TSTP Solution File: ITP232^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP232^1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n022.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 : 600s
% DateTime : Sun Jul 17 00:29:50 EDT 2022
% Result : Theorem 1.30s 1.51s
% Output : Proof 1.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP232^1 : TPTP v8.1.0. Released v8.1.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 2 17:11:36 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.30/1.51 % SZS status Theorem
% 1.30/1.51 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 1.30/1.51 % Inferences: 40
% 1.30/1.51 % SZS output start Proof
% 1.30/1.51 thf(ty_vEBT_VEBT, type, vEBT_VEBT : $tType).
% 1.30/1.51 thf(ty_list_VEBT_VEBT, type, list_VEBT_VEBT : $tType).
% 1.30/1.51 thf(ty_nat, type, nat : $tType).
% 1.30/1.51 thf(ty_set_VEBT_VEBT, type, set_VEBT_VEBT : $tType).
% 1.30/1.51 thf(ty_num, type, num : $tType).
% 1.30/1.51 thf(ty_summary, type, summary : vEBT_VEBT).
% 1.30/1.51 thf(ty_nth_VEBT_VEBT, type, nth_VEBT_VEBT : (list_VEBT_VEBT>nat>vEBT_VEBT)).
% 1.30/1.51 thf(ty_vEBT_VEBT_high, type, vEBT_VEBT_high : (nat>nat>nat)).
% 1.30/1.51 thf(ty_vEBT_vebt_insert, type, vEBT_vebt_insert : (vEBT_VEBT>nat>vEBT_VEBT)).
% 1.30/1.51 thf(ty_numeral_numeral_nat, type, numeral_numeral_nat : (num>nat)).
% 1.30/1.51 thf(ty_treeList, type, treeList : list_VEBT_VEBT).
% 1.30/1.51 thf(ty_bit0, type, bit0 : (num>num)).
% 1.30/1.51 thf(ty_deg, type, deg : nat).
% 1.30/1.51 thf(ty_member_VEBT_VEBT, type, member_VEBT_VEBT : (vEBT_VEBT>set_VEBT_VEBT>$o)).
% 1.30/1.51 thf(ty_mi, type, mi : nat).
% 1.30/1.51 thf(ty_na, type, na : nat).
% 1.30/1.51 thf(ty_ord_less_nat, type, ord_less_nat : (nat>nat>$o)).
% 1.30/1.51 thf(ty_set_VEBT_VEBT2, type, set_VEBT_VEBT2 : (list_VEBT_VEBT>set_VEBT_VEBT)).
% 1.30/1.51 thf(ty_vEBT_VEBT_low, type, vEBT_VEBT_low : (nat>nat>nat)).
% 1.30/1.51 thf(ty_one, type, one : num).
% 1.30/1.51 thf(ty_vEBT_V8194947554948674370ptions, type, vEBT_V8194947554948674370ptions : (vEBT_VEBT>nat>$o)).
% 1.30/1.51 thf(ty_power_power_nat, type, power_power_nat : (nat>nat>nat)).
% 1.30/1.51 thf(ty_ord_less_eq_nat, type, ord_less_eq_nat : (nat>nat>$o)).
% 1.30/1.51 thf(ty_vEBT_VEBT_minNull, type, vEBT_VEBT_minNull : (vEBT_VEBT>$o)).
% 1.30/1.51 thf(ty_ma, type, ma : nat).
% 1.30/1.51 thf(ty_m, type, m : nat).
% 1.30/1.51 thf(sP1,plain,sP1 <=> (mi = ma),introduced(definition,[new_symbols(definition,[sP1])])).
% 1.30/1.51 thf(conj_0,conjecture,(~((![X1:nat]:(~(((vEBT_V8194947554948674370ptions @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ mi) @ na))) @ X1))))))).
% 1.30/1.51 thf(h0,negated_conjecture,(![X1:nat]:(~(((vEBT_V8194947554948674370ptions @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ mi) @ na))) @ X1)))),inference(assume_negation,[status(cth)],[conj_0])).
% 1.30/1.51 thf(h1,assumption,((ord_less_nat @ ((vEBT_VEBT_high @ mi) @ na)) @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ m)),introduced(assumption,[])).
% 1.30/1.51 thf(h2,assumption,((ord_less_nat @ ((vEBT_VEBT_low @ mi) @ na)) @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ na)),introduced(assumption,[])).
% 1.30/1.51 thf(h3,assumption,((ord_less_eq_nat @ mi) @ ma),introduced(assumption,[])).
% 1.30/1.51 thf(h4,assumption,((ord_less_nat @ ma) @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ deg)),introduced(assumption,[])).
% 1.30/1.51 thf(h5,assumption,sP1,introduced(assumption,[])).
% 1.30/1.51 thf(h6,assumption,(![X1:nat]:(((ord_less_nat @ X1) @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ m)) => (~((((((vEBT_VEBT_high @ ma) @ na) = X1) => ((vEBT_V8194947554948674370ptions @ ((nth_VEBT_VEBT @ treeList) @ X1)) @ ((vEBT_VEBT_low @ ma) @ na))) => (~((![X2:nat]:((~(((((vEBT_VEBT_high @ X2) @ na) = X1) => (~(((vEBT_V8194947554948674370ptions @ ((nth_VEBT_VEBT @ treeList) @ X1)) @ ((vEBT_VEBT_low @ X2) @ na))))))) => (~((((ord_less_nat @ mi) @ X2) => (~(((ord_less_eq_nat @ X2) @ ma))))))))))))))),introduced(assumption,[])).
% 1.30/1.51 thf(h7,assumption,(~(sP1)),introduced(assumption,[])).
% 1.30/1.51 thf(h8,assumption,(![X1:vEBT_VEBT]:(((member_VEBT_VEBT @ X1) @ (set_VEBT_VEBT2 @ treeList)) => (![X2:nat]:(~(((vEBT_V8194947554948674370ptions @ X1) @ X2)))))),introduced(assumption,[])).
