TSTP Solution File: SET640^3 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET640^3 : 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/sandbox/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 : Sun May 5 09:07:47 EDT 2024
% Result : Theorem 0.12s 0.35s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET640^3 : TPTP v8.1.2. Released v3.6.0.
% 0.06/0.12 % 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
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri May 3 16:53:37 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.33 This is a TH0_THM_EQU_NAR problem
% 0.12/0.33 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/tmp/tmp.tR1WlJiYhi/Vampire---4.8_6964
% 0.12/0.35 % (7079)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.12/0.35 % (7073)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)
% 0.12/0.35 % (7076)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.12/0.35 % (7074)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)
% 0.12/0.35 % (7078)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)
% 0.12/0.35 % (7075)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)
% 0.12/0.35 % (7080)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)
% 0.12/0.35 % (7076)Instruction limit reached!
% 0.12/0.35 % (7076)------------------------------
% 0.12/0.35 % (7076)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35 % (7076)Termination reason: Unknown
% 0.12/0.35 % (7076)Termination phase: shuffling
% 0.12/0.35
% 0.12/0.35 % (7076)Memory used [KB]: 1023
% 0.12/0.35 % (7076)Time elapsed: 0.004 s
% 0.12/0.35 % (7076)Instructions burned: 4 (million)
% 0.12/0.35 % (7076)------------------------------
% 0.12/0.35 % (7076)------------------------------
% 0.12/0.35 % (7077)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)
% 0.12/0.35 % (7074)Instruction limit reached!
% 0.12/0.35 % (7074)------------------------------
% 0.12/0.35 % (7074)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35 % (7074)Termination reason: Unknown
% 0.12/0.35 % (7074)Termination phase: Property scanning
% 0.12/0.35
% 0.12/0.35 % (7074)Memory used [KB]: 1023
% 0.12/0.35 % (7074)Time elapsed: 0.004 s
% 0.12/0.35 % (7074)Instructions burned: 5 (million)
% 0.12/0.35 % (7074)------------------------------
% 0.12/0.35 % (7074)------------------------------
% 0.12/0.35 % (7077)Instruction limit reached!
% 0.12/0.35 % (7077)------------------------------
% 0.12/0.35 % (7077)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35 % (7077)Termination reason: Unknown
% 0.12/0.35 % (7077)Termination phase: shuffling
% 0.12/0.35
% 0.12/0.35 % (7077)Memory used [KB]: 1023
% 0.12/0.35 % (7077)Time elapsed: 0.002 s
% 0.12/0.35 % (7077)Instructions burned: 2 (million)
% 0.12/0.35 % (7080)Instruction limit reached!
% 0.12/0.35 % (7080)------------------------------
% 0.12/0.35 % (7080)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35 % (7077)------------------------------
% 0.12/0.35 % (7077)------------------------------
% 0.12/0.35 % (7080)Termination reason: Unknown
% 0.12/0.35 % (7080)Termination phase: Property scanning
% 0.12/0.35
% 0.12/0.35 % (7080)Memory used [KB]: 1023
% 0.12/0.35 % (7080)Time elapsed: 0.003 s
% 0.12/0.35 % (7080)Instructions burned: 5 (million)
% 0.12/0.35 % (7080)------------------------------
% 0.12/0.35 % (7080)------------------------------
% 0.12/0.35 % (7073)First to succeed.
% 0.12/0.35 % (7078)Also succeeded, but the first one will report.
% 0.12/0.35 % (7073)Refutation found. Thanks to Tanya!
% 0.12/0.35 % SZS status Theorem for Vampire---4
% 0.12/0.35 % SZS output start Proof for Vampire---4
% 0.12/0.35 thf(func_def_0, type, in: $i > ($i > $o) > $o).
% 0.12/0.35 thf(func_def_2, type, is_a: $i > ($i > $o) > $o).
% 0.12/0.35 thf(func_def_3, type, emptyset: $i > $o).
% 0.12/0.35 thf(func_def_4, type, unord_pair: $i > $i > $i > $o).
% 0.12/0.35 thf(func_def_5, type, singleton: $i > $i > $o).
% 0.12/0.35 thf(func_def_6, type, union: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.35 thf(func_def_7, type, excl_union: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.35 thf(func_def_8, type, intersection: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.35 thf(func_def_9, type, setminus: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.35 thf(func_def_10, type, complement: ($i > $o) > $i > $o).
% 0.12/0.35 thf(func_def_11, type, disjoint: ($i > $o) > ($i > $o) > $o).
% 0.12/0.35 thf(func_def_12, type, subset: ($i > $o) > ($i > $o) > $o).
% 0.12/0.35 thf(func_def_13, type, meets: ($i > $o) > ($i > $o) > $o).
% 0.12/0.35 thf(func_def_14, type, misses: ($i > $o) > ($i > $o) > $o).
% 0.12/0.35 thf(func_def_15, type, cartesian_product: ($i > $o) > ($i > $o) > $i > $i > $o).
