TSTP Solution File: ITP029^1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP029^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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 : Mon May 20 22:22:13 EDT 2024

% Result   : Theorem 9.04s 3.38s
% Output   : Refutation 9.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  116
% Syntax   : Number of formulae    :  210 (  78 unt;  24 typ;   0 def)
%            Number of atoms       :  444 ( 134 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 1292 (  90   ~;  24   |;  24   &; 936   @)
%                                         (   0 <=>; 218  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Number of types       :    8 (   7 usr)
%            Number of type conns  :   93 (  93   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  17 usr;   9 con; 0-4 aty)
%            Number of variables   :  478 (   8   ^ 420   !;  50   ?; 478   :)

% Comments : 
%------------------------------------------------------------------------------
thf(binary594033953_set_a_type,type,
    binary594033953_set_a: $tType ).

thf(binary1439146945Tree_a_type,type,
    binary1439146945Tree_a: $tType ).

thf(set_set_set_a_type,type,
    set_set_set_a: $tType ).

thf(set_set_a_type,type,
    set_set_a: $tType ).

thf(set_a_type,type,
    set_a: $tType ).

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

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

thf(binary717961607le_T_a_type,type,
    binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).

thf(binary476621312_Tip_a_type,type,
    binary476621312_Tip_a: binary1439146945Tree_a ).

thf(binary256242811Tree_a_type,type,
    binary256242811Tree_a: binary1439146945Tree_a > set_a ).

thf(binary945792244etOf_a_type,type,
    binary945792244etOf_a: binary1439146945Tree_a > set_a ).

thf(binary1721989714Tree_a_type,type,
    binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).

thf(binary670562003pred_a_type,type,
    binary670562003pred_a: ( a > int ) > a > a > binary1439146945Tree_a > $o ).

thf(bot_bot_set_a_type,type,
    bot_bot_set_a: set_a ).

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

thf(ord_less_eq_set_a_type,type,
    ord_less_eq_set_a: set_a > set_a > $o ).

thf(pred_chain_a_type,type,
    pred_chain_a: set_a > ( a > a > $o ) > set_a > $o ).

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

thf(a2_type,type,
    a2: a ).

thf(b_type,type,
    b: a ).

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

thf(t1_type,type,
    t1: binary1439146945Tree_a ).

thf(t2_type,type,
    t2: binary1439146945Tree_a ).

thf(x_type,type,
    x: a ).

thf(76,axiom,
    ! [A: int] :
    ? [B: int] : ( ord_less_int @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_gt__ex) ).

thf(385,plain,
    ! [A: int] :
    ? [B: int] : ( ord_less_int @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(27,axiom,
    ! [A: int] :
    ? [B: int] :
    ! [C: int] :
      ( ( ord_less_int @ C @ B )
     => ( C != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_minf_I4_J) ).

thf(185,plain,
    ! [A: int] :
    ? [B: int] :
    ! [C: int] :
      ( ( ord_less_int @ C @ B )
     => ( C != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(28,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_int @ B @ C )
       => ( ord_less_int @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_order_Ostrict__trans) ).

thf(189,plain,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_int @ B @ C )
       => ( ord_less_int @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(67,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ~ ( ord_less_int @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_less__asym) ).

thf(348,plain,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ~ ( ord_less_int @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(87,axiom,
    ( ( member_a @ a2 @ ( binary945792244etOf_a @ t1 ) )
   => ( a2 = b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062) ).

thf(403,plain,
    ( ( member_a @ a2 @ ( binary945792244etOf_a @ t1 ) )
   => ( a2 = b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(88,axiom,
    member_a @ a2 @ ( binary945792244etOf_a @ t2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_adef1) ).

thf(406,plain,
    member_a @ a2 @ ( binary945792244etOf_a @ t2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(63,axiom,
    ! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
      ( ? [E: int] :
        ! [F: int] :
          ( ( ord_less_int @ E @ F )
         => ( ( A @ F )
            = ( B @ F ) ) )
     => ( ? [E: int] :
          ! [F: int] :
            ( ( ord_less_int @ E @ F )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ? [E: int] :
          ! [F: int] :
            ( ( ord_less_int @ E @ F )
           => ( ( ( A @ F )
                | ( C @ F ) )
              = ( ( B @ F )
                | ( D @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_pinf_I2_J) ).