% 1.30/1.51 thf(h9,assumption,(~((vEBT_VEBT_minNull @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ mi) @ na))))),introduced(assumption,[])).
% 1.30/1.51 thf(h10,assumption,(((vEBT_vebt_insert @ summary) @ ((vEBT_VEBT_high @ mi) @ na)) = summary),introduced(assumption,[])).
% 1.30/1.51 thf(1,plain,$false,inference(tab_conflict,[status(thm),assumptions([h9,h7,h5,h3,h4,h1,h2,h0])],[h5,h7])).
% 1.30/1.51 thf(2,plain,$false,inference(tab_conflict,[status(thm),assumptions([h10,h7,h5,h3,h4,h1,h2,h0])],[h5,h7])).
% 1.30/1.51 thf(fact_2__092_060open_062_Iif_AminNull_A_ItreeList_A_B_Ahigh_Ami_An_J_Athen_Avebt__insert_Asummary_A_Ihigh_Ami_An_J_Aelse_Asummary_J_A_061_Asummary_092_060close_062,axiom,((vEBT_VEBT_minNull @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ mi) @ na))) => (((vEBT_vebt_insert @ summary) @ ((vEBT_VEBT_high @ mi) @ na)) = summary))).
% 1.30/1.51 thf(3,plain,$false,inference(tab_imp,[status(thm),assumptions([h7,h5,h3,h4,h1,h2,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[fact_2__092_060open_062_Iif_AminNull_A_ItreeList_A_B_Ahigh_Ami_An_J_Athen_Avebt__insert_Asummary_A_Ihigh_Ami_An_J_Aelse_Asummary_J_A_061_Asummary_092_060close_062,1,2,h9,h10])).
% 1.30/1.51 thf(pax30, axiom, (p30=>![X15:vEBT_VEBT]:(fmember_VEBT_VEBT @ X15 @ (fset_VEBT_VEBT2 @ ftreeList)=>![X2:nat]:~(fvEBT_V8194947554948674370ptions @ X15 @ X2))), file('<stdin>', pax30)).
% 1.30/1.51 thf(pax21, axiom, (p21=>![X16:nat, X17:list_VEBT_VEBT]:(ford_less_nat @ X16 @ (fsize_s6755466524823107622T_VEBT @ X17)=>fmember_VEBT_VEBT @ (fnth_VEBT_VEBT @ X17 @ X16) @ (fset_VEBT_VEBT2 @ X17))), file('<stdin>', pax21)).
% 1.30/1.51 thf(pax3, axiom, (p3=>(fna)=(fm)), file('<stdin>', pax3)).
% 1.30/1.51 thf(ax34, axiom, p30, file('<stdin>', ax34)).
% 1.30/1.51 thf(ax18, axiom, p21, file('<stdin>', ax18)).
% 1.30/1.51 thf(pax1, axiom, (p1=>![X27:vEBT_VEBT]:(~(fvEBT_VEBT_minNull @ X27)=>~(![X23:nat]:~(fvEBT_V8194947554948674370ptions @ X27 @ X23)))), file('<stdin>', pax1)).
% 1.30/1.51 thf(pax36, axiom, (p36=>![X7:nat, X2:nat, X5:nat]:(ford_less_nat @ X7 @ (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ (fplus_plus_nat @ X2 @ X5))=>ford_less_nat @ (fvEBT_VEBT_high @ X7 @ X2) @ (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ X5))), file('<stdin>', pax36)).
% 1.30/1.51 thf(pax10, axiom, (p10=>(fdeg)=(fplus_plus_nat @ fna @ fm)), file('<stdin>', pax10)).
% 1.30/1.51 thf(ax36, axiom, p3, file('<stdin>', ax36)).
% 1.30/1.51 thf(pax32, axiom, (p32=>(fsize_s6755466524823107622T_VEBT @ ftreeList)=(fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ fm)), file('<stdin>', pax32)).
% 1.30/1.51 thf(pax5, axiom, (p5=>(fmi)=(fma)), file('<stdin>', pax5)).
% 1.30/1.51 thf(nax2, axiom, (p2<=fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))), file('<stdin>', nax2)).
% 1.30/1.51 thf(ax37, axiom, ~(p2), file('<stdin>', ax37)).
% 1.30/1.51 thf(ax38, axiom, p1, file('<stdin>', ax38)).
% 1.30/1.51 thf(ax4, axiom, p36, file('<stdin>', ax4)).
% 1.30/1.51 thf(ax29, axiom, p10, file('<stdin>', ax29)).
% 1.30/1.51 thf(ax8, axiom, p32, file('<stdin>', ax8)).
% 1.30/1.51 thf(pax39, axiom, (p39=>ford_less_nat @ fma @ (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ fdeg)), file('<stdin>', pax39)).
% 1.30/1.51 thf(ax10, axiom, p5, file('<stdin>', ax10)).
% 1.30/1.51 thf(ax1, axiom, p39, file('<stdin>', ax1)).
% 1.30/1.51 thf(c_0_20, plain, ![X78:vEBT_VEBT, X79:nat]:(~p30|(~fmember_VEBT_VEBT @ X78 @ (fset_VEBT_VEBT2 @ ftreeList)|~fvEBT_V8194947554948674370ptions @ X78 @ X79)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax30])])])])).
% 1.30/1.51 thf(c_0_21, plain, ![X90:nat, X91:list_VEBT_VEBT]:(~p21|(~ford_less_nat @ X90 @ (fsize_s6755466524823107622T_VEBT @ X91)|fmember_VEBT_VEBT @ (fnth_VEBT_VEBT @ X91 @ X90) @ (fset_VEBT_VEBT2 @ X91))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax21])])])).
% 1.30/1.51 thf(c_0_22, plain, (~p3|(fna)=(fm)), inference(fof_nnf,[status(thm)],[pax3])).
