%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP034^1 : 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 04:01:39 EDT 2023

% Result   : Theorem 0.19s 0.60s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_set_a,type,
    set_a: $tType ).

thf(ty_a,type,
    a: $tType ).

thf(ty_int,type,
    int: $tType ).

thf(ty_binary1439146945Tree_a,type,
    binary1439146945Tree_a: $tType ).

thf(ty_t2,type,
    t2: binary1439146945Tree_a ).

thf(ty_binary339557810e_rm_a,type,
    binary339557810e_rm_a: ( a > int ) > binary1439146945Tree_a > a ).

thf(ty_binary717961607le_T_a,type,
    binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).

thf(ty_t1,type,
    t1: binary1439146945Tree_a ).

thf(ty_binary476621312_Tip_a,type,
    binary476621312_Tip_a: binary1439146945Tree_a ).

thf(ty_h,type,
    h: a > int ).

thf(ty_binary945792244etOf_a,type,
    binary945792244etOf_a: binary1439146945Tree_a > set_a ).

thf(ty_x,type,
    x: a ).

thf(ty_ord_less_int,type,
    ord_less_int: int > int > $o ).

thf(ty_binary1721989714Tree_a,type,
    binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).

thf(ty_member_a,type,
    member_a: a > set_a > $o ).

thf(ty_binary1217730267_wrm_a,type,
    binary1217730267_wrm_a: ( a > int ) > binary1439146945Tree_a > binary1439146945Tree_a ).

thf(sP1,plain,
    ( sP1
  <=> ( ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
      = ( binary339557810e_rm_a @ h @ t2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( h @ ( binary339557810e_rm_a @ h @ t2 ) )
      = ( h @ ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( binary1721989714Tree_a @ h @ t2 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( t2 = binary476621312_Tip_a ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ord_less_int @ ( h @ l ) @ ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( binary1721989714Tree_a @ h @ t1 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ( binary339557810e_rm_a @ h @ t2 )
      = ( binary339557810e_rm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(conj_0,conjecture,
    sP3 ).

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

thf(h1,assumption,
    ( ~ sP6
   => ~ sP5 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ! [X1: a] :
      ( ( member_a @ X1 @ ( binary945792244etOf_a @ ( binary1217730267_wrm_a @ h @ t2 ) ) )
     => ( ord_less_int @ ( h @ X1 ) @ ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ( ( t1 != binary476621312_Tip_a )
   => ~ sP8 ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ! [X1: a] :
      ( ( member_a @ X1 @ ( binary945792244etOf_a @ ( binary1217730267_wrm_a @ h @ t1 ) ) )
     => ( ord_less_int @ ( h @ X1 ) @ ( h @ ( binary339557810e_rm_a @ h @ t1 ) ) ) ),
    introduced(assumption,[]) ).

thf(fact_2_t2nTip,axiom,
    ~ sP6 ).

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h5,h3,h1,h0])],[h3,fact_2_t2nTip]) ).

thf(2,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h6,h3,h1,h0])],[h3,fact_2_t2nTip]) ).

thf(fact_35_h1,axiom,
    ( ~ ( ( t1 != binary476621312_Tip_a )
       => ~ sP8 )
   => ! [X1: a] :
        ( ( member_a @ X1 @ ( binary945792244etOf_a @ ( binary1217730267_wrm_a @ h @ t1 ) ) )
       => ( ord_less_int @ ( h @ X1 ) @ ( h @ ( binary339557810e_rm_a @ h @ t1 ) ) ) ) ) ).

thf(3,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h3,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_35_h1,1,2,h5,h6]) ).

thf(h7,assumption,
    t1 = binary476621312_Tip_a,
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ sP8,
    introduced(assumption,[]) ).

thf(fact_8_s2,axiom,
    sP5 ).

thf(4,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h5,h4,h1,h0])],[fact_8_s2,h4]) ).

thf(fact_7_s1,axiom,
    sP8 ).

thf(5,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h8,h5,h4,h1,h0])],[fact_7_s1,h8]) ).

thf(6,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h5,h4,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h5,4,5,h7,h8]) ).

thf(7,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h6,h4,h1,h0])],[fact_8_s2,h4]) ).

thf(8,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h4,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_35_h1,6,7,h5,h6]) ).

thf(9,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h1,3,8,h3,h4]) ).

thf(10,plain,
    ( sP4
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP7
    | sP3
    | ~ sP4
    | sP2 ),
    inference(mating_rule,[status(thm)],]) ).

thf(12,plain,
    ~ sP2,
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP1
    | sP9 ),
    inference(symeq,[status(thm)],]) ).

thf(fact_1_rm__res,axiom,
    sP1 ).

thf(fact_0_hLess,axiom,
    sP7 ).

thf(14,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h7,h5,h2,h0])],[10,11,12,13,h0,fact_1_rm__res,fact_0_hLess]) ).

thf(15,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h8,h5,h2,h0])],[fact_7_s1,h8]) ).

thf(16,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h5,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h5,14,15,h7,h8]) ).

thf(17,plain,
    ( sP4
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP7
    | sP3
    | ~ sP4
    | sP2 ),
    inference(mating_rule,[status(thm)],]) ).

thf(19,plain,
    ~ sP2,
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP1
    | sP9 ),
    inference(symeq,[status(thm)],]) ).

thf(21,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h6,h2,h0])],[17,18,19,20,h0,fact_1_rm__res,fact_0_hLess]) ).

thf(22,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_35_h1,16,21,h5,h6]) ).

thf(fact_36_h2,axiom,
    ( ~ ( ~ sP6
       => ~ sP5 )
   => ! [X1: a] :
        ( ( member_a @ X1 @ ( binary945792244etOf_a @ ( binary1217730267_wrm_a @ h @ t2 ) ) )
       => ( ord_less_int @ ( h @ X1 ) @ ( h @ ( binary339557810e_rm_a @ h @ t2 ) ) ) ) ) ).

thf(23,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_36_h2,9,22,h1,h2]) ).

thf(0,theorem,
    sP3,
    inference(contra,[status(thm),contra(discharge,[h0])],[23,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ITP034^1 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n027.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 11:05:51 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.60  % SZS status Theorem
% 0.19/0.60  % Mode: cade22sinegrackle2x6978
% 0.19/0.60  % Steps: 4010
% 0.19/0.60  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------