%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP232^3 : 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 : 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 09:29:54 AM UTC 2026
% Result : Theorem 23.07s 23.85s
% Output : Proof 23.07s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_num,type,
num: $tType ).
thf(ty_vEBT_VEBT,type,
vEBT_VEBT: $tType ).
thf(ty_power_power_nat,type,
power_power_nat: nat > nat > nat ).
thf(ty_one,type,
one: num ).
thf(ty_vEBT_VEBT_minNull,type,
vEBT_VEBT_minNull: vEBT_VEBT > $o ).
thf(ty_vEBT_VEBT_low,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(ty_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ty_mi,type,
mi: nat ).
thf(ty_vEBT_V8194947554948674370ptions,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(ty_treeList,type,
treeList: list_VEBT_VEBT ).
thf(ty_na,type,
na: nat ).
thf(ty_m,type,
m: nat ).
thf(ty_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(ty_xa,type,
xa: nat ).
thf(ty_nth_VEBT_VEBT,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(ty_vEBT_VEBT_high,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(ty_ma,type,
ma: nat ).
thf(ty_deg,type,
deg: nat ).
thf(ty_bit0,type,
bit0: num > num ).
thf(ty_numeral_numeral_nat,type,
numeral_numeral_nat: num > nat ).
thf(sP1,plain,
( sP1
<=> ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: vEBT_VEBT] :
( ~ ( vEBT_VEBT_minNull @ X1 )
=> ~ ! [X2: nat] :
~ ( vEBT_V8194947554948674370ptions @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ sP1
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(conj_0,conjecture,
~ sP2 ).
thf(h0,negated_conjecture,
sP2,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
ord_less_nat @ ( vEBT_VEBT_high @ mi @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ),
introduced(assumption,[]) ).
thf(h2,assumption,
ord_less_nat @ ( vEBT_VEBT_low @ mi @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ),
introduced(assumption,[]) ).
thf(h3,assumption,
ord_less_eq_nat @ mi @ ma,
introduced(assumption,[]) ).
thf(h4,assumption,
ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ),
introduced(assumption,[]) ).
thf(h5,assumption,
xa != mi,
introduced(assumption,[]) ).
thf(h6,assumption,
xa != ma,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| sP1
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_1_False,axiom,
~ sP1 ).
thf(fact_0_not__min__Null__member,axiom,
sP3 ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0])],[1,2,h0,fact_1_False,fact_0_not__min__Null__member]) ).
thf(fact_9_mimaxrel,axiom,
~ ( ( xa != mi )
=> ( xa = ma ) ) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[fact_9_mimaxrel,3,h5,h6]) ).
thf(fact_1509__C6_C,axiom,
~ ( ( ord_less_eq_nat @ mi @ ma )
=> ~ ( ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[fact_1509__C6_C,4,h3,h4]) ).
thf(fact_1525_highlowprop,axiom,
~ ( ( ord_less_nat @ ( vEBT_VEBT_high @ mi @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
=> ~ ( ord_less_nat @ ( vEBT_VEBT_low @ mi @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[fact_1525_highlowprop,5,h1,h2]) ).
thf(0,theorem,
~ sP2,
inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ITP232^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.00/0.10 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.30 % Computer : n022.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Thu Feb 26 13:46:51 EST 2026
% 0.12/0.30 % CPUTime :
% 23.07/23.85 % SZS status Theorem
% 23.07/23.85 % Mode: cade22sinegrackle2xfaf3
% 23.07/23.85 % Steps: 2650
% 23.07/23.85 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------