%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP239^3 : 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 : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Feb 28 09:29:57 AM UTC 2026
% Result : Theorem 0.96s 1.14s
% Output : Proof 0.96s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_list_VEBT_VEBT,type,
list_VEBT_VEBT: $tType ).
thf(ty_option_nat,type,
option_nat: $tType ).
thf(ty_real,type,
real: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_vEBT_VEBT,type,
vEBT_VEBT: $tType ).
thf(ty_option4927543243414619207at_nat,type,
option4927543243414619207at_nat: $tType ).
thf(ty_num,type,
num: $tType ).
thf(ty_product_prod_nat_nat,type,
product_prod_nat_nat: $tType ).
thf(ty_set_VEBT_VEBT,type,
set_VEBT_VEBT: $tType ).
thf(ty_vEBT_vebt_member,type,
vEBT_vebt_member: vEBT_VEBT > nat > $o ).
thf(ty_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(ty_mi,type,
mi: nat ).
thf(ty_vEBT_VEBT_high,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(ty_vEBT_VEBT_mul,type,
vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
thf(ty_ord_less_eq_real,type,
ord_less_eq_real: real > real > $o ).
thf(ty_m,type,
m: nat ).
thf(ty_power_power_nat,type,
power_power_nat: nat > nat > nat ).
thf(ty_some_P7363390416028606310at_nat,type,
some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
thf(ty_vEBT_Node,type,
vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(ty_summary,type,
summary: vEBT_VEBT ).
thf(ty_eigen__6,type,
eigen__6: nat ).
thf(ty_eigen__1,type,
eigen__1: nat ).
thf(ty_ma,type,
ma: nat ).
thf(ty_vEBT_vebt_mint,type,
vEBT_vebt_mint: vEBT_VEBT > option_nat ).
thf(ty_some_nat,type,
some_nat: nat > option_nat ).
thf(ty_if_option_nat,type,
if_option_nat: $o > option_nat > option_nat > option_nat ).
thf(ty_eigen__3,type,
eigen__3: nat ).
thf(ty_vEBT_VEBT_low,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(ty_vEBT_VEBT_greater,type,
vEBT_VEBT_greater: option_nat > option_nat > $o ).
thf(ty_treeList,type,
treeList: list_VEBT_VEBT ).
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_vEBT_VEBT_add,type,
vEBT_VEBT_add: option_nat > option_nat > option_nat ).
thf(ty_zero_zero_real,type,
zero_zero_real: real ).
thf(ty_one,type,
one: num ).
thf(ty_vEBT_vebt_maxt,type,
vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
thf(ty_eigen__2,type,
eigen__2: nat ).
thf(ty_eigen__0,type,
eigen__0: real ).
thf(ty_numeral_numeral_real,type,
numeral_numeral_real: num > real ).
thf(ty_divide_divide_nat,type,
divide_divide_nat: nat > nat > nat ).
thf(ty_eigen__4,type,
eigen__4: nat ).
thf(ty_eigen__5,type,
eigen__5: nat ).
thf(ty_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ty_bit0,type,
bit0: num > num ).
thf(ty_za,type,
za: nat ).
thf(ty_set_VEBT_VEBT2,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
thf(ty_xa,type,
xa: nat ).
thf(ty_deg,type,
deg: nat ).
thf(ty_numeral_numeral_nat,type,
numeral_numeral_nat: num > nat ).
thf(ty_pr,type,
pr: nat ).
thf(ty_the_nat,type,
the_nat: option_nat > nat ).
thf(ty_member_VEBT_VEBT,type,
member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
thf(ty_none_nat,type,
none_nat: option_nat ).
thf(ty_size_s6755466524823107622T_VEBT,type,
size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
thf(ty_nth_VEBT_VEBT,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(ty_cos_real,type,
cos_real: real > real ).
thf(ty_vEBT_V8194947554948674370ptions,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(ty_vEBT_vebt_pred,type,
vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
thf(sP1,plain,
( sP1
<=> ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( za = ma ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( za = mi ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
!= none_nat )
=> ~ ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( mi = ma ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(conj_0,conjecture,
sP1 ).
thf(h0,negated_conjecture,
~ sP1,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,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(h2,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(h3,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(h4,assumption,
~ ( ( ord_less_eq_real @ zero_zero_real @ eigen__0 )
=> ~ ( ord_less_eq_real @ eigen__0 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ( cos_real @ eigen__0 )
= zero_zero_real ),
introduced(assumption,[]) ).
thf(h6,assumption,
ord_less_eq_real @ zero_zero_real @ eigen__0,
introduced(assumption,[]) ).
