%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP236^3 : 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 : n011.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 09:29:56 AM UTC 2026
% Result : Theorem 1.03s 1.29s
% Output : Proof 1.03s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_num,type,
num: $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_option_nat,type,
option_nat: $tType ).
thf(ty_set_VEBT_VEBT,type,
set_VEBT_VEBT: $tType ).
thf(ty_eigen__0,type,
eigen__0: nat ).
thf(ty_bit0,type,
bit0: num > num ).
thf(ty_eigen__117,type,
eigen__117: nat ).
thf(ty_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ty_m,type,
m: nat ).
thf(ty_vEBT_VEBT_low,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(ty_eigen__1,type,
eigen__1: nat ).
thf(ty_nth_VEBT_VEBT,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(ty_n,type,
n: nat ).
thf(ty_mi,type,
mi: nat ).
thf(ty_member_VEBT_VEBT,type,
member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
thf(ty_vEBT_VEBT_high,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(ty_power_power_nat,type,
power_power_nat: nat > nat > nat ).
thf(ty_vEBT_V8194947554948674370ptions,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(ty_treeList,type,
treeList: list_VEBT_VEBT ).
thf(ty_numeral_numeral_nat,type,
numeral_numeral_nat: num > nat ).
thf(ty_vEBT_vebt_maxt,type,
vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
thf(ty_eigen__34,type,
eigen__34: nat ).
thf(ty_ma,type,
ma: nat ).
thf(ty_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(ty_one,type,
one: num ).
thf(ty_summary,type,
summary: vEBT_VEBT ).
thf(ty_thesis,type,
thesis: $o ).
thf(ty_set_VEBT_VEBT2,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
thf(ty_eigen__116,type,
eigen__116: nat ).
thf(ty_some_nat,type,
some_nat: nat > option_nat ).
thf(ty_maxs,type,
maxs: nat ).
thf(ty_eigen__115,type,
eigen__115: nat ).
thf(sP1,plain,
( sP1
<=> ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ eigen__1 )
=> thesis ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( mi = ma ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: nat] :
( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ X1 )
=> thesis ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ eigen__34 )
=> thesis ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> thesis ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ eigen__34 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(conj_1,conjecture,
sP5 ).
thf(h0,negated_conjecture,
~ sP5,
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(h1,assumption,
sP2,
introduced(assumption,[]) ).
thf(h2,assumption,
! [X1: nat] :
( ( ord_less_nat @ X1 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
=> ~ ( ( ( ( vEBT_VEBT_high @ ma @ n )
= X1 )
=> ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X1 ) @ ( vEBT_VEBT_low @ ma @ n ) ) )
=> ~ ! [X2: nat] :
( ~ ( ( ( vEBT_VEBT_high @ X2 @ n )
= X1 )
=> ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X1 ) @ ( vEBT_VEBT_low @ X2 @ n ) ) )
=> ~ ( ( ord_less_nat @ mi @ X2 )
=> ~ ( ord_less_eq_nat @ X2 @ ma ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ( some_nat @ eigen__115 )
= ( vEBT_vebt_maxt @ summary ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ treeList ) )
=> ! [X2: nat] :
~ ( vEBT_V8194947554948674370ptions @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ eigen__117,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h6,h4,h3,h1,h0])],[h1,h4]) ).
thf(fact_0__092_060open_062_092_060exists_062x_O_Aboth__member__options_A_ItreeList_A_B_Amaxs_J_Ax_092_060close_062,axiom,
~ ! [X1: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ X1 ) ).
thf(2,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__117)],[fact_0__092_060open_062_092_060exists_062x_O_Aboth__member__options_A_ItreeList_A_B_Amaxs_J_Ax_092_060close_062,1,h6]) ).
thf(h7,assumption,
vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ eigen__116,
introduced(assumption,[]) ).
thf(fact_12_assms_I2_J,axiom,
~ sP2 ).
thf(3,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h7,h5,h3,h1,h0])],[h1,fact_12_assms_I2_J]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__116)],[fact_0__092_060open_062_092_060exists_062x_O_Aboth__member__options_A_ItreeList_A_B_Amaxs_J_Ax_092_060close_062,3,h7]) ).
thf(fact_4__C5_C_I7_J,axiom,
( sP2
=> ! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ treeList ) )
=> ! [X2: nat] :
~ ( vEBT_V8194947554948674370ptions @ X1 @ X2 ) ) ) ).
thf(5,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[fact_4__C5_C_I7_J,2,4,h4,h5]) ).
thf(fact_22__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxs_O_ASome_Amaxs_A_061_Avebt__maxt_Asummary_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [X1: nat] :
( ( some_nat @ X1 )
!= ( vEBT_vebt_maxt @ summary ) ) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__115)],[fact_22__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxs_O_ASome_Amaxs_A_061_Avebt__maxt_Asummary_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,5,h3]) ).
thf(h8,assumption,
( ( some_nat @ eigen__0 )
= ( vEBT_vebt_maxt @ summary ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP7,
introduced(assumption,[]) ).
thf(7,plain,
( ~ sP4
| ~ sP7
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(conj_0,axiom,
sP3 ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h4,h8,h2,h0])],[7,8,h0,conj_0,h9]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h8,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__34)],[fact_0__092_060open_062_092_060exists_062x_O_Aboth__member__options_A_ItreeList_A_B_Amaxs_J_Ax_092_060close_062,9,h9]) ).
thf(h10,assumption,
sP6,
introduced(assumption,[]) ).
thf(11,plain,
( ~ sP1
| ~ sP6
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP3
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h5,h8,h2,h0])],[11,12,h0,conj_0,h10]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h8,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[fact_0__092_060open_062_092_060exists_062x_O_Aboth__member__options_A_ItreeList_A_B_Amaxs_J_Ax_092_060close_062,13,h10]) ).
thf(15,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h2,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[fact_4__C5_C_I7_J,10,14,h4,h5]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__0)],[fact_22__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxs_O_ASome_Amaxs_A_061_Avebt__maxt_Asummary_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,15,h8]) ).
thf(fact_1855__C5_C_I10_J,axiom,
( ~ sP2
=> ! [X1: nat] :
( ( ord_less_nat @ X1 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
=> ~ ( ( ( ( vEBT_VEBT_high @ ma @ n )
= X1 )
=> ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X1 ) @ ( vEBT_VEBT_low @ ma @ n ) ) )
=> ~ ! [X2: nat] :
( ~ ( ( ( vEBT_VEBT_high @ X2 @ n )
= X1 )
=> ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X1 ) @ ( vEBT_VEBT_low @ X2 @ n ) ) )
=> ~ ( ( ord_less_nat @ mi @ X2 )
=> ~ ( ord_less_eq_nat @ X2 @ ma ) ) ) ) ) ) ).
thf(17,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_1855__C5_C_I10_J,6,16,h1,h2]) ).
thf(0,theorem,
sP5,
inference(contra,[status(thm),contra(discharge,[h0])],[17,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP236^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.11/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.33 % Computer : n011.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Thu Feb 26 15:57:17 EST 2026
% 0.16/0.33 % CPUTime :
% 1.03/1.29 % SZS status Theorem
% 1.03/1.29 % Mode: cade22sinegrackle2x6978
% 1.03/1.29 % Steps: 13383
% 1.03/1.29 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------