% 0.12/0.35 thf(func_def_16, type, pair_rel: $i > $i > $i > $i > $o).
% 0.12/0.35 thf(func_def_17, type, id_rel: ($i > $o) > $i > $i > $o).
% 0.12/0.35 thf(func_def_18, type, sub_rel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.12/0.35 thf(func_def_19, type, is_rel_on: ($i > $i > $o) > ($i > $o) > ($i > $o) > $o).
% 0.12/0.35 thf(func_def_20, type, restrict_rel_domain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.12/0.35 thf(func_def_21, type, rel_diagonal: $i > $i > $o).
% 0.12/0.35 thf(func_def_22, type, rel_composition: ($i > $i > $o) > ($i > $i > $o) > $i > $i > $o).
% 0.12/0.35 thf(func_def_23, type, reflexive: ($i > $i > $o) > $o).
% 0.12/0.35 thf(func_def_24, type, irreflexive: ($i > $i > $o) > $o).
% 0.12/0.35 thf(func_def_25, type, symmetric: ($i > $i > $o) > $o).
% 0.12/0.35 thf(func_def_26, type, transitive: ($i > $i > $o) > $o).
% 0.12/0.35 thf(func_def_27, type, equiv_rel: ($i > $i > $o) > $o).
% 0.12/0.35 thf(func_def_28, type, rel_codomain: ($i > $i > $o) > $i > $o).
% 0.12/0.35 thf(func_def_29, type, rel_domain: ($i > $i > $o) > $i > $o).
% 0.12/0.35 thf(func_def_30, type, rel_inverse: ($i > $i > $o) > $i > $i > $o).
% 0.12/0.35 thf(func_def_31, type, equiv_classes: ($i > $i > $o) > ($i > $o) > $o).
% 0.12/0.35 thf(func_def_32, type, restrict_rel_codomain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.12/0.35 thf(func_def_33, type, rel_field: ($i > $i > $o) > $i > $o).
% 0.12/0.35 thf(func_def_34, type, well_founded: ($i > $i > $o) > $o).
% 0.12/0.35 thf(func_def_35, type, upwards_well_founded: ($i > $i > $o) > $o).
% 0.12/0.35 thf(func_def_52, type, sK0: $i > $i > $o).
% 0.12/0.35 thf(func_def_53, type, sK1: $i > $i > $o).
% 0.12/0.35 thf(f160,plain,(
% 0.12/0.35 $false),
% 0.12/0.35 inference(trivial_inequality_removal,[],[f159])).
% 0.12/0.35 thf(f159,plain,(
% 0.12/0.35 ($true = $false)),
% 0.12/0.35 inference(beta_eta_normalization,[],[f158])).
% 0.12/0.35 thf(f158,plain,(
% 0.12/0.35 (((^[Y0 : $i]: ($true)) @ sK4) = $false)),
% 0.12/0.35 inference(sigma_clausification,[],[f157])).
% 0.12/0.35 thf(f157,plain,(
% 0.12/0.35 ($false = (!! @ $i @ (^[Y0 : $i]: ($true))))),
% 0.12/0.35 inference(beta_eta_normalization,[],[f156])).
% 0.12/0.35 thf(f156,plain,(
% 0.12/0.35 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ($true)))) @ sK3) = $false)),
% 0.12/0.35 inference(sigma_clausification,[],[f155])).
% 0.12/0.35 thf(f155,plain,(
% 0.12/0.35 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ($true))))))),
% 0.12/0.35 inference(boolean_simplification,[],[f154])).
% 0.12/0.35 thf(f154,plain,(
% 0.12/0.35 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y0 @ Y1) => $true))))))),
% 0.12/0.35 inference(boolean_simplification,[],[f153])).
% 0.12/0.35 thf(f153,plain,(
% 0.12/0.35 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y0 @ Y1) => ($true & $true)))))))),
% 0.12/0.35 inference(beta_eta_normalization,[],[f152])).
% 0.12/0.35 thf(f152,plain,(
% 0.12/0.35 ($true != ((^[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))))))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($true)))))),
% 0.12/0.35 inference(definition_unfolding,[],[f130,f121,f116])).
% 0.12/0.35 thf(f116,plain,(
% 0.12/0.35 (cartesian_product = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y0 @ Y2) & (Y1 @ Y3))))))))))),
% 0.12/0.35 inference(cnf_transformation,[],[f88])).
% 0.12/0.35 thf(f88,plain,(
% 0.12/0.35 (cartesian_product = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y0 @ Y2) & (Y1 @ Y3))))))))))),
% 0.12/0.35 inference(fool_elimination,[],[f87])).
% 0.12/0.35 thf(f87,plain,(
% 0.12/0.35 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i, X3 : $i] : ((X1 @ X3) & (X0 @ X2))) = cartesian_product)),
% 0.12/0.35 inference(rectify,[],[f15])).
% 0.12/0.35 thf(f15,axiom,(
% 0.12/0.35 ((^[X0 : $i > $o, X2 : $i > $o, X3 : $i, X4 : $i] : ((X2 @ X4) & (X0 @ X3))) = cartesian_product)),
% 0.12/0.35 file('/export/starexec/sandbox/tmp/tmp.tR1WlJiYhi/Vampire---4.8_6964',cartesian_product)).
