%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP245^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : lash -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 : 300s
% DateTime : Sat Feb 28 09:29:59 AM UTC 2026
% Result : Theorem 177.32s 177.65s
% Output : Proof 177.32s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_num,type,
num: $tType ).
thf(ty_option4927543243414619207at_nat,type,
option4927543243414619207at_nat: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_option_nat,type,
option_nat: $tType ).
thf(ty_real,type,
real: $tType ).
thf(ty_list_VEBT_VEBT,type,
list_VEBT_VEBT: $tType ).
thf(ty_product_prod_nat_nat,type,
product_prod_nat_nat: $tType ).
thf(ty_vEBT_VEBT,type,
vEBT_VEBT: $tType ).
thf(ty_zero_zero_real,type,
zero_zero_real: real ).
thf(ty_vEBT_vebt_maxt,type,
vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
thf(ty_some_P7363390416028606310at_nat,type,
some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
thf(ty_vEBT_vebt_mint,type,
vEBT_vebt_mint: vEBT_VEBT > option_nat ).
thf(ty_cos_real,type,
cos_real: real > real ).
thf(ty_vEBT_VEBT_high,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(ty_size_s6755466524823107622T_VEBT,type,
size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
thf(ty_product_Pair_nat_nat,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(ty_na,type,
na: nat ).
thf(ty_the_nat,type,
the_nat: option_nat > nat ).
thf(ty_numeral_numeral_real,type,
numeral_numeral_real: num > real ).
thf(ty_eigen__0,type,
eigen__0: real ).
thf(ty_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ty_treeList,type,
treeList: list_VEBT_VEBT ).
thf(ty_m,type,
m: nat ).
thf(ty_bit0,type,
bit0: num > num ).
thf(ty_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(ty_vEBT_VEBT_mul,type,
vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
thf(ty_vEBT_Node,type,
vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(ty_vEBT_VEBT_low,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(ty_ord_less_eq_real,type,
ord_less_eq_real: real > real > $o ).
thf(ty_ma,type,
ma: nat ).
thf(ty_some_nat,type,
some_nat: nat > option_nat ).
thf(ty_vEBT_vebt_succ,type,
vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
thf(ty_summary,type,
summary: vEBT_VEBT ).
thf(ty_minus_minus_nat,type,
minus_minus_nat: nat > nat > nat ).
thf(ty_one,type,
one: num ).
thf(ty_ia,type,
ia: nat ).
thf(ty_none_nat,type,
none_nat: option_nat ).
thf(ty_divide_divide_nat,type,
divide_divide_nat: nat > nat > nat ).
thf(ty_power_power_nat,type,
power_power_nat: nat > nat > nat ).
thf(ty_vEBT_VEBT_add,type,
vEBT_VEBT_add: option_nat > option_nat > option_nat ).
thf(ty_vEBT_vebt_member,type,
vEBT_vebt_member: vEBT_VEBT > nat > $o ).
thf(ty_mi,type,
mi: nat ).
thf(ty_vEBT_VEBT_less,type,
vEBT_VEBT_less: option_nat > option_nat > $o ).
thf(ty_xa,type,
xa: nat ).
thf(ty_numeral_numeral_nat,type,
numeral_numeral_nat: num > nat ).
thf(ty_suc,type,
suc: nat > nat ).
thf(ty_deg,type,
deg: nat ).
