%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP056^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n027.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 : Thu Aug 31 04:01:48 EDT 2023

% Result   : Theorem 0.18s 0.41s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_list_c1059388851t_unit,type,
    list_c1059388851t_unit: $tType ).

thf(ty_nth_co1649820636t_unit,type,
    nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).

thf(ty_one_one_nat,type,
    one_one_nat: nat ).

thf(ty_nil_co1338500125t_unit,type,
    nil_co1338500125t_unit: list_c1059388851t_unit ).

thf(ty_size_s1406904903t_unit,type,
    size_s1406904903t_unit: list_c1059388851t_unit > nat ).

thf(ty_n,type,
    n: nat ).

thf(ty_last_c571238084t_unit,type,
    last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).

thf(ty_fe,type,
    fe: nat > list_c1059388851t_unit ).

thf(ty_minus_minus_nat,type,
    minus_minus_nat: nat > nat > nat ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: list_c1059388851t_unit] :
        ( ( X1 != nil_co1338500125t_unit )
       => ( ( last_c571238084t_unit @ X1 )
          = ( nth_co1649820636t_unit @ X1 @ ( minus_minus_nat @ ( size_s1406904903t_unit @ X1 ) @ one_one_nat ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( ( fe @ n )
       != nil_co1338500125t_unit )
     => ( ( last_c571238084t_unit @ ( fe @ n ) )
        = ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( fe @ n )
      = nil_co1338500125t_unit ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( last_c571238084t_unit @ ( fe @ n ) )
      = ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(conj_0,conjecture,
    sP4 ).

thf(h0,negated_conjecture,
    ~ sP4,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP2
    | sP3
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP1
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_1_LastIsLastIndex,axiom,
    sP1 ).

thf(fact_0_FeNNotEmpty,axiom,
    ~ sP3 ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,h0,fact_1_LastIsLastIndex,fact_0_FeNNotEmpty]) ).

thf(0,theorem,
    sP4,
    inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP056^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.33  % Computer : n027.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33  % CPULimit : 300
% 0.15/0.33  % WCLimit  : 300
% 0.15/0.33  % DateTime : Sun Aug 27 11:00:05 EDT 2023
% 0.15/0.34  % CPUTime  : 
% 0.18/0.41  % SZS status Theorem
% 0.18/0.41  % Mode: cade22sinegrackle2x6978
% 0.18/0.41  % Steps: 68
% 0.18/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------