TSTP Solution File: SET646^3 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET646^3 : TPTP v8.1.2. 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 : n025.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 : Sun May 5 09:07:48 EDT 2024
% Result : Theorem 0.12s 0.38s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET646^3 : TPTP v8.1.2. Released v3.6.0.
% 0.06/0.14 % 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
% 0.12/0.35 % Computer : n025.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri May 3 16:47:38 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.35 This is a TH0_THM_EQU_NAR problem
% 0.12/0.35 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/tmp/tmp.EvgzfDd5wZ/Vampire---4.8_18811
% 0.12/0.37 % (18928)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.12/0.37 % (18925)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.12/0.37 % (18924)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.12/0.37 % (18927)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.12/0.37 % (18922)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 Vampire---4 for (2999ds/4Mi)
% 0.12/0.37 % (18924)Instruction limit reached!
% 0.12/0.37 % (18924)------------------------------
% 0.12/0.37 % (18924)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37 % (18926)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.12/0.37 % (18924)Termination reason: Unknown
% 0.12/0.37 % (18924)Termination phase: shuffling
% 0.12/0.37
% 0.12/0.37 % (18924)Memory used [KB]: 1023
% 0.12/0.37 % (18925)Instruction limit reached!
% 0.12/0.37 % (18925)------------------------------
% 0.12/0.37 % (18925)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37 % (18925)Termination reason: Unknown
% 0.12/0.37 % (18925)Termination phase: shuffling
% 0.12/0.37
% 0.12/0.37 % (18925)Memory used [KB]: 1023
% 0.12/0.37 % (18925)Time elapsed: 0.003 s
% 0.12/0.37 % (18925)Instructions burned: 2 (million)
% 0.12/0.37 % (18925)------------------------------
% 0.12/0.37 % (18925)------------------------------
% 0.12/0.37 % (18924)Time elapsed: 0.002 s
% 0.12/0.37 % (18924)Instructions burned: 2 (million)
% 0.12/0.37 % (18924)------------------------------
% 0.12/0.37 % (18924)------------------------------
% 0.12/0.37 % (18923)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 Vampire---4 for (2999ds/27Mi)
% 0.12/0.37 % (18928)Instruction limit reached!
% 0.12/0.37 % (18928)------------------------------
% 0.12/0.37 % (18928)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37 % (18928)Termination reason: Unknown
% 0.12/0.37 % (18928)Termination phase: shuffling
% 0.12/0.37
% 0.12/0.37 % (18928)Memory used [KB]: 1023
% 0.12/0.37 % (18928)Time elapsed: 0.003 s
% 0.12/0.37 % (18928)Instructions burned: 3 (million)
% 0.12/0.37 % (18928)------------------------------
% 0.12/0.37 % (18928)------------------------------
% 0.12/0.37 % (18922)Instruction limit reached!
% 0.12/0.37 % (18922)------------------------------
% 0.12/0.37 % (18922)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37 % (18922)Termination reason: Unknown
% 0.12/0.37 % (18922)Termination phase: Property scanning
% 0.12/0.37
% 0.12/0.37 % (18922)Memory used [KB]: 1023
% 0.12/0.37 % (18922)Time elapsed: 0.004 s
% 0.12/0.37 % (18922)Instructions burned: 5 (million)
% 0.12/0.37 % (18922)------------------------------
% 0.12/0.37 % (18922)------------------------------
% 0.12/0.37 % (18921)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.12/0.37 % (18927)First to succeed.
% 0.12/0.38 % (18923)Also succeeded, but the first one will report.
% 0.12/0.38 % (18926)Also succeeded, but the first one will report.
% 0.12/0.38 % (18927)Refutation found. Thanks to Tanya!
% 0.12/0.38 % SZS status Theorem for Vampire---4
% 0.12/0.38 % SZS output start Proof for Vampire---4
% 0.12/0.38 thf(func_def_0, type, in: $i > ($i > $o) > $o).
% 0.12/0.38 thf(func_def_2, type, is_a: $i > ($i > $o) > $o).
% 0.12/0.38 thf(func_def_3, type, emptyset: $i > $o).
% 0.12/0.38 thf(func_def_4, type, unord_pair: $i > $i > $i > $o).
% 0.12/0.38 thf(func_def_5, type, singleton: $i > $i > $o).
% 0.12/0.38 thf(func_def_6, type, union: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_7, type, excl_union: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_8, type, intersection: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_9, type, setminus: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_10, type, complement: ($i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_11, type, disjoint: ($i > $o) > ($i > $o) > $o).
% 0.12/0.38 thf(func_def_12, type, subset: ($i > $o) > ($i > $o) > $o).
% 0.12/0.38 thf(func_def_13, type, meets: ($i > $o) > ($i > $o) > $o).
% 0.12/0.38 thf(func_def_14, type, misses: ($i > $o) > ($i > $o) > $o).
% 0.12/0.38 thf(func_def_15, type, cartesian_product: ($i > $o) > ($i > $o) > $i > $i > $o).