% 1.30/1.51 thf(c_0_23, plain, ![X3:vEBT_VEBT, X1:nat]:(~p30|~fmember_VEBT_VEBT @ X3 @ (fset_VEBT_VEBT2 @ ftreeList)|~fvEBT_V8194947554948674370ptions @ X3 @ X1), inference(split_conjunct,[status(thm)],[c_0_20])).
% 1.30/1.51 thf(c_0_24, plain, p30, inference(split_conjunct,[status(thm)],[ax34])).
% 1.30/1.51 thf(c_0_25, plain, ![X1:nat, X8:list_VEBT_VEBT]:(fmember_VEBT_VEBT @ (fnth_VEBT_VEBT @ X8 @ X1) @ (fset_VEBT_VEBT2 @ X8)|~p21|~ford_less_nat @ X1 @ (fsize_s6755466524823107622T_VEBT @ X8)), inference(split_conjunct,[status(thm)],[c_0_21])).
% 1.30/1.51 thf(c_0_26, plain, p21, inference(split_conjunct,[status(thm)],[ax18])).
% 1.30/1.51 thf(c_0_27, plain, ![X130:vEBT_VEBT]:(~p1|(fvEBT_VEBT_minNull @ X130|fvEBT_V8194947554948674370ptions @ X130 @ (esk52_1 @ X130))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1])])])])])).
% 1.30/1.51 thf(c_0_28, plain, ![X52:nat, X53:nat, X54:nat]:(~p36|(~ford_less_nat @ X52 @ (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ (fplus_plus_nat @ X53 @ X54))|ford_less_nat @ (fvEBT_VEBT_high @ X52 @ X53) @ (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ X54))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax36])])])).
% 1.30/1.51 thf(c_0_29, plain, (~p10|(fdeg)=(fplus_plus_nat @ fna @ fm)), inference(fof_nnf,[status(thm)],[pax10])).
% 1.30/1.51 thf(c_0_30, plain, ((fna)=(fm)|~p3), inference(split_conjunct,[status(thm)],[c_0_22])).
% 1.30/1.51 thf(c_0_31, plain, p3, inference(split_conjunct,[status(thm)],[ax36])).
% 1.30/1.51 thf(c_0_32, plain, (~p32|(fsize_s6755466524823107622T_VEBT @ ftreeList)=(fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ fm)), inference(fof_nnf,[status(thm)],[pax32])).
% 1.30/1.51 thf(c_0_33, plain, (~p5|(fmi)=(fma)), inference(fof_nnf,[status(thm)],[pax5])).
% 1.30/1.51 thf(c_0_34, plain, (~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))|p2), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax2])])).
% 1.30/1.51 thf(c_0_35, plain, ~p2, inference(fof_simplification,[status(thm)],[ax37])).
% 1.30/1.51 thf(c_0_36, plain, ![X3:vEBT_VEBT, X1:nat]:(~fmember_VEBT_VEBT @ X3 @ (fset_VEBT_VEBT2 @ ftreeList)|~fvEBT_V8194947554948674370ptions @ X3 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24])])).
% 1.30/1.51 thf(c_0_37, plain, ![X1:nat, X8:list_VEBT_VEBT]:(fmember_VEBT_VEBT @ (fnth_VEBT_VEBT @ X8 @ X1) @ (fset_VEBT_VEBT2 @ X8)|~ford_less_nat @ X1 @ (fsize_s6755466524823107622T_VEBT @ X8)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25, c_0_26])])).
% 1.30/1.51 thf(c_0_38, plain, ![X3:vEBT_VEBT]:(fvEBT_VEBT_minNull @ X3|fvEBT_V8194947554948674370ptions @ X3 @ (esk52_1 @ X3)|~p1), inference(split_conjunct,[status(thm)],[c_0_27])).
% 1.30/1.51 thf(c_0_39, plain, p1, inference(split_conjunct,[status(thm)],[ax38])).
% 1.30/1.51 thf(c_0_40, plain, ![X1:nat, X2:nat, X5:nat]:(ford_less_nat @ (fvEBT_VEBT_high @ X1 @ X2) @ (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ X5)|~p36|~ford_less_nat @ X1 @ (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ (fplus_plus_nat @ X2 @ X5))), inference(split_conjunct,[status(thm)],[c_0_28])).
% 1.30/1.51 thf(c_0_41, plain, p36, inference(split_conjunct,[status(thm)],[ax4])).
% 1.30/1.51 thf(c_0_42, plain, ((fdeg)=(fplus_plus_nat @ fna @ fm)|~p10), inference(split_conjunct,[status(thm)],[c_0_29])).
% 1.30/1.51 thf(c_0_43, plain, (fm)=(fna), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_31])])).
% 1.30/1.51 thf(c_0_44, plain, p10, inference(split_conjunct,[status(thm)],[ax29])).
% 1.30/1.51 thf(c_0_45, plain, ((fsize_s6755466524823107622T_VEBT @ ftreeList)=(fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ fm)|~p32), inference(split_conjunct,[status(thm)],[c_0_32])).
% 1.30/1.51 thf(c_0_46, plain, p32, inference(split_conjunct,[status(thm)],[ax8])).
% 1.30/1.51 thf(c_0_47, plain, (~p39|ford_less_nat @ fma @ (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ fdeg)), inference(fof_nnf,[status(thm)],[pax39])).
% 1.30/1.51 thf(c_0_48, plain, ((fmi)=(fma)|~p5), inference(split_conjunct,[status(thm)],[c_0_33])).
% 1.30/1.51 thf(c_0_49, plain, p5, inference(split_conjunct,[status(thm)],[ax10])).
% 1.30/1.51 thf(c_0_50, plain, (p2|~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))), inference(split_conjunct,[status(thm)],[c_0_34])).
% 1.30/1.51 thf(c_0_51, plain, ~p2, inference(split_conjunct,[status(thm)],[c_0_35])).