thf(ty_vEBT_invar_vebt,type,
vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
thf(ty_nth_VEBT_VEBT,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(sP1,plain,
( sP1
<=> ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ ia ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ~ ( ( ord_less_nat @ ia @ ma )
=> ~ ( ord_less_nat @ mi @ ia ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) )
=> ~ ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ia @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: list_VEBT_VEBT,X2: vEBT_VEBT,X3: nat] :
( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ X1 @ X2 ) @ X3 )
=> ~ ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg )
=> ~ ( ~ ( ( X3 != mi )
=> ( X3 = ma ) )
=> ~ ( ~ ( ~ ( ( ord_less_nat @ X3 @ ma )
=> ~ ( ord_less_nat @ mi @ X3 ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ X1 ) ) )
=> ~ ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ X1 @ ( vEBT_VEBT_high @ X3 @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X3 @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: vEBT_VEBT,X2: nat] :
( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ X1 ) @ X2 )
=> ~ ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg )
=> ~ ( ~ ( ( X2 != mi )
=> ( X2 = ma ) )
=> ~ ( ~ ( ~ ( ( ord_less_nat @ X2 @ ma )
=> ~ ( ord_less_nat @ mi @ X2 ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) )
=> ~ ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP1
=> ~ ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg )
=> ~ ( ~ ( ( ia != mi )
=> ( ia = ma ) )
=> ~ sP2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: nat,X2: list_VEBT_VEBT,X3: vEBT_VEBT,X4: nat] :
( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ X1 @ X2 @ X3 ) @ X4 )
=> ~ ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X1 )
=> ~ ( ~ ( ( X4 != mi )
=> ( X4 = ma ) )
=> ~ ( ~ ( ~ ( ( ord_less_nat @ X4 @ ma )
=> ~ ( ord_less_nat @ mi @ X4 ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ X1 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ X2 ) ) )
=> ~ ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ X2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ X1 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ X1 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ( ord_less_nat @ ia @ ma )
=> ~ ( ord_less_nat @ mi @ ia ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ia = ma ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ord_less_nat @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ia = mi ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP9
=> ~ ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ia @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ~ sP10
=> sP8 )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ sP10
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: nat,X2: nat,X3: nat,X4: list_VEBT_VEBT,X5: vEBT_VEBT,X6: nat] :
( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X1 @ X2 ) ) @ X3 @ X4 @ X5 ) @ X6 )
=> ~ ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X3 )
=> ~ ( ~ ( ( X6 != X1 )
=> ( X6 = X2 ) )
=> ~ ( ~ ( ~ ( ( ord_less_nat @ X6 @ X2 )
=> ~ ( ord_less_nat @ X1 @ X6 ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_high @ X6 @ ( divide_divide_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ X4 ) ) )
=> ~ ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ X4 @ ( vEBT_VEBT_high @ X6 @ ( divide_divide_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X6 @ ( divide_divide_nat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: nat] :
( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ X1 )
=> ~ ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg )
=> ~ ( ~ ( ( X1 != mi )
=> ( X1 = ma ) )
=> ~ ( ~ ( ~ ( ( ord_less_nat @ X1 @ ma )
=> ~ ( ord_less_nat @ mi @ X1 ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_high @ X1 @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) )
=> ~ ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ X1 @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X1 @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: nat,X2: nat,X3: list_VEBT_VEBT,X4: vEBT_VEBT,X5: nat] :
( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ X1 ) ) @ X2 @ X3 @ X4 ) @ X5 )
=> ~ ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 )
=> ~ ( ~ ( ( X5 != mi )
=> ( X5 = X1 ) )
=> ~ ( ~ ( ~ ( ( ord_less_nat @ X5 @ X1 )
=> ~ ( ord_less_nat @ mi @ X5 ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_high @ X5 @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ X3 ) ) )
=> ~ ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ X3 @ ( vEBT_VEBT_high @ X5 @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X5 @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg )
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ia @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(conj_0,conjecture,
( ~ sP13
=> ~ sP11 ) ).
thf(h0,negated_conjecture,
~ ( ~ sP13
=> ~ sP11 ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h2,assumption,
sP11,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ~ ( ( ord_less_eq_real @ zero_zero_real @ eigen__0 )
=> ~ ( ord_less_eq_real @ eigen__0 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
=> ( ( cos_real @ eigen__0 )
!= zero_zero_real ) )
=> ~ ! [X1: real] :
( ~ ( ~ ( ( ord_less_eq_real @ zero_zero_real @ X1 )
=> ~ ( ord_less_eq_real @ X1 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
=> ( ( cos_real @ X1 )
!= zero_zero_real ) )
=> ( X1 = eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( ( ord_less_eq_real @ zero_zero_real @ eigen__0 )
=> ~ ( ord_less_eq_real @ eigen__0 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
=> ( ( cos_real @ eigen__0 )
!= zero_zero_real ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
! [X1: real] :
( ~ ( ~ ( ( ord_less_eq_real @ zero_zero_real @ X1 )
=> ~ ( ord_less_eq_real @ X1 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
=> ( ( cos_real @ X1 )
!= zero_zero_real ) )
=> ( X1 = eigen__0 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ( ord_less_eq_real @ zero_zero_real @ eigen__0 )
=> ~ ( ord_less_eq_real @ eigen__0 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
( ( cos_real @ eigen__0 )
= zero_zero_real ),
introduced(assumption,[]) ).
thf(h10,assumption,
ord_less_eq_real @ zero_zero_real @ eigen__0,
introduced(assumption,[]) ).
thf(h11,assumption,
ord_less_eq_real @ eigen__0 @ ( numeral_numeral_real @ ( bit0 @ one ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
( ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
= none_nat )
=> ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= none_nat ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
( ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
!= none_nat )
=> ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
( ~ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
!= none_nat )
=> ~ ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
=> ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
( ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
!= none_nat )
=> ~ ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
=> ~ ( ( ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
= none_nat )
=> ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= none_nat ) )
=> ~ ( ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
!= none_nat )
=> ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
( ( size_s6755466524823107622T_VEBT @ treeList )
= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
vEBT_invar_vebt @ summary @ m,
introduced(assumption,[]) ).