thf(314,plain,
    ! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
      ( ? [E: int] :
        ! [F: int] :
          ( ( ord_less_int @ E @ F )
         => ( ( A @ F )
            = ( B @ F ) ) )
     => ( ? [E: int] :
          ! [F: int] :
            ( ( ord_less_int @ E @ F )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ? [E: int] :
          ! [F: int] :
            ( ( ord_less_int @ E @ F )
           => ( ( ( A @ F )
                | ( C @ F ) )
              = ( ( B @ F )
                | ( D @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(17,axiom,
    ( ( binary945792244etOf_a @ binary476621312_Tip_a )
    = bot_bot_set_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_setOf_Osimps_I1_J) ).

thf(138,plain,
    ( ( binary945792244etOf_a @ binary476621312_Tip_a )
    = bot_bot_set_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(44,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ~ ( ord_less_int @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_order_Oasym) ).

thf(249,plain,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ~ ( ord_less_int @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(69,axiom,
    ! [A: int,B: int] :
      ( ~ ( ord_less_int @ A @ B )
     => ( ( A != B )
       => ( ord_less_int @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_linorder__cases) ).

thf(352,plain,
    ! [A: int,B: int] :
      ( ~ ( ord_less_int @ A @ B )
     => ( ( A != B )
       => ( ord_less_int @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(90,axiom,
    binary670562003pred_a @ h @ a2 @ b @ binary476621312_Tip_a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__092_060open_062sorted__distinct__pred_Ah_Aa_Ab_ATip_092_060close_062) ).

thf(408,plain,
    binary670562003pred_a @ h @ a2 @ b @ binary476621312_Tip_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(52,axiom,
    ! [A: int,B: int] :
      ( ( A != B )
      = ( ( ord_less_int @ A @ B )
        | ( ord_less_int @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_neq__iff) ).

thf(276,plain,
    ! [A: int,B: int] :
      ( ( A != B )
      = ( ( ord_less_int @ A @ B )
        | ( ord_less_int @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(12,axiom,
    ! [A: set_a] :
      ( ! [B: a] :
          ~ ( member_a @ B @ A )
     => ( A = bot_bot_set_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_equals0I) ).

thf(120,plain,
    ! [A: set_a] :
      ( ! [B: a] :
          ~ ( member_a @ B @ A )
     => ( A = bot_bot_set_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(32,axiom,
    ! [A: a > int] : ( binary1721989714Tree_a @ A @ binary476621312_Tip_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_sortedTree_Osimps_I1_J) ).

thf(202,plain,
    ! [A: a > int] : ( binary1721989714Tree_a @ A @ binary476621312_Tip_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(78,axiom,
    binary1721989714Tree_a @ h @ t1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_s1) ).

thf(389,plain,
    binary1721989714Tree_a @ h @ t1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(30,axiom,
    ! [A: int] :
    ? [B: int] : ( ord_less_int @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_lt__ex) ).

thf(196,plain,
    ! [A: int] :
    ? [B: int] : ( ord_less_int @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(83,axiom,
    ( ( h @ a2 )
    = ( h @ b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_hahb) ).

thf(396,plain,
    ( ( h @ a2 )
    = ( h @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(93,axiom,
    ( ( member_a @ a2 @ ( binary945792244etOf_a @ t1 ) )
    | ( a2 = x )
    | ( member_a @ a2 @ ( binary945792244etOf_a @ t2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060or_062_Aa_A_061_Ax_A_092_060or_062_Aa_A_092_060in_062_AsetOf_At2_092_060close_062) ).

thf(411,plain,
    ( ( member_a @ a2 @ ( binary945792244etOf_a @ t1 ) )
    | ( a2 = x )
    | ( member_a @ a2 @ ( binary945792244etOf_a @ t2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(42,axiom,
    ! [A: a > int,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
      ( ( binary1721989714Tree_a @ A @ ( binary717961607le_T_a @ B @ C @ D ) )
     => ( binary1721989714Tree_a @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_sortLemmaL) ).

thf(243,plain,
    ! [A: a > int,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
      ( ( binary1721989714Tree_a @ A @ ( binary717961607le_T_a @ B @ C @ D ) )
     => ( binary1721989714Tree_a @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(62,axiom,
    ! [A: int] :
    ? [B: int] :
    ! [C: int] :
      ( ( ord_less_int @ C @ B )
     => ~ ( ord_less_int @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_minf_I7_J) ).

