%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP073^1 : 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 : n015.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 04:01:53 EDT 2023

% Result   : Theorem 0.20s 0.45s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_hF_Mirabelle_hf,type,
    hF_Mirabelle_hf: $tType ).

thf(ty_ord_le976219883lle_hf,type,
    ord_le976219883lle_hf: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).

thf(ty_hF_Mirabelle_hmem,type,
    hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).

thf(ty_b,type,
    b: hF_Mirabelle_hf ).

thf(ty_a,type,
    a: hF_Mirabelle_hf ).

thf(sP1,plain,
    ( sP1
  <=> ( ord_le976219883lle_hf
      = ( ^ [X1: hF_Mirabelle_hf,X2: hF_Mirabelle_hf] :
          ! [X3: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ X3 @ X1 )
           => ( hF_Mirabelle_hmem @ X3 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ord_le976219883lle_hf @ a @ b ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( sP2
      = ( ! [X1: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ X1 @ a )
           => ( hF_Mirabelle_hmem @ X1 @ b ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: hF_Mirabelle_hf] :
        ( ( ord_le976219883lle_hf @ a @ X1 )
        = ( ! [X2: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ X2 @ a )
             => ( hF_Mirabelle_hmem @ X2 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: hF_Mirabelle_hf] :
        ( ( hF_Mirabelle_hmem @ X1 @ a )
       => ( hF_Mirabelle_hmem @ X1 @ b ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( ord_le976219883lle_hf @ a )
      = ( ^ [X1: hF_Mirabelle_hf] :
          ! [X2: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ X2 @ a )
           => ( hF_Mirabelle_hmem @ X2 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: hF_Mirabelle_hf] :
        ( ( ord_le976219883lle_hf @ X1 )
        = ( ^ [X2: hF_Mirabelle_hf] :
            ! [X3: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ X3 @ X1 )
             => ( hF_Mirabelle_hmem @ X3 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(conj_1,conjecture,
    sP2 ).

thf(h0,negated_conjecture,
    ~ sP2,
    inference(assume_negation,[status(cth)],[conj_1]) ).

thf(1,plain,
    ( ~ sP3
    | sP2
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP4
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP6
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP7
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP1
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(conj_0,axiom,
    sP5 ).

thf(fact_6_less__eq__hf__def,axiom,
    sP1 ).

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,h0,conj_0,fact_6_less__eq__hf__def]) ).

thf(0,theorem,
    sP2,
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ITP073^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n015.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sun Aug 27 14:46:09 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.45  % SZS status Theorem
% 0.20/0.45  % Mode: cade22sinegrackle2x6978
% 0.20/0.45  % Steps: 55
% 0.20/0.45  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------