TSTP Solution File: ITP269^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP269^1 : 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 : n018.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 00:30:19 EDT 2022
% Result : Theorem 23.93s 24.02s
% Output : Proof 23.93s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_vEBT_VEBT,type,
vEBT_VEBT: $tType ).
thf(ty_option_nat,type,
option_nat: $tType ).
thf(ty_list_VEBT_VEBT,type,
list_VEBT_VEBT: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_set_VEBT_VEBT,type,
set_VEBT_VEBT: $tType ).
thf(ty_num,type,
num: $tType ).
thf(ty_eigen__14,type,
eigen__14: nat ).
thf(ty_eigen__6,type,
eigen__6: nat ).
thf(ty_summin,type,
summin: nat ).
thf(ty_eigen__12,type,
eigen__12: nat ).
thf(ty_vEBT_vebt_mint,type,
vEBT_vebt_mint: vEBT_VEBT > option_nat ).
thf(ty_plus_plus_nat,type,
plus_plus_nat: nat > nat > nat ).
thf(ty_eigen__2,type,
eigen__2: nat ).
thf(ty_eigen__16,type,
eigen__16: nat ).
thf(ty_nth_VEBT_VEBT,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(ty_eigen__7,type,
eigen__7: nat ).
thf(ty_vEBT_VEBT_high,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(ty_the_nat,type,
the_nat: option_nat > nat ).
thf(ty_if_nat,type,
if_nat: $o > nat > nat > nat ).
thf(ty_eigen__15,type,
eigen__15: nat ).
thf(ty_eigen__1,type,
eigen__1: nat ).
thf(ty_numeral_numeral_nat,type,
numeral_numeral_nat: num > nat ).
thf(ty_eigen__0,type,
eigen__0: nat ).
thf(ty_treeList,type,
treeList: list_VEBT_VEBT ).
thf(ty_bit0,type,
bit0: num > num ).
thf(ty_eigen__4,type,
eigen__4: nat ).
thf(ty_deg,type,
deg: nat ).
thf(ty_times_times_nat,type,
times_times_nat: nat > nat > nat ).
thf(ty_eigen__5,type,
eigen__5: nat ).
thf(ty_vEBT_vebt_delete,type,
vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
thf(ty_eigen__11,type,
eigen__11: nat ).
thf(ty_eigen__3,type,
eigen__3: nat ).
thf(ty_eigen__17,type,
eigen__17: nat ).
thf(ty_eigen__10,type,
eigen__10: nat ).
thf(ty_member_VEBT_VEBT,type,
member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
thf(ty_mi,type,
mi: nat ).
thf(ty_eigen__8,type,
eigen__8: nat ).
thf(ty_na,type,
na: nat ).
thf(ty_eigen__13,type,
eigen__13: nat ).
thf(ty_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(ty_eigen__9,type,
eigen__9: nat ).
thf(ty_set_VEBT_VEBT2,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
thf(ty_list_u1324408373059187874T_VEBT,type,
list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(ty_vEBT_VEBT_low,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(ty_one,type,
one: num ).
thf(ty_eigen__18,type,
eigen__18: nat ).
thf(ty_vEBT_V8194947554948674370ptions,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(ty_some_nat,type,
some_nat: nat > option_nat ).
thf(ty_power_power_nat,type,
power_power_nat: nat > nat > nat ).
thf(ty_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ty_vEBT_vebt_maxt,type,
vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
thf(ty_ma,type,
ma: nat ).
thf(ty_m,type,
m: nat ).
thf(ty_divide_divide_nat,type,
divide_divide_nat: nat > nat > nat ).
thf(ty_lx,type,
lx: nat ).
thf(sP1,plain,
( sP1
<=> ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
= ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
= ma ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ord_less_nat @ ( if_nat @ sP2 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ma ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(conj_0,conjecture,
sP3 ).
thf(h0,negated_conjecture,
~ sP3,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
( ( some_nat @ eigen__0 )
= ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ summin ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
ord_less_eq_nat @ mi @ ma,
introduced(assumption,[]) ).
thf(h3,assumption,
ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ( sP2
=> sP1 )
=> ~ ( ~ sP2
=> sP2 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
=> ! [X2: nat] :
~ ( vEBT_V8194947554948674370ptions @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP2
=> sP1 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ sP2
=> sP2 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP2,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
sP3,
introduced(assumption,[]) ).
thf(h11,assumption,
ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ ( if_nat @ sP2 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ma ),
introduced(assumption,[]) ).
thf(h12,assumption,
vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ eigen__1,
introduced(assumption,[]) ).
thf(h13,assumption,
ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ),
introduced(assumption,[]) ).