thf(312,plain,
    ! [A: int] :
    ? [B: int] :
    ! [C: int] :
      ( ( ord_less_int @ C @ B )
     => ~ ( ord_less_int @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(34,axiom,
    ! [A: int,B: int] :
      ( ( ~ ( ord_less_int @ A @ B ) )
      = ( ( ord_less_int @ B @ A )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_not__less__iff__gr__or__eq) ).

thf(206,plain,
    ! [A: int,B: int] :
      ( ( ~ ( ord_less_int @ A @ B ) )
      = ( ( ord_less_int @ B @ A )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(60,axiom,
    ! [A: a > int,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
      ( ( binary1721989714Tree_a @ A @ ( binary717961607le_T_a @ B @ C @ D ) )
      = ( ( binary1721989714Tree_a @ A @ B )
        & ! [E: a] :
            ( ( member_a @ E @ ( binary945792244etOf_a @ B ) )
           => ( ord_less_int @ ( A @ E ) @ ( A @ C ) ) )
        & ! [E: a] :
            ( ( member_a @ E @ ( binary945792244etOf_a @ D ) )
           => ( ord_less_int @ ( A @ C ) @ ( A @ E ) ) )
        & ( binary1721989714Tree_a @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_sortedTree_Osimps_I2_J) ).

thf(307,plain,
    ! [A: a > int,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
      ( ( binary1721989714Tree_a @ A @ ( binary717961607le_T_a @ B @ C @ D ) )
      = ( ( binary1721989714Tree_a @ A @ B )
        & ! [E: a] :
            ( ( member_a @ E @ ( binary945792244etOf_a @ B ) )
           => ( ord_less_int @ ( A @ E ) @ ( A @ C ) ) )
        & ! [E: a] :
            ( ( member_a @ E @ ( binary945792244etOf_a @ D ) )
           => ( ord_less_int @ ( A @ C ) @ ( A @ E ) ) )
        & ( binary1721989714Tree_a @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(55,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
      | ( A = B )
      | ( ord_less_int @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_less__linear) ).

thf(292,plain,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
      | ( A = B )
      | ( ord_less_int @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(50,axiom,
    ! [A: int,B: int] :
      ( ( A != B )
     => ( ~ ( ord_less_int @ A @ B )
       => ( ord_less_int @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_neqE) ).

thf(270,plain,
    ! [A: int,B: int] :
      ( ( A != B )
     => ( ~ ( ord_less_int @ A @ B )
       => ( ord_less_int @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(6,axiom,
    ! [A: set_a,B: set_a] :
      ( ( ord_less_eq_set_a @ A @ B )
     => ( ( ord_less_eq_set_a @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_subset__antisym) ).

thf(102,plain,
    ! [A: set_a,B: set_a] :
      ( ( ord_less_eq_set_a @ A @ B )
     => ( ( ord_less_eq_set_a @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(74,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_int @ B @ C )
       => ( ord_less_int @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_less__trans) ).

thf(380,plain,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_int @ B @ C )
       => ( ord_less_int @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(11,axiom,
    ! [A: set_a] :
      ( ( ? [B: a] : ( member_a @ B @ A ) )
      = ( A != bot_bot_set_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_ex__in__conv) ).

thf(117,plain,
    ! [A: set_a] :
      ( ( ? [B: a] : ( member_a @ B @ A ) )
      = ( A != bot_bot_set_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(37,axiom,
    ! [A: int] :
    ? [B: int] :
    ! [C: int] :
      ( ( ord_less_int @ C @ B )
     => ( ord_less_int @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_minf_I5_J) ).

thf(220,plain,
    ! [A: int] :
    ? [B: int] :
    ! [C: int] :
      ( ( ord_less_int @ C @ B )
     => ( ord_less_int @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(72,axiom,
    ! [A: int,B: int,C: int > int,D: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_int @ ( C @ B ) @ D )
       => ( ! [E: int,F: int] :
              ( ( ord_less_int @ E @ F )
             => ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_order__less__subst2) ).

thf(366,plain,
    ! [A: int,B: int,C: int > int,D: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_int @ ( C @ B ) @ D )
       => ( ! [E: int,F: int] :
              ( ( ord_less_int @ E @ F )
             => ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(58,axiom,
    ! [A: set_a,B: set_a] :
      ( ! [C: a] :
          ( ( member_a @ C @ A )
         => ( member_a @ C @ B ) )
     => ( ord_less_eq_set_a @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_subsetI) ).

