).
% 0.15/0.32 thf(f162,plain,(
% 0.15/0.32 ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (sK1 @ Y0)) => (sK2 @ Y0)))) = $true)),
% 0.15/0.32 inference(beta_eta_normalization,[],[f155])).
% 0.15/0.32 thf(f155,plain,(
% 0.15/0.32 (((^[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) @ sK2) = $true)),
% 0.15/0.32 inference(definition_unfolding,[],[f119,f139,f129])).
% 0.15/0.32 thf(f129,plain,(
% 0.15/0.32 (rel_domain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.15/0.32 inference(cnf_transformation,[],[f48])).
% 0.15/0.32 thf(f48,plain,(
% 0.15/0.32 (rel_domain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.15/0.32 inference(fool_elimination,[],[f47])).
% 0.15/0.32 thf(f47,plain,(
% 0.15/0.32 ((^[X0 : $i > $i > $o, X1 : $i] : (? [X2] : (X0 @ X1 @ X2))) = rel_domain)),
% 0.15/0.32 inference(rectify,[],[f29])).
% 0.15/0.32 thf(f29,axiom,(
% 0.15/0.32 ((^[X8 : $i > $i > $o, X0 : $i] : (? [X2] : (X8 @ X0 @ X2))) = rel_domain)),
% 0.15/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',rel_domain)).
% 0.15/0.32 thf(f119,plain,(
% 0.15/0.32 ($true = (subset @ (rel_domain @ sK1) @ sK2))),
% 0.15/0.32 inference(cnf_transformation,[],[f111])).
% 0.15/0.32 thf(f182,plain,(
% 0.15/0.32 ((sK2 @ sK5) = $false) | ~spl3_2),
% 0.15/0.32 inference(avatar_component_clause,[],[f180])).
% 0.15/0.32 thf(f180,plain,(
% 0.15/0.32 spl3_2 <=> ((sK2 @ sK5) = $false)),
% 0.15/0.32 introduced(avatar_definition,[new_symbols(naming,[spl3_2])])).
% 0.15/0.32 thf(f183,plain,(
% 0.15/0.32 spl3_1 | spl3_2),
% 0.15/0.32 inference(avatar_split_clause,[],[f174,f180,f176])).
% 0.15/0.32 thf(f174,plain,(
% 0.15/0.32 ((sK2 @ sK5) = $false) | ((sK0 @ sK4) = $false)),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f172])).
% 0.15/0.32 thf(f172,plain,(
% 0.15/0.32 (((sK2 @ sK5) & (sK0 @ sK4)) = $false)),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f171])).
% 0.15/0.32 % SZS output end Proof for theBenchmark
% 0.15/0.32 % (28440)------------------------------
% 0.15/0.32 % (28440)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (28440)Termination reason: Refutation
% 0.15/0.32
% 0.15/0.32 % (28440)Memory used [KB]: 5628
% 0.15/0.32 % (28440)Time elapsed: 0.006 s
% 0.15/0.32 % (28440)Instructions burned: 11 (million)
% 0.15/0.32 % (28440)------------------------------
% 0.15/0.32 % (28440)------------------------------
% 0.15/0.32 % (28433)Success in time 0.007 s
% 0.15/0.32 % Vampire---4.8 exiting
%------------------------------------------------------------------------------