thf(h14,assumption,
ord_less_nat @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ( sP2
=> sP1 )
=> ~ ( ~ sP2
=> sP2 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
! [X1: nat] :
( ( ord_less_nat @ X1 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
=> ~ ( ( ( ( vEBT_VEBT_high @ ( if_nat @ sP2 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ma ) @ na )
= X1 )
=> ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ X1 ) @ ( vEBT_VEBT_low @ ( if_nat @ sP2 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ma ) @ na ) ) )
=> ~ ! [X2: nat] :
( ~ ( ( ( vEBT_VEBT_high @ X2 @ na )
= X1 )
=> ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ X1 ) @ ( vEBT_VEBT_low @ X2 @ na ) ) )
=> ~ ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ X2 )
=> ~ ( ord_less_eq_nat @ X2 @ ( if_nat @ sP2 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ma ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
( sP2
=> sP1 ),
introduced(assumption,[]) ).
thf(h18,assumption,
( ~ sP2
=> sP2 ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h20,assumption,
sP1,
introduced(assumption,[]) ).
thf(h21,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ eigen__2,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h21,h8,h19,h17,h18,h15,h13,h14,h12,h10,h11,h8,h9,h6,h4,h2,h3,h1,h0])],[h8,h19]) ).
thf(fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,axiom,
~ ! [X1: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ X1 ) ).
thf(2,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h19,h17,h18,h15,h13,h14,h12,h10,h11,h8,h9,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__2)],[fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,1,h21]) ).
thf(h22,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ eigen__3,
introduced(assumption,[]) ).
thf(3,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h22,h8,h19,h17,h18,h15,h13,h14,h12,h10,h11,h8,h9,h6,h4,h2,h3,h1,h0])],[h8,h19]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h19,h17,h18,h15,h13,h14,h12,h10,h11,h8,h9,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h22]),tab_negall(eigenvar,eigen__3)],[fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,3,h22]) ).
thf(5,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h19,h17,h18,h15,h13,h14,h12,h10,h11,h8,h9,h6,h4,h2,h3,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h8])],[h18,2,4,h8,h8]) ).
thf(h23,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ eigen__4,
introduced(assumption,[]) ).
thf(6,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h23,h8,h20,h17,h18,h15,h13,h14,h12,h10,h11,h8,h9,h6,h4,h2,h3,h1,h0])],[h20,h9]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h20,h17,h18,h15,h13,h14,h12,h10,h11,h8,h9,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__4)],[fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,6,h23]) ).
thf(h24,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ eigen__5,
introduced(assumption,[]) ).
thf(8,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h24,h8,h20,h17,h18,h15,h13,h14,h12,h10,h11,h8,h9,h6,h4,h2,h3,h1,h0])],[h20,h9]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h20,h17,h18,h15,h13,h14,h12,h10,h11,h8,h9,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__5)],[fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,8,h24]) ).
thf(10,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h20,h17,h18,h15,h13,h14,h12,h10,h11,h8,h9,h6,h4,h2,h3,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h8])],[h18,7,9,h8,h8]) ).
thf(11,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h17,h18,h15,h13,h14,h12,h10,h11,h8,h9,h6,h4,h2,h3,h1,h0]),tab_imp(discharge,[h19]),tab_imp(discharge,[h20])],[h17,5,10,h19,h20]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h12,h10,h11,h8,h9,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,11,h17,h18]) ).
thf(h25,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ eigen__6,
introduced(assumption,[]) ).
thf(13,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h25,h16,h13,h14,h12,h10,h11,h8,h9,h6,h4,h2,h3,h1,h0])],[h10,h0]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h13,h14,h12,h10,h11,h8,h9,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__6)],[fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,13,h25]) ).
thf(fact_15__C115_C,axiom,
( ( ( sP2
=> sP1 )
=> ~ ( ~ sP2
=> sP2 ) )
=> ! [X1: nat] :
( ( ord_less_nat @ X1 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
=> ~ ( ( ( ( vEBT_VEBT_high @ ( if_nat @ sP2 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ma ) @ na )
= X1 )
=> ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ X1 ) @ ( vEBT_VEBT_low @ ( if_nat @ sP2 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ma ) @ na ) ) )
=> ~ ! [X2: nat] :
( ~ ( ( ( vEBT_VEBT_high @ X2 @ na )
= X1 )
=> ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ X1 ) @ ( vEBT_VEBT_low @ X2 @ na ) ) )
=> ~ ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ X2 )
=> ~ ( ord_less_eq_nat @ X2 @ ( if_nat @ sP2 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ma ) ) ) ) ) ) ) ).