% 1.30/1.51 thf(c_0_52, plain, ![X2:nat, X1:nat]:(~fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ X1) @ X2|~ford_less_nat @ X1 @ (fsize_s6755466524823107622T_VEBT @ ftreeList)), inference(spm,[status(thm)],[c_0_36, c_0_37])).
% 1.30/1.51 thf(c_0_53, plain, ![X3:vEBT_VEBT]:(fvEBT_V8194947554948674370ptions @ X3 @ (esk52_1 @ X3)|fvEBT_VEBT_minNull @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_39])])).
% 1.30/1.51 thf(c_0_54, plain, ![X1:nat, X2:nat, X5:nat]:(ford_less_nat @ (fvEBT_VEBT_high @ X1 @ X2) @ (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ X5)|~ford_less_nat @ X1 @ (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ (fplus_plus_nat @ X2 @ X5))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40, c_0_41])])).
% 1.30/1.51 thf(c_0_55, plain, (fplus_plus_nat @ fna @ fna)=(fdeg), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42, c_0_43]), c_0_44])])).
% 1.30/1.51 thf(c_0_56, plain, (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ fna)=(fsize_s6755466524823107622T_VEBT @ ftreeList), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_43]), c_0_46])])).
% 1.30/1.51 thf(c_0_57, plain, (ford_less_nat @ fma @ (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ fdeg)|~p39), inference(split_conjunct,[status(thm)],[c_0_47])).
% 1.30/1.51 thf(c_0_58, plain, (fma)=(fmi), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48, c_0_49])])).
% 1.30/1.51 thf(c_0_59, plain, p39, inference(split_conjunct,[status(thm)],[ax1])).
% 1.30/1.51 thf(c_0_60, plain, ~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)), inference(sr,[status(thm)],[c_0_50, c_0_51])).
% 1.30/1.51 thf(c_0_61, plain, ![X1:nat]:(fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ X1)|~ford_less_nat @ X1 @ (fsize_s6755466524823107622T_VEBT @ ftreeList)), inference(spm,[status(thm)],[c_0_52, c_0_53])).
% 1.30/1.51 thf(c_0_62, plain, ![X1:nat]:(ford_less_nat @ (fvEBT_VEBT_high @ X1 @ fna) @ (fsize_s6755466524823107622T_VEBT @ ftreeList)|~ford_less_nat @ X1 @ (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ fdeg)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55]), c_0_56])).
% 1.30/1.51 thf(c_0_63, plain, ford_less_nat @ fmi @ (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ fdeg), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57, c_0_58]), c_0_59])])).
% 1.30/1.51 thf(c_0_64, plain, ~ford_less_nat @ (fvEBT_VEBT_high @ fmi @ fna) @ (fsize_s6755466524823107622T_VEBT @ ftreeList), inference(spm,[status(thm)],[c_0_60, c_0_61])).
% 1.30/1.51 thf(c_0_65, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63]), c_0_64]), ['proof']).
% 1.30/1.51 thf(4,plain,$false,inference(eprover,[status(thm),assumptions([h9,h8,h5,h3,h4,h1,h2,h0])],[])).
% 1.30/1.51 thf(pax30, axiom, (p30=>![X40:vEBT_VEBT]:(fmember_VEBT_VEBT @ X40 @ (fset_VEBT_VEBT2 @ ftreeList)=>![X2:nat]:~(fvEBT_V8194947554948674370ptions @ X40 @ X2))), file('<stdin>', pax30)).
% 1.30/1.51 thf(pax21, axiom, (p21=>![X41:nat, X42:list_VEBT_VEBT]:(ford_less_nat @ X41 @ (fsize_s6755466524823107622T_VEBT @ X42)=>fmember_VEBT_VEBT @ (fnth_VEBT_VEBT @ X42 @ X41) @ (fset_VEBT_VEBT2 @ X42))), file('<stdin>', pax21)).
% 1.30/1.51 thf(pax3, axiom, (p3=>(fna)=(fm)), file('<stdin>', pax3)).
% 1.30/1.51 thf(ax49, axiom, p30, file('<stdin>', ax49)).
% 1.30/1.51 thf(ax33, axiom, p21, file('<stdin>', ax33)).
% 1.30/1.51 thf(pax1, axiom, (p1=>![X52:vEBT_VEBT]:(~(fvEBT_VEBT_minNull @ X52)=>~(![X48:nat]:~(fvEBT_V8194947554948674370ptions @ X52 @ X48)))), file('<stdin>', pax1)).
% 1.30/1.51 thf(pax32, axiom, (p32=>(fsize_s6755466524823107622T_VEBT @ ftreeList)=(fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ fm)), file('<stdin>', pax32)).
% 1.30/1.51 thf(ax51, axiom, p3, file('<stdin>', ax51)).
% 1.30/1.51 thf(nax2, axiom, (p2<=fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))), file('<stdin>', nax2)).
% 1.30/1.51 thf(ax53, axiom, ~(p2), file('<stdin>', ax53)).
% 1.30/1.51 thf(ax54, axiom, p1, file('<stdin>', ax54)).
% 1.30/1.51 thf(pax43, axiom, (p43=>ford_less_nat @ (fvEBT_VEBT_high @ fmi @ fna) @ (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ fm)), file('<stdin>', pax43)).
% 1.30/1.51 thf(ax23, axiom, p32, file('<stdin>', ax23)).
% 1.30/1.51 thf(ax12, axiom, p43, file('<stdin>', ax12)).
% 1.30/1.51 thf(c_0_14, plain, ![X181:vEBT_VEBT, X182:nat]:(~p30|(~fmember_VEBT_VEBT @ X181 @ (fset_VEBT_VEBT2 @ ftreeList)|~fvEBT_V8194947554948674370ptions @ X181 @ X182)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax30])])])])).
% 1.30/1.51 thf(c_0_15, plain, ![X193:nat, X194:list_VEBT_VEBT]:(~p21|(~ford_less_nat @ X193 @ (fsize_s6755466524823107622T_VEBT @ X194)|fmember_VEBT_VEBT @ (fnth_VEBT_VEBT @ X194 @ X193) @ (fset_VEBT_VEBT2 @ X194))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax21])])])).