% 0.12/0.38 thf(func_def_16, type, pair_rel: $i > $i > $i > $i > $o).
% 0.12/0.38 thf(func_def_17, type, id_rel: ($i > $o) > $i > $i > $o).
% 0.12/0.38 thf(func_def_18, type, sub_rel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_19, type, is_rel_on: ($i > $i > $o) > ($i > $o) > ($i > $o) > $o).
% 0.12/0.38 thf(func_def_20, type, restrict_rel_domain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.12/0.38 thf(func_def_21, type, rel_diagonal: $i > $i > $o).
% 0.12/0.38 thf(func_def_22, type, rel_composition: ($i > $i > $o) > ($i > $i > $o) > $i > $i > $o).
% 0.12/0.38 thf(func_def_23, type, reflexive: ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_24, type, irreflexive: ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_25, type, symmetric: ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_26, type, transitive: ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_27, type, equiv_rel: ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_28, type, rel_codomain: ($i > $i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_29, type, rel_domain: ($i > $i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_30, type, rel_inverse: ($i > $i > $o) > $i > $i > $o).
% 0.12/0.38 thf(func_def_31, type, equiv_classes: ($i > $i > $o) > ($i > $o) > $o).
% 0.12/0.38 thf(func_def_32, type, restrict_rel_codomain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.12/0.38 thf(func_def_33, type, rel_field: ($i > $i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_34, type, well_founded: ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_35, type, upwards_well_founded: ($i > $i > $o) > $o).
% 0.12/0.38 thf(f158,plain,(
% 0.12/0.38 $false),
% 0.12/0.38 inference(trivial_inequality_removal,[],[f157])).
% 0.12/0.38 thf(f157,plain,(
% 0.12/0.38 ($false = $true)),
% 0.12/0.38 inference(beta_eta_normalization,[],[f156])).
% 0.12/0.38 thf(f156,plain,(
% 0.12/0.38 (((^[Y0 : $i]: ($true)) @ sK4) = $false)),
% 0.12/0.38 inference(sigma_clausification,[],[f155])).
% 0.12/0.38 thf(f155,plain,(
% 0.12/0.38 ($false = (!! @ $i @ (^[Y0 : $i]: ($true))))),
% 0.12/0.38 inference(beta_eta_normalization,[],[f154])).
% 0.12/0.38 thf(f154,plain,(
% 0.12/0.38 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ($true)))) @ sK3))),
% 0.12/0.38 inference(sigma_clausification,[],[f153])).
% 0.12/0.38 thf(f153,plain,(
% 0.12/0.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ($true))))) != $true)),
% 0.12/0.38 inference(boolean_simplification,[],[f152])).
% 0.12/0.38 thf(f152,plain,(
% 0.12/0.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK1 = Y1) | (sK0 = Y0)) => $true))))) != $true)),
% 0.12/0.38 inference(boolean_simplification,[],[f151])).
% 0.12/0.38 thf(f151,plain,(
% 0.12/0.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK1 = Y1) | (sK0 = Y0)) => ($true & $true)))))) != $true)),
% 0.12/0.38 inference(beta_eta_normalization,[],[f150])).
% 0.12/0.38 thf(f150,plain,(
% 0.12/0.38 (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 = Y3) | (Y0 = Y2))))))))) @ sK0 @ sK1) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 @ Y3) & (Y0 @ Y2))))))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($true)))) != $true)),
% 0.12/0.38 inference(definition_unfolding,[],[f125,f145,f122,f132])).
% 0.12/0.38 thf(f132,plain,(
% 0.12/0.38 (cartesian_product = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 @ Y3) & (Y0 @ Y2))))))))))),
% 0.12/0.38 inference(cnf_transformation,[],[f93])).
% 0.12/0.38 thf(f93,plain,(
% 0.12/0.38 (cartesian_product = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 @ Y3) & (Y0 @ Y2))))))))))),
% 0.12/0.38 inference(fool_elimination,[],[f92])).
% 0.12/0.38 thf(f92,plain,(
% 0.12/0.38 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i, X3 : $i] : ((X0 @ X2) & (X1 @ X3))) = cartesian_product)),
% 0.12/0.38 inference(rectify,[],[f15])).
% 0.12/0.38 thf(f15,axiom,(
% 0.12/0.38 ((^[X0 : $i > $o, X2 : $i > $o, X3 : $i, X4 : $i] : ((X0 @ X3) & (X2 @ X4))) = cartesian_product)),
% 0.12/0.38 file('/export/starexec/sandbox2/tmp/tmp.EvgzfDd5wZ/Vampire---4.8_18811',cartesian_product)).
% 0.12/0.38 thf(f122,plain,(
% 0.12/0.38 (pair_rel = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 = Y3) | (Y0 = Y2))))))))))),
% 0.12/0.38 inference(cnf_transformation,[],[f79])).
% 0.12/0.38 thf(f79,plain,(
% 0.12/0.38 (pair_rel = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 = Y3) | (Y0 = Y2))))))))))),
% 0.12/0.38 inference(fool_elimination,[],[f78])).