thf(302,plain,
    ! [A: set_a,B: set_a] :
      ( ! [C: a] :
          ( ( member_a @ C @ A )
         => ( member_a @ C @ B ) )
     => ( ord_less_eq_set_a @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(29,axiom,
    ! [A: int] :
    ? [B: int] :
    ! [C: int] :
      ( ( ord_less_int @ C @ B )
     => ( C != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_minf_I3_J) ).

thf(192,plain,
    ! [A: int] :
    ? [B: int] :
    ! [C: int] :
      ( ( ord_less_int @ C @ B )
     => ( C != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(89,axiom,
    member_a @ b @ ( binary945792244etOf_a @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_bdef) ).

thf(407,plain,
    member_a @ b @ ( binary945792244etOf_a @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(71,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( B = C )
       => ( ord_less_int @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_ord__less__eq__trans) ).

thf(361,plain,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( B = C )
       => ( ord_less_int @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(4,axiom,
    ! [A: a] :
      ~ ( member_a @ A @ bot_bot_set_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_empty__iff) ).

thf(97,plain,
    ! [A: a] :
      ~ ( member_a @ A @ bot_bot_set_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(64,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_less__imp__not__eq) ).

thf(324,plain,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(65,axiom,
    ! [A: int] :
    ? [B: int] :
    ! [C: int] :
      ( ( ord_less_int @ B @ C )
     => ( ord_less_int @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_pinf_I7_J) ).

thf(328,plain,
    ! [A: int] :
    ? [B: int] :
    ! [C: int] :
      ( ( ord_less_int @ B @ C )
     => ( ord_less_int @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(13,axiom,
    ! [A: set_a] :
      ( ( ! [B: a] :
            ~ ( member_a @ B @ A ) )
      = ( A = bot_bot_set_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_all__not__in__conv) ).

thf(124,plain,
    ! [A: set_a] :
      ( ( ! [B: a] :
            ~ ( member_a @ B @ A ) )
      = ( A = bot_bot_set_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(36,axiom,
    ! [A: int,B: int,C: int > int,D: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: int,F: int] :
              ( ( ord_less_int @ E @ F )
             => ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ord__less__eq__subst) ).

thf(212,plain,
    ! [A: int,B: int,C: int > int,D: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: int,F: int] :
              ( ( ord_less_int @ E @ F )
             => ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(3,axiom,
    pred_chain_a = pred_chain_a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_pred__on_Ochain_Ocong) ).

thf(96,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(80,axiom,
    ord_less_int @ ( h @ x ) @ ( h @ a2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_o2) ).

thf(393,plain,
    ord_less_int @ ( h @ x ) @ ( h @ a2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(23,axiom,
    ! [A: binary1439146945Tree_a,B: a,C: binary1439146945Tree_a,D: binary1439146945Tree_a,E: a,F: binary1439146945Tree_a] :
      ( ( ( binary717961607le_T_a @ A @ B @ C )
        = ( binary717961607le_T_a @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Tree_Oinject) ).

thf(173,plain,
    ! [A: binary1439146945Tree_a,B: a,C: binary1439146945Tree_a,D: binary1439146945Tree_a,E: a,F: binary1439146945Tree_a] :
      ( ( ( binary717961607le_T_a @ A @ B @ C )
        = ( binary717961607le_T_a @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(7,axiom,
    ( ( binary256242811Tree_a @ binary476621312_Tip_a )
    = bot_bot_set_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_Tree_Osimps_I14_J) ).

thf(105,plain,
    ( ( binary256242811Tree_a @ binary476621312_Tip_a )
    = bot_bot_set_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(48,axiom,
    binary1721989714Tree_a @ h @ t2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_s2) ).

thf(266,plain,
    binary1721989714Tree_a @ h @ t2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(84,axiom,
    member_a @ a2 @ ( binary945792244etOf_a @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_adef) ).

thf(398,plain,
    member_a @ a2 @ ( binary945792244etOf_a @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(57,axiom,
    ! [A: int,B: int > int,C: int,D: int] :
      ( ( ord_less_int @ A @ ( B @ C ) )
     => ( ( ord_less_int @ C @ D )
       => ( ! [E: int,F: int] :
              ( ( ord_less_int @ E @ F )
             => ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_order__less__subst1) ).