thf(h7,assumption,
ord_less_eq_real @ eigen__0 @ ( numeral_numeral_real @ ( bit0 @ one ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
( ~ sP4
=> ( ( vEBT_vebt_pred @ ( 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_pred @ ( 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(h9,assumption,
( sP4
=> ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= ( if_option_nat
@ ( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
= none_nat )
@ ( if_option_nat @ ( ord_less_nat @ mi @ xa ) @ ( some_nat @ mi ) @ none_nat )
@ ( 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_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP4,
introduced(assumption,[]) ).
thf(h11,assumption,
( ( vEBT_vebt_pred @ ( 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_pred @ ( 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(fact_2_abe,axiom,
sP1 ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[fact_2_abe,h0]) ).
thf(h12,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h13,assumption,
( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= ( if_option_nat
@ ( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
= none_nat )
@ ( if_option_nat @ ( ord_less_nat @ mi @ xa ) @ ( some_nat @ mi ) @ none_nat )
@ ( 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_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(fact_960_i1,axiom,
sP4 ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[fact_960_i1,h12]) ).
thf(h14,assumption,
( ( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
= none_nat )
=> ~ ( ( ( ord_less_nat @ mi @ xa )
=> ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= ( some_nat @ mi ) ) )
=> ~ ( ~ ( ord_less_nat @ mi @ xa )
=> ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= none_nat ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
( ( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
!= none_nat )
=> ( ( vEBT_vebt_pred @ ( 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_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
!= none_nat ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ( ( ord_less_nat @ mi @ xa )
=> ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= ( some_nat @ mi ) ) )
=> ~ ( ~ ( ord_less_nat @ mi @ xa )
=> ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= none_nat ) ) ),
introduced(assumption,[]) ).
thf(3,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[fact_2_abe,h0]) ).
thf(h18,assumption,
( ( ord_less_nat @ mi @ xa )
=> ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= ( some_nat @ mi ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
( ~ ( ord_less_nat @ mi @ xa )
=> ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= none_nat ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( ord_less_nat @ mi @ xa ),
introduced(assumption,[]) ).
thf(h21,assumption,
( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= ( some_nat @ mi ) ),
introduced(assumption,[]) ).
thf(4,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h20,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[fact_2_abe,h0]) ).
thf(h22,assumption,
ord_less_nat @ mi @ xa,
introduced(assumption,[]) ).
thf(h23,assumption,
( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= none_nat ),
introduced(assumption,[]) ).
thf(5,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h22,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[fact_2_abe,h0]) ).
thf(h24,assumption,
( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
= none_nat ),
introduced(assumption,[]) ).
thf(h25,assumption,
( ( vEBT_vebt_pred @ ( 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_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(6,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h24,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[fact_2_abe,h0]) ).
thf(h26,assumption,
( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
= none_nat ),
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(7,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h26,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[fact_2_abe,h0]) ).
thf(h28,assumption,
( ( some_nat @ eigen__1 )
= ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ pr ) ) ),
introduced(assumption,[]) ).
thf(h29,assumption,
( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
= ( some_nat @ eigen__2 ) ),
introduced(assumption,[]) ).
thf(h30,assumption,
vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ za,
introduced(assumption,[]) ).
thf(h31,assumption,
ord_less_nat @ za @ xa,
introduced(assumption,[]) ).
thf(h32,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h33,assumption,
! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ treeList ) )
=> ! [X2: nat] :
~ ( vEBT_V8194947554948674370ptions @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(8,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h32,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[fact_2_abe,h0]) ).
thf(h34,assumption,
( ~ sP3
=> sP2 ),
introduced(assumption,[]) ).
thf(h35,assumption,
~ ( ( ord_less_nat @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h36,assumption,
sP3,
introduced(assumption,[]) ).
thf(h37,assumption,
sP2,
introduced(assumption,[]) ).
thf(fact_3_False,axiom,
~ sP3 ).
thf(9,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h36,h34,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h36,fact_3_False]) ).
thf(h38,assumption,
sP5,
introduced(assumption,[]) ).
thf(h39,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,[]) ).
thf(h40,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ pr ) @ eigen__6,
introduced(assumption,[]) ).
thf(h41,assumption,
ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ),
introduced(assumption,[]) ).
thf(h42,assumption,
ord_less_nat @ ( vEBT_VEBT_low @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ),
introduced(assumption,[]) ).
thf(h43,assumption,
( ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
!= ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ),
introduced(assumption,[]) ).
thf(h44,assumption,
vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ),
introduced(assumption,[]) ).
thf(fact_67__092_060open_062mi_A_092_060noteq_062_Ama_092_060close_062,axiom,
~ sP5 ).
thf(10,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h43,h41,h42,h40,h38,h37,h34,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h38,fact_67__092_060open_062mi_A_092_060noteq_062_Ama_092_060close_062]) ).
thf(11,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h44,h41,h42,h40,h38,h37,h34,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h38,fact_67__092_060open_062mi_A_092_060noteq_062_Ama_092_060close_062]) ).