% 0.12/0.38 thf(f78,plain,(
% 0.12/0.38 ((^[X0 : $i, X1 : $i, X2 : $i, X3 : $i] : ((X0 = X2) | (X1 = X3))) = pair_rel)),
% 0.12/0.38 inference(rectify,[],[f16])).
% 0.12/0.38 thf(f16,axiom,(
% 0.12/0.38 ((^[X0 : $i, X2 : $i, X3 : $i, X4 : $i] : ((X0 = X3) | (X2 = X4))) = pair_rel)),
% 0.12/0.38 file('/export/starexec/sandbox2/tmp/tmp.EvgzfDd5wZ/Vampire---4.8_18811',pair_rel)).
% 0.12/0.38 thf(f145,plain,(
% 0.12/0.38 (sub_rel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 0.12/0.38 inference(cnf_transformation,[],[f72])).
% 0.12/0.38 thf(f72,plain,(
% 0.12/0.38 (sub_rel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 0.12/0.38 inference(fool_elimination,[],[f71])).
% 0.12/0.38 thf(f71,plain,(
% 0.12/0.38 (sub_rel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X3 @ X2) => (X1 @ X3 @ X2)))))),
% 0.12/0.38 inference(rectify,[],[f18])).
% 0.12/0.38 thf(f18,axiom,(
% 0.12/0.38 (sub_rel = (^[X6 : $i > $i > $o, X7 : $i > $i > $o] : (! [X2,X0] : ((X6 @ X0 @ X2) => (X7 @ X0 @ X2)))))),
% 0.12/0.38 file('/export/starexec/sandbox2/tmp/tmp.EvgzfDd5wZ/Vampire---4.8_18811',sub_rel)).
% 0.12/0.38 thf(f125,plain,(
% 0.12/0.38 ((sub_rel @ (pair_rel @ sK0 @ sK1) @ (cartesian_product @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($true)))) != $true)),
% 0.12/0.38 inference(cnf_transformation,[],[f110])).
% 0.12/0.38 thf(f110,plain,(
% 0.12/0.38 ((sub_rel @ (pair_rel @ sK0 @ sK1) @ (cartesian_product @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($true)))) != $true)),
% 0.12/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f108,f109])).
% 0.12/0.38 thf(f109,plain,(
% 0.12/0.38 ? [X0,X1] : ((sub_rel @ (pair_rel @ X0 @ X1) @ (cartesian_product @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($true)))) != $true) => ((sub_rel @ (pair_rel @ sK0 @ sK1) @ (cartesian_product @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($true)))) != $true)),
% 0.12/0.38 introduced(choice_axiom,[])).
% 0.12/0.38 thf(f108,plain,(
% 0.12/0.38 ? [X0,X1] : ((sub_rel @ (pair_rel @ X0 @ X1) @ (cartesian_product @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($true)))) != $true)),
% 0.12/0.38 inference(ennf_transformation,[],[f47])).
% 0.12/0.38 thf(f47,plain,(
% 0.12/0.38 ~! [X0,X1] : ((sub_rel @ (pair_rel @ X0 @ X1) @ (cartesian_product @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($true)))) = $true)),
% 0.12/0.38 inference(fool_elimination,[],[f46])).
% 0.12/0.38 thf(f46,plain,(
% 0.12/0.38 ~! [X0,X1] : (sub_rel @ (pair_rel @ X0 @ X1) @ (cartesian_product @ (^[X2 : $i] : ($true)) @ (^[X3 : $i] : ($true))))),
% 0.12/0.38 inference(rectify,[],[f37])).
% 0.12/0.38 thf(f37,negated_conjecture,(
% 0.12/0.38 ~! [X0,X2] : (sub_rel @ (pair_rel @ X0 @ X2) @ (cartesian_product @ (^[X0 : $i] : ($true)) @ (^[X0 : $i] : ($true))))),
% 0.12/0.38 inference(negated_conjecture,[],[f36])).
% 0.12/0.38 thf(f36,conjecture,(
% 0.12/0.38 ! [X0,X2] : (sub_rel @ (pair_rel @ X0 @ X2) @ (cartesian_product @ (^[X0 : $i] : ($true)) @ (^[X0 : $i] : ($true))))),
% 0.12/0.38 file('/export/starexec/sandbox2/tmp/tmp.EvgzfDd5wZ/Vampire---4.8_18811',thm)).
% 0.12/0.38 % SZS output end Proof for Vampire---4
% 0.12/0.38 % (18927)------------------------------
% 0.12/0.38 % (18927)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.38 % (18927)Termination reason: Refutation
% 0.12/0.38
% 0.12/0.38 % (18927)Memory used [KB]: 5628
% 0.12/0.38 % (18927)Time elapsed: 0.006 s
% 0.12/0.38 % (18927)Instructions burned: 7 (million)
% 0.12/0.38 % (18927)------------------------------
% 0.12/0.38 % (18927)------------------------------
% 0.12/0.38 % (18920)Success in time 0.019 s
% 0.12/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------