% 0.12/0.35 thf(f121,plain,(
% 0.12/0.35 (sub_rel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 0.12/0.35 inference(cnf_transformation,[],[f90])).
% 0.12/0.35 thf(f90,plain,(
% 0.12/0.35 (sub_rel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 0.12/0.35 inference(fool_elimination,[],[f89])).
% 0.12/0.35 thf(f89,plain,(
% 0.12/0.35 ((^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X3 @ X2) => (X1 @ X3 @ X2)))) = sub_rel)),
% 0.12/0.35 inference(rectify,[],[f18])).
% 0.12/0.35 thf(f18,axiom,(
% 0.12/0.35 ((^[X6 : $i > $i > $o, X7 : $i > $i > $o] : (! [X2,X0] : ((X6 @ X0 @ X2) => (X7 @ X0 @ X2)))) = sub_rel)),
% 0.12/0.35 file('/export/starexec/sandbox/tmp/tmp.tR1WlJiYhi/Vampire---4.8_6964',sub_rel)).
% 0.12/0.35 thf(f130,plain,(
% 0.12/0.35 ((sub_rel @ sK1 @ (cartesian_product @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($true)))) != $true)),
% 0.12/0.35 inference(cnf_transformation,[],[f110])).
% 0.12/0.35 thf(f110,plain,(
% 0.12/0.35 ($true = (sub_rel @ sK1 @ sK0)) & ((sub_rel @ sK1 @ (cartesian_product @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($true)))) != $true)),
% 0.12/0.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f108,f109])).
% 0.12/0.35 thf(f109,plain,(
% 0.12/0.35 ? [X0 : $i > $i > $o,X1 : $i > $i > $o] : (($true = (sub_rel @ X1 @ X0)) & ($true != (sub_rel @ X1 @ (cartesian_product @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($true)))))) => (($true = (sub_rel @ sK1 @ sK0)) & ((sub_rel @ sK1 @ (cartesian_product @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($true)))) != $true))),
% 0.12/0.35 introduced(choice_axiom,[])).
% 0.12/0.35 thf(f108,plain,(
% 0.12/0.35 ? [X0 : $i > $i > $o,X1 : $i > $i > $o] : (($true = (sub_rel @ X1 @ X0)) & ($true != (sub_rel @ X1 @ (cartesian_product @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($true))))))),
% 0.12/0.35 inference(ennf_transformation,[],[f86])).
% 0.12/0.35 thf(f86,plain,(
% 0.12/0.35 ~! [X0 : $i > $i > $o,X1 : $i > $i > $o] : (($true = (sub_rel @ X1 @ X0)) => ($true = (sub_rel @ X1 @ (cartesian_product @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($true))))))),
% 0.12/0.35 inference(fool_elimination,[],[f85])).
% 0.12/0.35 thf(f85,plain,(
% 0.12/0.35 ~! [X0 : $i > $i > $o,X1 : $i > $i > $o] : ((sub_rel @ X1 @ X0) => (sub_rel @ X1 @ (cartesian_product @ (^[X2 : $i] : ($true)) @ (^[X3 : $i] : ($true)))))),
% 0.12/0.35 inference(rectify,[],[f37])).
% 0.12/0.35 thf(f37,negated_conjecture,(
% 0.12/0.35 ~! [X14 : $i > $i > $o,X8 : $i > $i > $o] : ((sub_rel @ X8 @ X14) => (sub_rel @ X8 @ (cartesian_product @ (^[X0 : $i] : ($true)) @ (^[X0 : $i] : ($true)))))),
% 0.12/0.35 inference(negated_conjecture,[],[f36])).
% 0.12/0.35 thf(f36,conjecture,(
% 0.12/0.35 ! [X14 : $i > $i > $o,X8 : $i > $i > $o] : ((sub_rel @ X8 @ X14) => (sub_rel @ X8 @ (cartesian_product @ (^[X0 : $i] : ($true)) @ (^[X0 : $i] : ($true)))))),
% 0.12/0.35 file('/export/starexec/sandbox/tmp/tmp.tR1WlJiYhi/Vampire---4.8_6964',thm)).
% 0.12/0.35 % SZS output end Proof for Vampire---4
% 0.12/0.35 % (7073)------------------------------
% 0.12/0.35 % (7073)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35 % (7073)Termination reason: Refutation
% 0.12/0.35
% 0.12/0.35 % (7073)Memory used [KB]: 5628
% 0.12/0.35 % (7073)Time elapsed: 0.006 s
% 0.12/0.35 % (7073)Instructions burned: 8 (million)
% 0.12/0.35 % (7073)------------------------------
% 0.12/0.35 % (7073)------------------------------
% 0.12/0.35 % (7072)Success in time 0.01 s
% 0.12/0.35 % Vampire---4.8 exiting
%------------------------------------------------------------------------------