thf(15,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h13,h14,h12,h10,h11,h8,h9,h6,h4,h2,h3,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[fact_15__C115_C,12,14,h15,h16]) ).
thf(fact_17_hlbound,axiom,
~ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h8,h9,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h13,h14])],[fact_17_hlbound,15,h13,h14]) ).
thf(fact_18_notemp,axiom,
~ ! [X1: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ X1 ) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h8,h9,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__1)],[fact_18_notemp,16,h12]) ).
thf(fact_21__C114_C,axiom,
~ ( sP3
=> ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ ( if_nat @ sP2 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ma ) ) ) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[fact_21__C114_C,17,h10,h11]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,18,h8,h9]) ).
thf(h26,assumption,
vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ eigen__7,
introduced(assumption,[]) ).
thf(h27,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ eigen__8,
introduced(assumption,[]) ).
thf(20,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h27,h8,h19,h17,h18,h15,h13,h14,h26,h10,h11,h19,h19,h7,h4,h2,h3,h1,h0])],[h8,h19]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h19,h17,h18,h15,h13,h14,h26,h10,h11,h19,h19,h7,h4,h2,h3,h1,h0]),tab_negall(discharge,[h27]),tab_negall(eigenvar,eigen__8)],[fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,20,h27]) ).
thf(h28,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ eigen__9,
introduced(assumption,[]) ).
thf(22,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h28,h8,h19,h17,h18,h15,h13,h14,h26,h10,h11,h19,h19,h7,h4,h2,h3,h1,h0])],[h8,h19]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h19,h17,h18,h15,h13,h14,h26,h10,h11,h19,h19,h7,h4,h2,h3,h1,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__9)],[fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,22,h28]) ).
thf(24,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h19,h17,h18,h15,h13,h14,h26,h10,h11,h19,h19,h7,h4,h2,h3,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h8])],[h18,21,23,h8,h8]) ).
thf(h29,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ eigen__10,
introduced(assumption,[]) ).
thf(25,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h29,h8,h20,h17,h18,h15,h13,h14,h26,h10,h11,h19,h19,h7,h4,h2,h3,h1,h0])],[h8,h19]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h20,h17,h18,h15,h13,h14,h26,h10,h11,h19,h19,h7,h4,h2,h3,h1,h0]),tab_negall(discharge,[h29]),tab_negall(eigenvar,eigen__10)],[fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,25,h29]) ).
thf(h30,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ eigen__11,
introduced(assumption,[]) ).
thf(27,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h30,h8,h20,h17,h18,h15,h13,h14,h26,h10,h11,h19,h19,h7,h4,h2,h3,h1,h0])],[h8,h19]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h20,h17,h18,h15,h13,h14,h26,h10,h11,h19,h19,h7,h4,h2,h3,h1,h0]),tab_negall(discharge,[h30]),tab_negall(eigenvar,eigen__11)],[fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,27,h30]) ).
thf(29,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h20,h17,h18,h15,h13,h14,h26,h10,h11,h19,h19,h7,h4,h2,h3,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h8])],[h18,26,28,h8,h8]) ).
thf(30,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h17,h18,h15,h13,h14,h26,h10,h11,h19,h19,h7,h4,h2,h3,h1,h0]),tab_imp(discharge,[h19]),tab_imp(discharge,[h20])],[h17,24,29,h19,h20]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h26,h10,h11,h19,h19,h7,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,30,h17,h18]) ).
thf(h31,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ eigen__12,
introduced(assumption,[]) ).
thf(32,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h31,h16,h13,h14,h26,h10,h11,h19,h19,h7,h4,h2,h3,h1,h0])],[h10,h0]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h13,h14,h26,h10,h11,h19,h19,h7,h4,h2,h3,h1,h0]),tab_negall(discharge,[h31]),tab_negall(eigenvar,eigen__12)],[fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,32,h31]) ).
thf(34,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h13,h14,h26,h10,h11,h19,h19,h7,h4,h2,h3,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[fact_15__C115_C,31,33,h15,h16]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h10,h11,h19,h19,h7,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h13,h14])],[fact_17_hlbound,34,h13,h14]) ).
thf(36,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h19,h19,h7,h4,h2,h3,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__7)],[fact_18_notemp,35,h26]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h19,h7,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[fact_21__C114_C,36,h10,h11]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h19,h19])],[h7,37,h19,h19]) ).
thf(39,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[h4,19,38,h6,h7]) ).
thf(h32,assumption,
vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ eigen__13,
introduced(assumption,[]) ).
thf(h33,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ eigen__14,
introduced(assumption,[]) ).
thf(40,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h33,h8,h19,h17,h18,h15,h13,h14,h32,h10,h11,h5,h2,h3,h1,h0])],[h8,h19]) ).