% 1.30/1.51 thf(c_0_16, plain, (~p3|(fna)=(fm)), inference(fof_nnf,[status(thm)],[pax3])).
% 1.30/1.51 thf(c_0_17, plain, ![X3:vEBT_VEBT, X2:nat]:(~p30|~fmember_VEBT_VEBT @ X3 @ (fset_VEBT_VEBT2 @ ftreeList)|~fvEBT_V8194947554948674370ptions @ X3 @ X2), inference(split_conjunct,[status(thm)],[c_0_14])).
% 1.30/1.51 thf(c_0_18, plain, p30, inference(split_conjunct,[status(thm)],[ax49])).
% 1.30/1.51 thf(c_0_19, plain, ![X2:nat, X1:list_VEBT_VEBT]:(fmember_VEBT_VEBT @ (fnth_VEBT_VEBT @ X1 @ X2) @ (fset_VEBT_VEBT2 @ X1)|~p21|~ford_less_nat @ X2 @ (fsize_s6755466524823107622T_VEBT @ X1)), inference(split_conjunct,[status(thm)],[c_0_15])).
% 1.30/1.51 thf(c_0_20, plain, p21, inference(split_conjunct,[status(thm)],[ax33])).
% 1.30/1.51 thf(c_0_21, plain, ![X233:vEBT_VEBT]:(~p1|(fvEBT_VEBT_minNull @ X233|fvEBT_V8194947554948674370ptions @ X233 @ (esk91_1 @ X233))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1])])])])])).
% 1.30/1.51 thf(c_0_22, plain, (~p32|(fsize_s6755466524823107622T_VEBT @ ftreeList)=(fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ fm)), inference(fof_nnf,[status(thm)],[pax32])).
% 1.30/1.51 thf(c_0_23, plain, ((fna)=(fm)|~p3), inference(split_conjunct,[status(thm)],[c_0_16])).
% 1.30/1.51 thf(c_0_24, plain, p3, inference(split_conjunct,[status(thm)],[ax51])).
% 1.30/1.51 thf(c_0_25, plain, (~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))|p2), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax2])])).
% 1.30/1.51 thf(c_0_26, plain, ~p2, inference(fof_simplification,[status(thm)],[ax53])).
% 1.30/1.51 thf(c_0_27, plain, ![X3:vEBT_VEBT, X2:nat]:(~fmember_VEBT_VEBT @ X3 @ (fset_VEBT_VEBT2 @ ftreeList)|~fvEBT_V8194947554948674370ptions @ X3 @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17, c_0_18])])).
% 1.30/1.51 thf(c_0_28, plain, ![X2:nat, X1:list_VEBT_VEBT]:(fmember_VEBT_VEBT @ (fnth_VEBT_VEBT @ X1 @ X2) @ (fset_VEBT_VEBT2 @ X1)|~ford_less_nat @ X2 @ (fsize_s6755466524823107622T_VEBT @ X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20])])).
% 1.30/1.51 thf(c_0_29, plain, ![X3:vEBT_VEBT]:(fvEBT_VEBT_minNull @ X3|fvEBT_V8194947554948674370ptions @ X3 @ (esk91_1 @ X3)|~p1), inference(split_conjunct,[status(thm)],[c_0_21])).
% 1.30/1.51 thf(c_0_30, plain, p1, inference(split_conjunct,[status(thm)],[ax54])).
% 1.30/1.51 thf(c_0_31, plain, (~p43|ford_less_nat @ (fvEBT_VEBT_high @ fmi @ fna) @ (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ fm)), inference(fof_nnf,[status(thm)],[pax43])).
% 1.30/1.51 thf(c_0_32, plain, ((fsize_s6755466524823107622T_VEBT @ ftreeList)=(fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ fm)|~p32), inference(split_conjunct,[status(thm)],[c_0_22])).
% 1.30/1.51 thf(c_0_33, plain, (fm)=(fna), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24])])).
% 1.30/1.51 thf(c_0_34, plain, p32, inference(split_conjunct,[status(thm)],[ax23])).
% 1.30/1.51 thf(c_0_35, plain, (p2|~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))), inference(split_conjunct,[status(thm)],[c_0_25])).
% 1.30/1.51 thf(c_0_36, plain, ~p2, inference(split_conjunct,[status(thm)],[c_0_26])).
% 1.30/1.51 thf(c_0_37, plain, ![X4:nat, X2:nat]:(~fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ X2) @ X4|~ford_less_nat @ X2 @ (fsize_s6755466524823107622T_VEBT @ ftreeList)), inference(spm,[status(thm)],[c_0_27, c_0_28])).
% 1.30/1.51 thf(c_0_38, plain, ![X3:vEBT_VEBT]:(fvEBT_V8194947554948674370ptions @ X3 @ (esk91_1 @ X3)|fvEBT_VEBT_minNull @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30])])).
% 1.30/1.51 thf(c_0_39, plain, (ford_less_nat @ (fvEBT_VEBT_high @ fmi @ fna) @ (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ fm)|~p43), inference(split_conjunct,[status(thm)],[c_0_31])).
% 1.30/1.51 thf(c_0_40, plain, (fpower_power_nat @ (fnumeral_numeral_nat @ (fbit0 @ fone)) @ fna)=(fsize_s6755466524823107622T_VEBT @ ftreeList), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_33]), c_0_34])])).
% 1.30/1.51 thf(c_0_41, plain, p43, inference(split_conjunct,[status(thm)],[ax12])).
% 1.30/1.51 thf(c_0_42, plain, ~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)), inference(sr,[status(thm)],[c_0_35, c_0_36])).
% 1.30/1.51 thf(c_0_43, plain, ![X2:nat]:(fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ X2)|~ford_less_nat @ X2 @ (fsize_s6755466524823107622T_VEBT @ ftreeList)), inference(spm,[status(thm)],[c_0_37, c_0_38])).
