%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP200^1 : 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 : n025.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 04:02:52 EDT 2023

% Result   : Theorem 0.19s 0.45s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_produc1418842292n_game,type,
    produc1418842292n_game: $tType ).

thf(ty_set_variable,type,
    set_variable: $tType ).

thf(ty_trm,type,
    trm: $tType ).

thf(ty_none_trm,type,
    none_trm: option_trm ).

thf(ty_none_fml,type,
    none_fml: option_fml ).

thf(ty_uSubst516392804stappf,type,
    uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).

thf(ty_uSubst516392818stappt,type,
    uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).

thf(ty_theta,type,
    theta: trm ).

thf(ty_eta,type,
    eta: trm ).

thf(ty_geq,type,
    geq: trm > trm > fml ).

thf(ty_sigma,type,
    sigma: produc1418842292n_game ).

thf(ty_ua,type,
    ua: set_variable ).

thf(sP1,plain,
    ( sP1
  <=> ( ( uSubst516392804stappf @ sigma @ ua @ ( geq @ theta @ eta ) )
      = none_fml ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: set_variable,X2: trm,X3: trm] :
        ( ( ( uSubst516392804stappf @ sigma @ X1 @ ( geq @ X2 @ X3 ) )
         != none_fml )
       => ~ ( ( ( uSubst516392818stappt @ sigma @ X1 @ X2 )
             != none_trm )
           => ( ( uSubst516392818stappt @ sigma @ X1 @ X3 )
              = none_trm ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( uSubst516392818stappt @ sigma @ ua @ theta )
      = none_trm ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ~ sP3
     => ( ( uSubst516392818stappt @ sigma @ ua @ eta )
        = none_trm ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ~ sP1
     => ~ sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: trm,X2: trm] :
        ( ( ( uSubst516392804stappf @ sigma @ ua @ ( geq @ X1 @ X2 ) )
         != none_fml )
       => ~ ( ( ( uSubst516392818stappt @ sigma @ ua @ X1 )
             != none_trm )
           => ( ( uSubst516392818stappt @ sigma @ ua @ X2 )
              = none_trm ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: produc1418842292n_game,X2: set_variable,X3: trm,X4: trm] :
        ( ( ( uSubst516392804stappf @ X1 @ X2 @ ( geq @ X3 @ X4 ) )
         != none_fml )
       => ~ ( ( ( uSubst516392818stappt @ X1 @ X2 @ X3 )
             != none_trm )
           => ( ( uSubst516392818stappt @ X1 @ X2 @ X4 )
              = none_trm ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: trm] :
        ( ( ( uSubst516392804stappf @ sigma @ ua @ ( geq @ theta @ X1 ) )
         != none_fml )
       => ~ ( ~ sP3
           => ( ( uSubst516392818stappt @ sigma @ ua @ X1 )
              = none_trm ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(conj_0,conjecture,
    ~ sP3 ).

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

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

thf(2,plain,
    ( ~ sP5
    | sP1
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP8
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP6
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP2
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP7
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_2_Geq_Oprems_I1_J,axiom,
    ~ sP1 ).

thf(fact_1_usubstappf__geq__conv,axiom,
    sP7 ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,h0,fact_2_Geq_Oprems_I1_J,fact_1_usubstappf__geq__conv]) ).

thf(0,theorem,
    ~ sP3,
    inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP200^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n025.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sun Aug 27 15:55:24 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.45  % SZS status Theorem
% 0.19/0.45  % Mode: cade22sinegrackle2x6978
% 0.19/0.45  % Steps: 321
% 0.19/0.45  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------