thf(fact_4_aaa,axiom,
( ( ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
= ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
=> ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
thf(12,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h41,h42,h40,h38,h37,h34,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h43]),tab_imp(discharge,[h44])],[fact_4_aaa,10,11,h43,h44]) ).
thf(fact_25__092_060open_062high_Ax_An_A_060_A2_A_094_An_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 ) ) @ na ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_low @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h40,h38,h37,h34,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h41,h42])],[fact_25__092_060open_062high_Ax_An_A_060_A2_A_094_An_A_092_060and_062_Alow_Ax_An_A_060_A2_A_094_An_092_060close_062,12,h41,h42]) ).
thf(fact_79__092_060open_062_092_060exists_062maxy_O_Aboth__member__options_A_ItreeList_A_B_Apr_J_Amaxy_092_060close_062,axiom,
~ ! [X1: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ pr ) @ X1 ) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h38,h37,h34,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h40]),tab_negall(eigenvar,eigen__6)],[fact_79__092_060open_062_092_060exists_062maxy_O_Aboth__member__options_A_ItreeList_A_B_Apr_J_Amaxy_092_060close_062,13,h40]) ).
thf(h45,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ pr ) @ eigen__5,
introduced(assumption,[]) ).
thf(fact_66__092_060open_062z_A_092_060noteq_062_Ama_092_060close_062,axiom,
~ sP2 ).
thf(15,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h43,h41,h42,h45,h39,h37,h34,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h37,fact_66__092_060open_062z_A_092_060noteq_062_Ama_092_060close_062]) ).
thf(16,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h44,h41,h42,h45,h39,h37,h34,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h37,fact_66__092_060open_062z_A_092_060noteq_062_Ama_092_060close_062]) ).
thf(17,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h41,h42,h45,h39,h37,h34,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h43]),tab_imp(discharge,[h44])],[fact_4_aaa,15,16,h43,h44]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h45,h39,h37,h34,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h41,h42])],[fact_25__092_060open_062high_Ax_An_A_060_A2_A_094_An_A_092_060and_062_Alow_Ax_An_A_060_A2_A_094_An_092_060close_062,17,h41,h42]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h39,h37,h34,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h45]),tab_negall(eigenvar,eigen__5)],[fact_79__092_060open_062_092_060exists_062maxy_O_Aboth__member__options_A_ItreeList_A_B_Apr_J_Amaxy_092_060close_062,18,h45]) ).
thf(fact_99__C4_Ohyps_C_I11_J,axiom,
( ~ sP5
=> ! [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 ) ) ) ) ) ) ).
thf(20,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h37,h34,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h38]),tab_imp(discharge,[h39])],[fact_99__C4_Ohyps_C_I11_J,14,19,h38,h39]) ).
thf(21,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h34,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h36]),tab_imp(discharge,[h37])],[h34,9,20,h36,h37]) ).
thf(h46,assumption,
ord_less_nat @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ),
introduced(assumption,[]) ).
thf(h47,assumption,
sP1,
introduced(assumption,[]) ).
thf(h48,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ pr ) @ eigen__4,
introduced(assumption,[]) ).
thf(22,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h43,h41,h42,h48,h38,h46,h47,h35,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h38,fact_67__092_060open_062mi_A_092_060noteq_062_Ama_092_060close_062]) ).
thf(23,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h44,h41,h42,h48,h38,h46,h47,h35,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h38,fact_67__092_060open_062mi_A_092_060noteq_062_Ama_092_060close_062]) ).
thf(24,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h41,h42,h48,h38,h46,h47,h35,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h43]),tab_imp(discharge,[h44])],[fact_4_aaa,22,23,h43,h44]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h48,h38,h46,h47,h35,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h41,h42])],[fact_25__092_060open_062high_Ax_An_A_060_A2_A_094_An_A_092_060and_062_Alow_Ax_An_A_060_A2_A_094_An_092_060close_062,24,h41,h42]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h38,h46,h47,h35,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h48]),tab_negall(eigenvar,eigen__4)],[fact_79__092_060open_062_092_060exists_062maxy_O_Aboth__member__options_A_ItreeList_A_B_Apr_J_Amaxy_092_060close_062,25,h48]) ).
thf(h49,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ pr ) @ eigen__3,
introduced(assumption,[]) ).
thf(27,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h43,h41,h42,h49,h39,h46,h47,h35,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h47,h0]) ).
thf(28,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h44,h41,h42,h49,h39,h46,h47,h35,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h47,h0]) ).