thf(298,plain,
    ! [A: int,B: int > int,C: int,D: int] :
      ( ( ord_less_int @ A @ ( B @ C ) )
     => ( ( ord_less_int @ C @ D )
       => ( ! [E: int,F: int] :
              ( ( ord_less_int @ E @ F )
             => ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(20,axiom,
    binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_s) ).

thf(148,plain,
    binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(53,axiom,
    ! [A: int,B: int] :
      ( ( A != B )
     => ( ~ ( ord_less_int @ A @ B )
       => ( ord_less_int @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_linorder__neqE__linordered__idom) ).

thf(279,plain,
    ! [A: int,B: int] :
      ( ( A != B )
     => ( ~ ( ord_less_int @ A @ B )
       => ( ord_less_int @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(25,axiom,
    ! [A: a > int,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
      ( ( binary1721989714Tree_a @ A @ ( binary717961607le_T_a @ B @ C @ D ) )
     => ( binary1721989714Tree_a @ A @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_sortLemmaR) ).

thf(180,plain,
    ! [A: a > int,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
      ( ( binary1721989714Tree_a @ A @ ( binary717961607le_T_a @ B @ C @ D ) )
     => ( binary1721989714Tree_a @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(21,axiom,
    ! [A: binary1439146945Tree_a > $o,B: binary1439146945Tree_a] :
      ( ( A @ binary476621312_Tip_a )
     => ( ! [C: binary1439146945Tree_a,D: a,E: binary1439146945Tree_a] :
            ( ( A @ C )
           => ( ( A @ E )
             => ( A @ ( binary717961607le_T_a @ C @ D @ E ) ) ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Tree_Oinduct) ).

thf(149,plain,
    ! [A: binary1439146945Tree_a > $o,B: binary1439146945Tree_a] :
      ( ( A @ binary476621312_Tip_a )
     => ( ! [C: binary1439146945Tree_a,D: a,E: binary1439146945Tree_a] :
            ( ( A @ C )
           => ( ( A @ E )
             => ( A @ ( binary717961607le_T_a @ C @ D @ E ) ) ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(24,axiom,
    ! [A: int] :
    ? [B: int] :
    ! [C: int] :
      ( ( ord_less_int @ B @ C )
     => ( C != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_pinf_I3_J) ).

thf(176,plain,
    ! [A: int] :
    ? [B: int] :
    ! [C: int] :
      ( ( ord_less_int @ B @ C )
     => ( C != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(33,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ~ ( ord_less_int @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_dual__order_Oasym) ).

thf(204,plain,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ~ ( ord_less_int @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(19,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_less__imp__neq) ).

thf(144,plain,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(68,axiom,
    ! [A: a,B: binary1439146945Tree_a,C: binary1439146945Tree_a] : ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ B @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_Tree_Oset__intros_I2_J) ).

thf(350,plain,
    ! [A: a,B: binary1439146945Tree_a,C: binary1439146945Tree_a] : ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ B @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(77,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ~ ( ord_less_int @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_less__imp__not__less) ).

thf(387,plain,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ~ ( ord_less_int @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(18,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_dual__order_Ostrict__implies__not__eq) ).

thf(140,plain,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(45,axiom,
    ! [A: binary1439146945Tree_a] :
      ( ( A != binary476621312_Tip_a )
     => ~ ! [B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
            ( A
           != ( binary717961607le_T_a @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Tree_Oexhaust) ).

thf(251,plain,
    ! [A: binary1439146945Tree_a] :
      ( ( A != binary476621312_Tip_a )
     => ~ ! [B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
            ( A
           != ( binary717961607le_T_a @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(31,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_order_Ostrict__implies__not__eq) ).

thf(198,plain,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(66,axiom,
    ! [A: int > int > $o,B: int,C: int] :
      ( ! [D: int,E: int] :
          ( ( ord_less_int @ D @ E )
         => ( A @ D @ E ) )
     => ( ! [D: int] : ( A @ D @ D )
       => ( ! [D: int,E: int] :
              ( ( A @ E @ D )
             => ( A @ D @ E ) )
         => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_linorder__less__wlog) ).

