%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP227^3 : 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 : n004.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 09:29:52 AM UTC 2026
% Result : Theorem 0.48s 0.95s
% Output : Proof 0.48s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_list_VEBT_VEBT,type,
list_VEBT_VEBT: $tType ).
thf(ty_vEBT_VEBT,type,
vEBT_VEBT: $tType ).
thf(ty_num,type,
num: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_set_VEBT_VEBT,type,
set_VEBT_VEBT: $tType ).
thf(ty_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(ty_mi,type,
mi: nat ).
thf(ty_power_power_nat,type,
power_power_nat: nat > nat > nat ).
thf(ty_member_VEBT_VEBT,type,
member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
thf(ty_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ty_bit0,type,
bit0: num > num ).
thf(ty_nth_VEBT_VEBT,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(ty_vEBT_VEBT_low,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(ty_treeList,type,
treeList: list_VEBT_VEBT ).
thf(ty_set_VEBT_VEBT2,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
thf(ty_one,type,
one: num ).
thf(ty_m,type,
m: nat ).
thf(ty_xa,type,
xa: nat ).
thf(ty_vEBT_V8194947554948674370ptions,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(ty_na,type,
na: nat ).
thf(ty_vEBT_VEBT_high,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(ty_numeral_numeral_nat,type,
numeral_numeral_nat: num > nat ).
thf(ty_ma,type,
ma: nat ).
thf(sP1,plain,
( sP1
<=> ( xa = mi ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( xa = ma ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( mi = ma ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(conj_0,conjecture,
~ ( ~ sP1
=> sP2 ) ).
thf(h0,negated_conjecture,
( ~ sP1
=> sP2 ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
sP2,
introduced(assumption,[]) ).
thf(h3,assumption,
sP3,
introduced(assumption,[]) ).
thf(h4,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(h5,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ treeList ) )
=> ! [X2: nat] :
~ ( vEBT_V8194947554948674370ptions @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h5,h3,h1,h0])],[h3,h5]) ).
thf(h7,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h7,h8,h6,h3,h1,h0])],[h1,h7]) ).
thf(fact_0_False,axiom,
~ ( ~ sP1
=> sP2 ) ).
thf(3,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[fact_0_False,2,h7,h8]) ).
thf(fact_2__C5_Ohyps_C_I6_J,axiom,
( sP3
=> ! [X1: vEBT_VEBT] :
( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ treeList ) )
=> ! [X2: nat] :
~ ( vEBT_V8194947554948674370ptions @ X1 @ X2 ) ) ) ).
thf(4,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_2__C5_Ohyps_C_I6_J,1,3,h5,h6]) ).
thf(5,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h7,h8,h5,h4,h1,h0])],[h1,h7]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h1,h0]),tab_negimp(discharge,[h7,h8])],[fact_0_False,5,h7,h8]) ).
thf(7,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h7,h8,h6,h4,h1,h0])],[h1,h7]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h1,h0]),tab_negimp(discharge,[h7,h8])],[fact_0_False,7,h7,h8]) ).
thf(9,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_2__C5_Ohyps_C_I6_J,6,8,h5,h6]) ).
thf(fact_89__C5_Ohyps_C_I9_J,axiom,
( ~ sP3
=> ! [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(10,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_89__C5_Ohyps_C_I9_J,4,9,h3,h4]) ).
thf(11,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h7,h8,h5,h3,h2,h0])],[h3,h5]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h2,h0]),tab_negimp(discharge,[h7,h8])],[fact_0_False,11,h7,h8]) ).
thf(13,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h7,h8,h6,h3,h2,h0])],[h2,h8]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h3,h2,h0]),tab_negimp(discharge,[h7,h8])],[fact_0_False,13,h7,h8]) ).
thf(15,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_2__C5_Ohyps_C_I6_J,12,14,h5,h6]) ).
thf(16,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h7,h8,h5,h4,h2,h0])],[h2,h8]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h2,h0]),tab_negimp(discharge,[h7,h8])],[fact_0_False,16,h7,h8]) ).
thf(18,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h7,h8,h6,h4,h2,h0])],[h2,h8]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h2,h0]),tab_negimp(discharge,[h7,h8])],[fact_0_False,18,h7,h8]) ).
thf(20,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_2__C5_Ohyps_C_I6_J,17,19,h5,h6]) ).
thf(21,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_89__C5_Ohyps_C_I9_J,15,20,h3,h4]) ).
thf(22,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[h0,10,21,h1,h2]) ).
thf(0,theorem,
~ ( ~ sP1
=> sP2 ),
inference(contra,[status(thm),contra(discharge,[h0])],[22,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP227^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.33 % Computer : n004.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
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Feb 26 10:59:41 EST 2026
% 0.16/0.34 % CPUTime :
% 0.48/0.95 % SZS status Theorem
% 0.48/0.95 % Mode: cade22sinegrackle2x6978
% 0.48/0.95 % Steps: 0
% 0.48/0.95 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------