% 1.30/1.51 thf(c_0_44, plain, ford_less_nat @ (fvEBT_VEBT_high @ fmi @ fna) @ (fsize_s6755466524823107622T_VEBT @ ftreeList), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_33]), c_0_40]), c_0_41])])).
% 1.30/1.51 thf(c_0_45, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_43]), c_0_44])]), ['proof']).
% 1.30/1.51 thf(5,plain,$false,inference(eprover,[status(thm),assumptions([h10,h8,h5,h3,h4,h1,h2,h0])],[])).
% 1.30/1.51 thf(6,plain,$false,inference(tab_imp,[status(thm),assumptions([h8,h5,h3,h4,h1,h2,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[fact_2__092_060open_062_Iif_AminNull_A_ItreeList_A_B_Ahigh_Ami_An_J_Athen_Avebt__insert_Asummary_A_Ihigh_Ami_An_J_Aelse_Asummary_J_A_061_Asummary_092_060close_062,4,5,h9,h10])).
% 1.30/1.51 thf(fact_5__C5_C,axiom,(sP1 => (![X1:vEBT_VEBT]:(((member_VEBT_VEBT @ X1) @ (set_VEBT_VEBT2 @ treeList)) => (![X2:nat]:(~(((vEBT_V8194947554948674370ptions @ X1) @ X2)))))))).
% 1.30/1.51 thf(7,plain,$false,inference(tab_imp,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[fact_5__C5_C,3,6,h7,h8])).
% 1.30/1.51 thf(pax82, axiom, (p82=>![X1:nat]:~(fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)) @ X1)), file('<stdin>', pax82)).
% 1.30/1.51 thf(pax1, axiom, (p1=>![X63:vEBT_VEBT]:(~(fvEBT_VEBT_minNull @ X63)=>~(![X59:nat]:~(fvEBT_V8194947554948674370ptions @ X63 @ X59)))), file('<stdin>', pax1)).
% 1.30/1.51 thf(nax2, axiom, (p2<=fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))), file('<stdin>', nax2)).
% 1.30/1.51 thf(ax81, axiom, ~(p2), file('<stdin>', ax81)).
% 1.30/1.51 thf(ax3, axiom, p82, file('<stdin>', ax3)).
% 1.30/1.51 thf(ax82, axiom, p1, file('<stdin>', ax82)).
% 1.30/1.51 thf(c_0_6, plain, ![X64:nat]:(~p82|~fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)) @ X64), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax82])])])])).
% 1.30/1.51 thf(c_0_7, plain, ![X286:vEBT_VEBT]:(~p1|(fvEBT_VEBT_minNull @ X286|fvEBT_V8194947554948674370ptions @ X286 @ (esk112_1 @ X286))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1])])])])])).
% 1.30/1.51 thf(c_0_8, plain, (~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))|p2), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax2])])).
% 1.30/1.51 thf(c_0_9, plain, ~p2, inference(fof_simplification,[status(thm)],[ax81])).
% 1.30/1.51 thf(c_0_10, plain, ![X1:nat]:(~p82|~fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)) @ X1), inference(split_conjunct,[status(thm)],[c_0_6])).
% 1.30/1.51 thf(c_0_11, plain, p82, inference(split_conjunct,[status(thm)],[ax3])).
% 1.30/1.51 thf(c_0_12, plain, ![X8:vEBT_VEBT]:(fvEBT_VEBT_minNull @ X8|fvEBT_V8194947554948674370ptions @ X8 @ (esk112_1 @ X8)|~p1), inference(split_conjunct,[status(thm)],[c_0_7])).
% 1.30/1.51 thf(c_0_13, plain, p1, inference(split_conjunct,[status(thm)],[ax82])).
% 1.30/1.51 thf(c_0_14, plain, (p2|~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))), inference(split_conjunct,[status(thm)],[c_0_8])).
% 1.30/1.51 thf(c_0_15, plain, ~p2, inference(split_conjunct,[status(thm)],[c_0_9])).
% 1.30/1.51 thf(c_0_16, plain, ![X1:nat]:~fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)) @ X1, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10, c_0_11])])).
% 1.30/1.51 thf(c_0_17, plain, ![X8:vEBT_VEBT]:(fvEBT_V8194947554948674370ptions @ X8 @ (esk112_1 @ X8)|fvEBT_VEBT_minNull @ X8), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 1.30/1.51 thf(c_0_18, plain, ~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)), inference(sr,[status(thm)],[c_0_14, c_0_15])).
% 1.30/1.51 thf(c_0_19, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16, c_0_17]), c_0_18]), ['proof']).
% 1.30/1.51 thf(8,plain,$false,inference(eprover,[status(thm),assumptions([h9,h7,h6,h3,h4,h1,h2,h0])],[])).
% 1.30/1.51 thf(pax82, axiom, (p82=>![X1:nat]:~(fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)) @ X1)), file('<stdin>', pax82)).
% 1.30/1.51 thf(pax1, axiom, (p1=>![X63:vEBT_VEBT]:(~(fvEBT_VEBT_minNull @ X63)=>~(![X59:nat]:~(fvEBT_V8194947554948674370ptions @ X63 @ X59)))), file('<stdin>', pax1)).
% 1.30/1.51 thf(nax2, axiom, (p2<=fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))), file('<stdin>', nax2)).
% 1.30/1.51 thf(ax92, axiom, ~(p2), file('<stdin>', ax92)).
% 1.30/1.51 thf(ax13, axiom, p82, file('<stdin>', ax13)).
% 1.30/1.51 thf(ax93, axiom, p1, file('<stdin>', ax93)).
% 1.30/1.51 thf(c_0_6, plain, ![X64:nat]:(~p82|~fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)) @ X64), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax82])])])])).
