%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP269^1 : 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 : n001.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 09:30:07 AM UTC 2026
% Result : Theorem 21.70s 21.33s
% Output : Proof 21.70s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_real,type,
real: $tType ).
thf(ty_num,type,
num: $tType ).
thf(ty_option_nat,type,
option_nat: $tType ).
thf(ty_vEBT_VEBT,type,
vEBT_VEBT: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_list_VEBT_VEBT,type,
list_VEBT_VEBT: $tType ).
thf(ty_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ty_divide_divide_nat,type,
divide_divide_nat: nat > nat > nat ).
thf(ty_eigen__4,type,
eigen__4: nat ).
thf(ty_lx,type,
lx: nat ).
thf(ty_eigen__0,type,
eigen__0: real ).
thf(ty_deg,type,
deg: nat ).
thf(ty_summin,type,
summin: nat ).
thf(ty_na,type,
na: nat ).
thf(ty_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(ty_vEBT_VEBT_low,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(ty_nth_VEBT_VEBT,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(ty_ma,type,
ma: nat ).
thf(ty_the_nat,type,
the_nat: option_nat > nat ).
thf(ty_plus_plus_nat,type,
plus_plus_nat: nat > nat > nat ).
thf(ty_numeral_numeral_real,type,
numeral_numeral_real: num > real ).
thf(ty_eigen__3,type,
eigen__3: nat ).
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_mi,type,
mi: nat ).
thf(ty_some_nat,type,
some_nat: nat > option_nat ).
thf(ty_numeral_numeral_nat,type,
numeral_numeral_nat: num > nat ).
thf(ty_m,type,
m: nat ).
thf(ty_if_nat,type,
if_nat: $o > nat > nat > nat ).
thf(ty_eigen__1,type,
eigen__1: nat ).
thf(ty_power_power_nat,type,
power_power_nat: nat > nat > nat ).
thf(ty_summary,type,
summary: vEBT_VEBT ).
thf(ty_eigen__2,type,
eigen__2: nat ).
thf(ty_one,type,
one: num ).
thf(ty_cos_real,type,
cos_real: real > real ).
thf(ty_vEBT_VEBT_high,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(ty_vEBT_vebt_delete,type,
vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
thf(ty_treeList,type,
treeList: list_VEBT_VEBT ).
thf(ty_times_times_nat,type,
times_times_nat: nat > nat > nat ).
thf(ty_xa,type,
xa: nat ).
thf(ty_bit0,type,
bit0: num > num ).
thf(ty_vEBT_V8194947554948674370ptions,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(ty_vEBT_vebt_mint,type,
vEBT_vebt_mint: vEBT_VEBT > option_nat ).
thf(ty_list_u1324408373059187874T_VEBT,type,
list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(ty_ord_less_eq_real,type,
ord_less_eq_real: real > real > $o ).
thf(sP1,plain,
( sP1
<=> ( ord_less_nat
@ ( if_nat
@ ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
= ma )
@ ( 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,[sP1])]) ).
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,
( ( some_nat @ eigen__1 )
= ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ summin ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
( ( some_nat @ eigen__2 )
= ( vEBT_vebt_mint @ summary ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
( ( xa = mi )
=> ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
= ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
( ( xa != mi )
=> ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
= xa ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
ord_less_eq_nat @ mi @ xa,
introduced(assumption,[]) ).
thf(h13,assumption,
ord_less_eq_nat @ xa @ ma,
introduced(assumption,[]) ).
thf(h14,assumption,
mi != ma,
introduced(assumption,[]) ).
thf(h15,assumption,
ord_less_nat @ xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ),
introduced(assumption,[]) ).
thf(h16,assumption,
ord_less_eq_nat @ mi @ ma,
introduced(assumption,[]) ).
thf(h17,assumption,
ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP1,
introduced(assumption,[]) ).
thf(h19,assumption,
( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
@ ( if_nat
@ ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
= ma )
@ ( 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(h20,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__3,
introduced(assumption,[]) ).
thf(h21,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(h22,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(h23,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ eigen__4,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h23,h21,h22,h20,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0])],[h18,h0]) ).
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([h21,h22,h20,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h9,h8,h6,h7,h4,h5,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_062,1,h23]) ).
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(3,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h21,h22])],[fact_17_hlbound,2,h21,h22]) ).
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(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__3)],[fact_18_notemp,3,h20]) ).
thf(fact_21__C114_C,axiom,
~ ( sP1
=> ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
@ ( if_nat
@ ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
= ma )
@ ( 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(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h10,h11,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[fact_21__C114_C,4,h18,h19]) ).
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(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[fact_103__C6_C,5,h16,h17]) ).
thf(fact_168__092_060open_062mi_A_092_060noteq_062_Ama_A_092_060and_062_Ax_A_060_A2_A_094_Adeg_092_060close_062,axiom,
~ ( ( mi != ma )
=> ~ ( ord_less_nat @ xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[fact_168__092_060open_062mi_A_092_060noteq_062_Ama_A_092_060and_062_Ax_A_060_A2_A_094_Adeg_092_060close_062,6,h14,h15]) ).
thf(fact_191_inrg,axiom,
~ ( ( ord_less_eq_nat @ mi @ xa )
=> ~ ( ord_less_eq_nat @ xa @ ma ) ) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[fact_191_inrg,7,h12,h13]) ).
thf(fact_456__092_060open_062summin_A_K_A2_A_094_An_A_L_Alx_A_061_A_Iif_Ax_A_061_Ami_Athen_Athe_A_Ivebt__mint_Asummary_J_A_K_A2_A_094_A_Ideg_Adiv_A2_J_A_L_Athe_A_Ivebt__mint_A_ItreeList_A_B_Athe_A_Ivebt__mint_Asummary_J_J_J_Aelse_Ax_J_092_060close_062,axiom,
~ ( ( ( xa = mi )
=> ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
= ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) ) )
=> ~ ( ( xa != mi )
=> ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
= xa ) ) ) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[fact_456__092_060open_062summin_A_K_A2_A_094_An_A_L_Alx_A_061_A_Iif_Ax_A_061_Ami_Athen_Athe_A_Ivebt__mint_Asummary_J_A_K_A2_A_094_A_Ideg_Adiv_A2_J_A_L_Athe_A_Ivebt__mint_A_ItreeList_A_B_Athe_A_Ivebt__mint_Asummary_J_J_J_Aelse_Ax_J_092_060close_062,8,h10,h11]) ).
thf(fact_523__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062summin_O_ASome_Asummin_A_061_Avebt__mint_Asummary_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [X1: nat] :
( ( some_nat @ X1 )
!= ( vEBT_vebt_mint @ summary ) ) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[fact_523__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062summin_O_ASome_Asummin_A_061_Avebt__mint_Asummary_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,9,h9]) ).
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(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[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_062,10,h8]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,11,h6,h7]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,12,h4,h5]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,13,h2,h3]) ).
thf(fact_7146_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(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_7146_cos__is__zero,14,h1]) ).
thf(0,theorem,
sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ITP269^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.00/0.11 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.32 % Computer : n001.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Fri Feb 27 09:54:50 EST 2026
% 0.14/0.32 % CPUTime :
% 21.70/21.33 % SZS status Theorem
% 21.70/21.33 % Mode: cade22sinegrackle2xfaf3
% 21.70/21.33 % Steps: 0
% 21.70/21.33 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------