%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP233^3 : 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 : n029.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 09:29:55 AM UTC 2026
% Result : Theorem 121.32s 130.25s
% Output : Proof 121.32s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_vEBT_vebt_insert,type,
vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
thf(ty_nth_VEBT_VEBT,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(ty_vEBT_V8194947554948674370ptions,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(ty_i,type,
i: nat ).
thf(ty_na,type,
na: nat ).
thf(ty_vEBT_VEBT_low,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(ty_vEBT_VEBT_high,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(ty_treeList,type,
treeList: list_VEBT_VEBT ).
thf(ty_list_u1324408373059187874T_VEBT,type,
list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(ty_xa,type,
xa: nat ).
thf(sP1,plain,
( sP1
<=> $false ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) )
= ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ i ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ i ) @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ i ) @ ( vEBT_VEBT_low @ xa @ na ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ i )
= ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(conj_0,conjecture,
~ sP4 ).
thf(h0,negated_conjecture,
sP4,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP3
| sP5
| sP1
| ~ sP2 ),
inference(mating_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP6
| sP2 ),
inference(symeq,[status(thm)],[]) ).
thf(3,plain,
( ~ sP4
| ~ sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(fact_3283_pinf_I10_J,axiom,
~ sP1 ).
thf(fact_3__C164_C,axiom,
sP6 ).
thf(fact_1__C166_C,axiom,
sP3 ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,fact_3283_pinf_I10_J,fact_3__C164_C,fact_1__C166_C,h0]) ).
thf(0,theorem,
~ sP4,
inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP233^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.13/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.33 % Computer : n029.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 14:22:29 EST 2026
% 0.16/0.33 % CPUTime :
% 121.32/130.25 % SZS status Theorem
% 121.32/130.25 % Mode: cade22sinegrackle2xec37
% 121.32/130.25 % Steps: 21866
% 121.32/130.25 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------