% 1.30/1.51 thf(c_0_7, plain, ![X286:vEBT_VEBT]:(~p1|(fvEBT_VEBT_minNull @ X286|fvEBT_V8194947554948674370ptions @ X286 @ (esk112_1 @ X286))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1])])])])])).
% 1.30/1.51 thf(c_0_8, plain, (~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))|p2), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax2])])).
% 1.30/1.51 thf(c_0_9, plain, ~p2, inference(fof_simplification,[status(thm)],[ax92])).
% 1.30/1.51 thf(c_0_10, plain, ![X1:nat]:(~p82|~fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)) @ X1), inference(split_conjunct,[status(thm)],[c_0_6])).
% 1.30/1.51 thf(c_0_11, plain, p82, inference(split_conjunct,[status(thm)],[ax13])).
% 1.30/1.51 thf(c_0_12, plain, ![X8:vEBT_VEBT]:(fvEBT_VEBT_minNull @ X8|fvEBT_V8194947554948674370ptions @ X8 @ (esk112_1 @ X8)|~p1), inference(split_conjunct,[status(thm)],[c_0_7])).
% 1.30/1.51 thf(c_0_13, plain, p1, inference(split_conjunct,[status(thm)],[ax93])).
% 1.30/1.51 thf(c_0_14, plain, (p2|~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))), inference(split_conjunct,[status(thm)],[c_0_8])).
% 1.30/1.51 thf(c_0_15, plain, ~p2, inference(split_conjunct,[status(thm)],[c_0_9])).
% 1.30/1.51 thf(c_0_16, plain, ![X1:nat]:~fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)) @ X1, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10, c_0_11])])).
% 1.30/1.51 thf(c_0_17, plain, ![X8:vEBT_VEBT]:(fvEBT_V8194947554948674370ptions @ X8 @ (esk112_1 @ X8)|fvEBT_VEBT_minNull @ X8), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 1.30/1.51 thf(c_0_18, plain, ~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)), inference(sr,[status(thm)],[c_0_14, c_0_15])).
% 1.30/1.51 thf(c_0_19, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16, c_0_17]), c_0_18]), ['proof']).
% 1.30/1.51 thf(9,plain,$false,inference(eprover,[status(thm),assumptions([h10,h7,h6,h3,h4,h1,h2,h0])],[])).
% 1.30/1.51 thf(10,plain,$false,inference(tab_imp,[status(thm),assumptions([h7,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[fact_2__092_060open_062_Iif_AminNull_A_ItreeList_A_B_Ahigh_Ami_An_J_Athen_Avebt__insert_Asummary_A_Ihigh_Ami_An_J_Aelse_Asummary_J_A_061_Asummary_092_060close_062,8,9,h9,h10])).
% 1.30/1.51 thf(pax82, axiom, (p82=>![X3:nat]:~(fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)) @ X3)), file('<stdin>', pax82)).
% 1.30/1.51 thf(pax1, axiom, (p1=>![X65:vEBT_VEBT]:(~(fvEBT_VEBT_minNull @ X65)=>~(![X61:nat]:~(fvEBT_V8194947554948674370ptions @ X65 @ X61)))), file('<stdin>', pax1)).
% 1.30/1.51 thf(nax2, axiom, (p2<=fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))), file('<stdin>', nax2)).
% 1.30/1.51 thf(ax271, axiom, ~(p2), file('<stdin>', ax271)).
% 1.30/1.51 thf(ax193, axiom, p82, file('<stdin>', ax193)).
% 1.30/1.51 thf(ax272, axiom, p1, file('<stdin>', ax272)).
% 1.30/1.51 thf(c_0_6, plain, ![X78:nat]:(~p82|~fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)) @ X78), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax82])])])])).
% 1.30/1.51 thf(c_0_7, plain, ![X300:vEBT_VEBT]:(~p1|(fvEBT_VEBT_minNull @ X300|fvEBT_V8194947554948674370ptions @ X300 @ (esk118_1 @ X300))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1])])])])])).
% 1.30/1.51 thf(c_0_8, plain, (~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))|p2), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax2])])).
% 1.30/1.51 thf(c_0_9, plain, ~p2, inference(fof_simplification,[status(thm)],[ax271])).
% 1.30/1.51 thf(c_0_10, plain, ![X3:nat]:(~p82|~fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)) @ X3), inference(split_conjunct,[status(thm)],[c_0_6])).
% 1.30/1.51 thf(c_0_11, plain, p82, inference(split_conjunct,[status(thm)],[ax193])).
% 1.30/1.51 thf(c_0_12, plain, ![X10:vEBT_VEBT]:(fvEBT_VEBT_minNull @ X10|fvEBT_V8194947554948674370ptions @ X10 @ (esk118_1 @ X10)|~p1), inference(split_conjunct,[status(thm)],[c_0_7])).
% 1.30/1.51 thf(c_0_13, plain, p1, inference(split_conjunct,[status(thm)],[ax272])).
% 1.30/1.51 thf(c_0_14, plain, (p2|~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))), inference(split_conjunct,[status(thm)],[c_0_8])).
% 1.30/1.51 thf(c_0_15, plain, ~p2, inference(split_conjunct,[status(thm)],[c_0_9])).
% 1.30/1.51 thf(c_0_16, plain, ![X3:nat]:~fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)) @ X3, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10, c_0_11])])).
% 1.30/1.51 thf(c_0_17, plain, ![X10:vEBT_VEBT]:(fvEBT_V8194947554948674370ptions @ X10 @ (esk118_1 @ X10)|fvEBT_VEBT_minNull @ X10), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 1.30/1.51 thf(c_0_18, plain, ~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)), inference(sr,[status(thm)],[c_0_14, c_0_15])).
% 1.30/1.51 thf(c_0_19, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16, c_0_17]), c_0_18]), ['proof']).
% 1.30/1.51 thf(11,plain,$false,inference(eprover,[status(thm),assumptions([h9,h8,h6,h3,h4,h1,h2,h0])],[])).