thf(29,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h41,h42,h49,h39,h46,h47,h35,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h43]),tab_imp(discharge,[h44])],[fact_4_aaa,27,28,h43,h44]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h49,h39,h46,h47,h35,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h41,h42])],[fact_25__092_060open_062high_Ax_An_A_060_A2_A_094_An_A_092_060and_062_Alow_Ax_An_A_060_A2_A_094_An_092_060close_062,29,h41,h42]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h39,h46,h47,h35,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h49]),tab_negall(eigenvar,eigen__3)],[fact_79__092_060open_062_092_060exists_062maxy_O_Aboth__member__options_A_ItreeList_A_B_Apr_J_Amaxy_092_060close_062,30,h49]) ).
thf(32,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h46,h47,h35,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h38]),tab_imp(discharge,[h39])],[fact_99__C4_Ohyps_C_I11_J,26,31,h38,h39]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h35,h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h46,h47])],[h35,32,h46,h47]) ).
thf(fact_102__C20_C,axiom,
( ~ ( ~ sP3
=> sP2 )
=> ~ ( ( ord_less_nat @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
=> ~ sP1 ) ) ).
thf(34,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h33,h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h34]),tab_imp(discharge,[h35])],[fact_102__C20_C,21,33,h34,h35]) ).
thf(fact_178__C4_Ohyps_C_I8_J,axiom,
( sP5
=> ! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ treeList ) )
=> ! [X2: nat] :
~ ( vEBT_V8194947554948674370ptions @ X1 @ X2 ) ) ) ).
thf(35,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h30,h31,h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h32]),tab_imp(discharge,[h33])],[fact_178__C4_Ohyps_C_I8_J,8,34,h32,h33]) ).
thf(fact_312__092_060open_062vebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Az_A_092_060and_062_Az_A_060_Ax_092_060close_062,axiom,
~ ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ za )
=> ~ ( ord_less_nat @ za @ xa ) ) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h29,h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h30,h31])],[fact_312__092_060open_062vebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Az_A_092_060and_062_Az_A_060_Ax_092_060close_062,35,h30,h31]) ).
thf(fact_636__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062pr_O_Avebt__pred_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Apr_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [X1: nat] :
( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
!= ( some_nat @ X1 ) ) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h28,h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h29]),tab_negall(eigenvar,eigen__2)],[fact_636__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062pr_O_Avebt__pred_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Apr_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,36,h29]) ).
thf(fact_944__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxy_O_ASome_Amaxy_A_061_Avebt__maxt_A_ItreeList_A_B_Apr_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [X1: nat] :
( ( some_nat @ X1 )
!= ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ pr ) ) ) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h27,h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__1)],[fact_944__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxy_O_ASome_Amaxy_A_061_Avebt__maxt_A_ItreeList_A_B_Apr_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,37,h28]) ).
thf(39,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h25,h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h26]),tab_imp(discharge,[h27])],[fact_960_i1,7,38,h26,h27]) ).
thf(40,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h23,h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h24]),tab_imp(discharge,[h25])],[h15,6,39,h24,h25]) ).
thf(41,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h21,h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h22]),tab_imp(discharge,[h23])],[h19,5,40,h22,h23]) ).
thf(42,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h18,h19,h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h20]),tab_imp(discharge,[h21])],[h18,4,41,h20,h21]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,42,h18,h19]) ).
thf(44,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h14,h15,h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h16]),tab_imp(discharge,[h17])],[h14,3,43,h16,h17]) ).
thf(fact_969__C2_C,axiom,
~ ( ( ( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
= none_nat )
=> ~ ( ( ( ord_less_nat @ mi @ xa )
=> ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= ( some_nat @ mi ) ) )
=> ~ ( ~ ( ord_less_nat @ mi @ xa )
=> ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= none_nat ) ) ) )
=> ~ ( ( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
!= none_nat )
=> ( ( vEBT_vebt_pred @ ( 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_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[fact_969__C2_C,44,h14,h15]) ).
thf(46,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h13])],[h9,2,45,h12,h13]) ).
thf(47,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h8,1,46,h10,h11]) ).
thf(fact_1245__C1_C,axiom,
~ ( ( ~ sP4
=> ( ( vEBT_vebt_pred @ ( 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_pred @ ( 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 ) ) ) ) ) ) ) )
=> ~ ( sP4
=> ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
= ( if_option_nat
@ ( ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
= none_nat )
@ ( if_option_nat @ ( ord_less_nat @ mi @ xa ) @ ( some_nat @ mi ) @ none_nat )
@ ( 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_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_pred @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[fact_1245__C1_C,47,h8,h9]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,48,h6,h7]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,49,h4,h5]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,50,h2,h3]) ).
thf(fact_7884_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(52,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_7884_cos__is__zero,51,h1]) ).
thf(0,theorem,
sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[52,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP239^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.11/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.34 % Computer : n025.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Feb 26 17:35:58 EST 2026
% 0.16/0.34 % CPUTime :
% 0.96/1.14 % SZS status Theorem
% 0.96/1.14 % Mode: cade22sinegrackle2x6978
% 0.96/1.14 % Steps: 0
% 0.96/1.14 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------