thf(41,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h19,h17,h18,h15,h13,h14,h32,h10,h11,h5,h2,h3,h1,h0]),tab_negall(discharge,[h33]),tab_negall(eigenvar,eigen__14)],[fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,40,h33]) ).
thf(h34,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ eigen__15,
introduced(assumption,[]) ).
thf(42,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h34,h8,h19,h17,h18,h15,h13,h14,h32,h10,h11,h5,h2,h3,h1,h0])],[h8,h19]) ).
thf(43,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h19,h17,h18,h15,h13,h14,h32,h10,h11,h5,h2,h3,h1,h0]),tab_negall(discharge,[h34]),tab_negall(eigenvar,eigen__15)],[fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,42,h34]) ).
thf(44,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h19,h17,h18,h15,h13,h14,h32,h10,h11,h5,h2,h3,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h8])],[h18,41,43,h8,h8]) ).
thf(h35,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ eigen__16,
introduced(assumption,[]) ).
thf(45,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h35,h8,h20,h17,h18,h15,h13,h14,h32,h10,h11,h5,h2,h3,h1,h0])],[h10,h0]) ).
thf(46,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h20,h17,h18,h15,h13,h14,h32,h10,h11,h5,h2,h3,h1,h0]),tab_negall(discharge,[h35]),tab_negall(eigenvar,eigen__16)],[fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,45,h35]) ).
thf(h36,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ eigen__17,
introduced(assumption,[]) ).
thf(47,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h36,h8,h20,h17,h18,h15,h13,h14,h32,h10,h11,h5,h2,h3,h1,h0])],[h10,h0]) ).
thf(48,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h20,h17,h18,h15,h13,h14,h32,h10,h11,h5,h2,h3,h1,h0]),tab_negall(discharge,[h36]),tab_negall(eigenvar,eigen__17)],[fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,47,h36]) ).
thf(49,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h20,h17,h18,h15,h13,h14,h32,h10,h11,h5,h2,h3,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h8])],[h18,46,48,h8,h8]) ).
thf(50,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h17,h18,h15,h13,h14,h32,h10,h11,h5,h2,h3,h1,h0]),tab_imp(discharge,[h19]),tab_imp(discharge,[h20])],[h17,44,49,h19,h20]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h32,h10,h11,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,50,h17,h18]) ).
thf(h37,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ eigen__18,
introduced(assumption,[]) ).
thf(52,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h37,h16,h13,h14,h32,h10,h11,h5,h2,h3,h1,h0])],[h10,h0]) ).
thf(53,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h13,h14,h32,h10,h11,h5,h2,h3,h1,h0]),tab_negall(discharge,[h37]),tab_negall(eigenvar,eigen__18)],[fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,52,h37]) ).
thf(54,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h13,h14,h32,h10,h11,h5,h2,h3,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[fact_15__C115_C,51,53,h15,h16]) ).
thf(55,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h32,h10,h11,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h13,h14])],[fact_17_hlbound,54,h13,h14]) ).
thf(56,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h5,h2,h3,h1,h0]),tab_negall(discharge,[h32]),tab_negall(eigenvar,eigen__13)],[fact_18_notemp,55,h32]) ).
thf(57,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[fact_21__C114_C,56,h10,h11]) ).
thf(fact_26__C112_C,axiom,
( ~ ( ( sP2
=> sP1 )
=> ~ ( ~ sP2
=> sP2 ) )
=> ! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
=> ! [X2: nat] :
~ ( vEBT_V8194947554948674370ptions @ X1 @ X2 ) ) ) ).
thf(58,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h3,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[fact_26__C112_C,39,57,h4,h5]) ).
thf(fact_103__C6_C,axiom,
~ ( ( ord_less_eq_nat @ mi @ ma )
=> ~ ( ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
thf(59,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[fact_103__C6_C,58,h2,h3]) ).
thf(fact_532__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062lx_O_ASome_Alx_A_061_Avebt__mint_A_ItreeList_A_B_Asummin_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [X1: nat] :
( ( some_nat @ X1 )
!= ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ summin ) ) ) ).
thf(60,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_532__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062lx_O_ASome_Alx_A_061_Avebt__mint_A_ItreeList_A_B_Asummin_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,59,h1]) ).
thf(0,theorem,
sP3,
inference(contra,[status(thm),contra(discharge,[h0])],[60,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ITP269^1 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 2 18:15:15 EDT 2022
% 0.14/0.36 % CPUTime :
% 23.93/24.02 % SZS status Theorem
% 23.93/24.02 % Mode: mode9a:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 23.93/24.02 % Inferences: 0
% 23.93/24.02 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------