thf(h18,assumption,
vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ treeList @ summary ) @ ia,
introduced(assumption,[]) ).
thf(h19,assumption,
( ~ sP10
=> ( ~ sP8
=> ~ ( ~ ( ord_less_nat @ ia @ mi )
=> ~ ( ~ ( ord_less_nat @ ia @ mi )
=> ~ ( ~ ( ord_less_nat @ ma @ ia )
=> ~ ( ~ ( ord_less_nat @ ma @ ia )
=> ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
=> ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ treeList @ summary ) @ ia ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ~ sP10
=> ( ~ sP8
=> ~ ( ~ ( ord_less_nat @ ia @ mi )
=> ~ ( ~ ( ord_less_nat @ ia @ mi )
=> ~ ( ~ ( ord_less_nat @ ma @ ia )
=> ~ ( ~ ( ord_less_nat @ ma @ ia )
=> ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
=> ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ),
introduced(assumption,[]) ).
thf(h23,assumption,
ord_less_nat @ ( vEBT_VEBT_low @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ),
introduced(assumption,[]) ).
thf(h24,assumption,
ord_less_nat @ xa @ ia,
introduced(assumption,[]) ).
thf(h25,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( sP7
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP2
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP2
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP12
| sP13
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP17
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP5
| ~ sP1
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP13
| sP10
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP15
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP4
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP16
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP14
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP11
| ~ sP9
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(fact_50_member__inv,axiom,
sP14 ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h24,h25,h22,h23,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h3,h4,h2,fact_50_member__inv,h25]) ).
thf(fact_2__092_060open_062x_A_060_Ai_A_092_060and_062_Avebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Ai_092_060close_062,axiom,
~ ( ( ord_less_nat @ xa @ ia )
=> ~ sP1 ) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h23,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h24,h25])],[fact_2__092_060open_062x_A_060_Ai_A_092_060and_062_Avebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Ai_092_060close_062,15,h24,h25]) ).
thf(fact_66__092_060open_062high_Ax_An_A_060_A2_A_094_Am_A_092_060and_062_Alow_Ax_An_A_060_A2_A_094_An_092_060close_062,axiom,
~ ( ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_low @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h22,h23])],[fact_66__092_060open_062high_Ax_An_A_060_A2_A_094_Am_A_092_060and_062_Alow_Ax_An_A_060_A2_A_094_An_092_060close_062,16,h22,h23]) ).
thf(h26,assumption,
~ ( ~ sP8
=> ~ ( ~ ( ord_less_nat @ ia @ mi )
=> ~ ( ~ ( ord_less_nat @ ia @ mi )
=> ~ ( ~ ( ord_less_nat @ ma @ ia )
=> ~ ( ~ ( ord_less_nat @ ma @ ia )
=> ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
=> ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
( ~ ( ord_less_nat @ ia @ mi )
=> ~ ( ~ ( ord_less_nat @ ia @ mi )
=> ~ ( ~ ( ord_less_nat @ ma @ ia )
=> ~ ( ~ ( ord_less_nat @ ma @ ia )
=> ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
=> ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(18,plain,
( sP7
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP2
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP2
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP12
| sP13
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( sP17
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP5
| ~ sP1
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP15
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP4
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP16
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP11
| ~ sP9
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP14
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP13
| sP10
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h24,h25,h22,h23,h4,h27,h3,h26,h20,h21,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0])],[18,19,20,21,22,23,24,25,26,27,28,29,30,31,h3,h4,h2,fact_50_member__inv,h25]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h23,h4,h27,h3,h26,h20,h21,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h24,h25])],[fact_2__092_060open_062x_A_060_Ai_A_092_060and_062_Avebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Ai_092_060close_062,32,h24,h25]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h27,h3,h26,h20,h21,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h22,h23])],[fact_66__092_060open_062high_Ax_An_A_060_A2_A_094_Am_A_092_060and_062_Alow_Ax_An_A_060_A2_A_094_An_092_060close_062,33,h22,h23]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h26,h20,h21,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h4,h27])],[h26,34,h4,h27]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h21,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h3,h26])],[h21,35,h3,h26]) ).