% 1.30/1.51 thf(pax82, axiom, (p82=>![X3:nat]:~(fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)) @ X3)), file('<stdin>', pax82)).
% 1.30/1.51 thf(pax1, axiom, (p1=>![X65:vEBT_VEBT]:(~(fvEBT_VEBT_minNull @ X65)=>~(![X61:nat]:~(fvEBT_V8194947554948674370ptions @ X65 @ X61)))), file('<stdin>', pax1)).
% 1.30/1.51 thf(nax2, axiom, (p2<=fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))), file('<stdin>', nax2)).
% 1.30/1.51 thf(ax282, axiom, ~(p2), file('<stdin>', ax282)).
% 1.30/1.51 thf(ax203, axiom, p82, file('<stdin>', ax203)).
% 1.30/1.51 thf(ax283, axiom, p1, file('<stdin>', ax283)).
% 1.30/1.51 thf(c_0_6, plain, ![X118:nat]:(~p82|~fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)) @ X118), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax82])])])])).
% 1.30/1.51 thf(c_0_7, plain, ![X340:vEBT_VEBT]:(~p1|(fvEBT_VEBT_minNull @ X340|fvEBT_V8194947554948674370ptions @ X340 @ (esk138_1 @ X340))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax1])])])])])).
% 1.30/1.51 thf(c_0_8, plain, (~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))|p2), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax2])])).
% 1.30/1.51 thf(c_0_9, plain, ~p2, inference(fof_simplification,[status(thm)],[ax282])).
% 1.30/1.51 thf(c_0_10, plain, ![X3:nat]:(~p82|~fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)) @ X3), inference(split_conjunct,[status(thm)],[c_0_6])).
% 1.30/1.51 thf(c_0_11, plain, p82, inference(split_conjunct,[status(thm)],[ax203])).
% 1.30/1.51 thf(c_0_12, plain, ![X10:vEBT_VEBT]:(fvEBT_VEBT_minNull @ X10|fvEBT_V8194947554948674370ptions @ X10 @ (esk138_1 @ X10)|~p1), inference(split_conjunct,[status(thm)],[c_0_7])).
% 1.30/1.51 thf(c_0_13, plain, p1, inference(split_conjunct,[status(thm)],[ax283])).
% 1.30/1.51 thf(c_0_14, plain, (p2|~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna))), inference(split_conjunct,[status(thm)],[c_0_8])).
% 1.30/1.51 thf(c_0_15, plain, ~p2, inference(split_conjunct,[status(thm)],[c_0_9])).
% 1.30/1.51 thf(c_0_16, plain, ![X3:nat]:~fvEBT_V8194947554948674370ptions @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)) @ X3, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10, c_0_11])])).
% 1.30/1.51 thf(c_0_17, plain, ![X10:vEBT_VEBT]:(fvEBT_V8194947554948674370ptions @ X10 @ (esk138_1 @ X10)|fvEBT_VEBT_minNull @ X10), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 1.30/1.51 thf(c_0_18, plain, ~fvEBT_VEBT_minNull @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fmi @ fna)), inference(sr,[status(thm)],[c_0_14, c_0_15])).
% 1.30/1.51 thf(c_0_19, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16, c_0_17]), c_0_18]), ['proof']).
% 1.30/1.51 thf(12,plain,$false,inference(eprover,[status(thm),assumptions([h10,h8,h6,h3,h4,h1,h2,h0])],[])).
% 1.30/1.51 thf(13,plain,$false,inference(tab_imp,[status(thm),assumptions([h8,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[fact_2__092_060open_062_Iif_AminNull_A_ItreeList_A_B_Ahigh_Ami_An_J_Athen_Avebt__insert_Asummary_A_Ihigh_Ami_An_J_Aelse_Asummary_J_A_061_Asummary_092_060close_062,11,12,h9,h10])).
% 1.30/1.51 thf(14,plain,$false,inference(tab_imp,[status(thm),assumptions([h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[fact_5__C5_C,10,13,h7,h8])).
% 1.30/1.51 thf(fact_1415__C7_C,axiom,((~(sP1)) => (![X1:nat]:(((ord_less_nat @ X1) @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ m)) => (~((((((vEBT_VEBT_high @ ma) @ na) = X1) => ((vEBT_V8194947554948674370ptions @ ((nth_VEBT_VEBT @ treeList) @ X1)) @ ((vEBT_VEBT_low @ ma) @ na))) => (~((![X2:nat]:((~(((((vEBT_VEBT_high @ X2) @ na) = X1) => (~(((vEBT_V8194947554948674370ptions @ ((nth_VEBT_VEBT @ treeList) @ X1)) @ ((vEBT_VEBT_low @ X2) @ na))))))) => (~((((ord_less_nat @ mi) @ X2) => (~(((ord_less_eq_nat @ X2) @ ma))))))))))))))))).
% 1.30/1.51 thf(15,plain,$false,inference(tab_imp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_1415__C7_C,7,14,h5,h6])).
% 1.30/1.51 thf(fact_1509__C6_C,axiom,(~((((ord_less_eq_nat @ mi) @ ma) => (~(((ord_less_nat @ ma) @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ deg)))))))).
% 1.30/1.51 thf(16,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[fact_1509__C6_C,15,h3,h4])).
% 1.30/1.51 thf(fact_1525_highlowprop,axiom,(~((((ord_less_nat @ ((vEBT_VEBT_high @ mi) @ na)) @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ m)) => (~(((ord_less_nat @ ((vEBT_VEBT_low @ mi) @ na)) @ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ na)))))))).
% 1.30/1.51 thf(17,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[fact_1525_highlowprop,16,h1,h2])).
% 1.30/1.51 thf(0,theorem,(~((![X1:nat]:(~(((vEBT_V8194947554948674370ptions @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ mi) @ na))) @ X1)))))),inference(contra,[status(thm),contra(discharge,[h0])],[17,h0])).
% 1.30/1.51 % SZS output end Proof
%------------------------------------------------------------------------------