%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP135^1 : 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 : n012.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 04:02:26 EDT 2023

% Result   : Theorem 20.24s 20.51s
% Output   : Proof 20.24s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_set_nat,type,
    set_nat: $tType ).

thf(ty_nat,type,
    nat: $tType ).

thf(ty_top_top_set_nat,type,
    top_top_set_nat: set_nat ).

thf(ty_member_nat,type,
    member_nat: nat > set_nat > $o ).

thf(ty_eigen__0,type,
    eigen__0: nat ).

thf(sP1,plain,
    ( sP1
  <=> ( ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) )
      = ( paraco1344940915le_Det @ ~ $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
      = ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
      = ( paraco1344940915le_Det @ ~ $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(conj_0,conjecture,
    sP3 ).

thf(h0,negated_conjecture,
    ~ sP3,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    member_nat @ eigen__0 @ top_top_set_nat,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP2
    | sP3
    | sP4
    | ~ sP1 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(2,plain,
    ~ sP4,
    inference(prop_rule,[status(thm)],]) ).

thf(fact_2_ih2,axiom,
    sP2 ).

thf(fact_1__092_060open_062change__tv_Af_A_Ieval_Ai_Ap2_J_A_061_ADet_ATrue_092_060close_062,axiom,
    sP1 ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,h0,fact_2_ih2,fact_1__092_060open_062change__tv_Af_A_Ieval_Ai_Ap2_J_A_061_ADet_ATrue_092_060close_062]) ).

thf(fact_120_UNIV__witness,axiom,
    ~ ! [X1: nat] :
        ~ ( member_nat @ X1 @ top_top_set_nat ) ).

thf(4,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_120_UNIV__witness,3,h1]) ).

thf(0,theorem,
    sP3,
    inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ITP135^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n012.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sun Aug 27 12:57:40 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 20.24/20.51  % SZS status Theorem
% 20.24/20.51  % Mode: cade22sinegrackle2xfaf3
% 20.24/20.51  % Steps: 292
% 20.24/20.51  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------