thf(fact_68__092_060open_062vebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_A_ISuc_A_ISuc_A_Ideg_A_N_A2_J_J_J_AtreeList_Asummary_J_Ai_A_061_A_Iif_Ai_A_061_Ami_Athen_ATrue_Aelse_Aif_Ai_A_061_Ama_Athen_ATrue_Aelse_Aif_Ai_A_060_Ami_Athen_AFalse_Aelse_Aif_Ama_A_060_Ai_Athen_AFalse_Aelse_Alet_Ah_A_061_Ahigh_Ai_A_ISuc_A_ISuc_A_Ideg_A_N_A2_J_J_Adiv_A2_J_059_Al_A_061_Alow_Ai_A_ISuc_A_ISuc_A_Ideg_A_N_A2_J_J_Adiv_A2_J_Ain_Aif_Ah_A_060_Alength_AtreeList_Athen_Avebt__member_A_ItreeList_A_B_Ah_J_Al_Aelse_AFalse_J_092_060close_062,axiom,
( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ treeList @ summary ) @ ia )
= ( ~ sP10
=> ( ~ sP8
=> ~ ( ~ ( ord_less_nat @ ia @ mi )
=> ~ ( ~ ( ord_less_nat @ ia @ mi )
=> ~ ( ~ ( ord_less_nat @ ma @ ia )
=> ~ ( ~ ( ord_less_nat @ ma @ ia )
=> ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
=> ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_high @ ia @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ) ) ) ) ) ) ) ) ).
thf(37,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_bq(discharge,[h18,h19]),tab_bq(discharge,[h20,h21])],[fact_68__092_060open_062vebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_A_ISuc_A_ISuc_A_Ideg_A_N_A2_J_J_J_AtreeList_Asummary_J_Ai_A_061_A_Iif_Ai_A_061_Ami_Athen_ATrue_Aelse_Aif_Ai_A_061_Ama_Athen_ATrue_Aelse_Aif_Ai_A_060_Ami_Athen_AFalse_Aelse_Aif_Ama_A_060_Ai_Athen_AFalse_Aelse_Alet_Ah_A_061_Ahigh_Ai_A_ISuc_A_ISuc_A_Ideg_A_N_A2_J_J_Adiv_A2_J_059_Al_A_061_Alow_Ai_A_ISuc_A_ISuc_A_Ideg_A_N_A2_J_J_Adiv_A2_J_Ain_Aif_Ah_A_060_Alength_AtreeList_Athen_Avebt__member_A_ItreeList_A_B_Ah_J_Al_Aelse_AFalse_J_092_060close_062,17,36,h18,h19,h20,h21]) ).
thf(fact_117__092_060open_062length_AtreeList_A_061_A2_A_094_Am_A_092_060and_062_Ainvar__vebt_Asummary_Am_092_060close_062,axiom,
~ ( ( ( size_s6755466524823107622T_VEBT @ treeList )
= ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
=> ~ ( vEBT_invar_vebt @ summary @ m ) ) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h16,h17])],[fact_117__092_060open_062length_AtreeList_A_061_A2_A_094_Am_A_092_060and_062_Ainvar__vebt_Asummary_Am_092_060close_062,37,h16,h17]) ).
thf(fact_994__C1_C,axiom,
~ ( ( ~ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
!= none_nat )
=> ~ ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
=> ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
=> ~ ( ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
!= none_nat )
=> ~ ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
=> ~ ( ( ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
= none_nat )
=> ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= none_nat ) )
=> ~ ( ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
!= none_nat )
=> ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[fact_994__C1_C,38,h14,h15]) ).
thf(fact_995__C2_C,axiom,
~ ( ( ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
= none_nat )
=> ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= none_nat ) )
=> ~ ( ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
!= none_nat )
=> ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[fact_995__C2_C,39,h12,h13]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h8,40,h10,h11]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h6,41,h8,h9]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,42,h6,h7]) ).
thf(fact_7886_cos__is__zero,axiom,
~ ! [X1: real] :
( ~ ( ~ ( ( ord_less_eq_real @ zero_zero_real @ X1 )
=> ~ ( ord_less_eq_real @ X1 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
=> ( ( cos_real @ X1 )
!= zero_zero_real ) )
=> ~ ! [X2: real] :
( ~ ( ~ ( ( ord_less_eq_real @ zero_zero_real @ X2 )
=> ~ ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
=> ( ( cos_real @ X2 )
!= zero_zero_real ) )
=> ( X2 = X1 ) ) ) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[fact_7886_cos__is__zero,43,h5]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,44,h3,h4]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,45,h1,h2]) ).
thf(0,theorem,
( ~ sP13
=> ~ sP11 ),
inference(contra,[status(thm),contra(discharge,[h0])],[46,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP245^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.11/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.33 % Computer : n022.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Thu Feb 26 21:01:06 EST 2026
% 0.15/0.33 % CPUTime :
% 177.32/177.65 % SZS status Theorem
% 177.32/177.65 % Mode: cade22sinegrackle2x84ac
% 177.32/177.65 % Steps: 355048
% 177.32/177.65 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------