thf(330,plain,
    ! [A: int > int > $o,B: int,C: int] :
      ( ! [D: int,E: int] :
          ( ( ord_less_int @ D @ E )
         => ( A @ D @ E ) )
     => ( ! [D: int] : ( A @ D @ D )
       => ( ! [D: int,E: int] :
              ( ( A @ E @ D )
             => ( A @ D @ E ) )
         => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(85,axiom,
    binary670562003pred_a @ h @ a2 @ b @ t2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_h2) ).

thf(399,plain,
    binary670562003pred_a @ h @ a2 @ b @ t2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(81,axiom,
    binary670562003pred_a @ h @ a2 @ b @ t1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_h1) ).

thf(394,plain,
    binary670562003pred_a @ h @ a2 @ b @ t1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(49,axiom,
    ! [A: int,B: int] :
      ( ~ ( ord_less_int @ A @ B )
     => ( ( ~ ( ord_less_int @ B @ A ) )
        = ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_antisym__conv3) ).

thf(267,plain,
    ! [A: int,B: int] :
      ( ~ ( ord_less_int @ A @ B )
     => ( ( ~ ( ord_less_int @ B @ A ) )
        = ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(46,axiom,
    ! [A: int,B: int,C: $o] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_int @ B @ A )
       => C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_less__imp__triv) ).

thf(255,plain,
    ! [A: int,B: int,C: $o] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_int @ B @ A )
       => C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(35,axiom,
    ! [A: a,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
      ( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
     => ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ B @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_Tree_Oset__intros_I1_J) ).

thf(209,plain,
    ! [A: a,B: binary1439146945Tree_a,C: a,D: binary1439146945Tree_a] :
      ( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
     => ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(9,axiom,
    ! [A: set_a,B: a > a > $o] : ( pred_chain_a @ A @ B @ bot_bot_set_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_pred__on_Ochain__empty) ).

thf(112,plain,
    ! [A: set_a,B: a > a > $o] : ( pred_chain_a @ A @ B @ bot_bot_set_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(70,axiom,
    ! [A: set_a,B: a > a > $o,C: a > a > $o,D: set_a] :
      ( ! [E: a,F: a] :
          ( ( member_a @ E @ A )
         => ( ( member_a @ F @ A )
           => ( ( B @ E @ F )
             => ( C @ E @ F ) ) ) )
     => ( ( pred_chain_a @ A @ B @ D )
       => ( pred_chain_a @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_chain__mono) ).

thf(355,plain,
    ! [A: set_a,B: a > a > $o,C: a > a > $o,D: set_a] :
      ( ! [E: a,F: a] :
          ( ( member_a @ E @ A )
         => ( ( member_a @ F @ A )
           => ( ( B @ E @ F )
             => ( C @ E @ F ) ) ) )
     => ( ( pred_chain_a @ A @ B @ D )
       => ( pred_chain_a @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(56,axiom,
    ! [A: a,B: binary1439146945Tree_a,C: binary1439146945Tree_a,D: a] :
      ( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
     => ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ C @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_Tree_Oset__intros_I3_J) ).

thf(295,plain,
    ! [A: a,B: binary1439146945Tree_a,C: binary1439146945Tree_a,D: a] :
      ( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
     => ( member_a @ A @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ C @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(54,axiom,
    ! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
      ( ? [E: int] :
        ! [F: int] :
          ( ( ord_less_int @ F @ E )
         => ( ( A @ F )
            = ( B @ F ) ) )
     => ( ? [E: int] :
          ! [F: int] :
            ( ( ord_less_int @ F @ E )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ? [E: int] :
          ! [F: int] :
            ( ( ord_less_int @ F @ E )
           => ( ( ( A @ F )
                | ( C @ F ) )
              = ( ( B @ F )
                | ( D @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_minf_I2_J) ).

thf(282,plain,
    ! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
      ( ? [E: int] :
        ! [F: int] :
          ( ( ord_less_int @ F @ E )
         => ( ( A @ F )
            = ( B @ F ) ) )
     => ( ? [E: int] :
          ! [F: int] :
            ( ( ord_less_int @ F @ E )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ? [E: int] :
          ! [F: int] :
            ( ( ord_less_int @ F @ E )
           => ( ( ( A @ F )
                | ( C @ F ) )
              = ( ( B @ F )
                | ( D @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(91,axiom,
    member_a @ b @ ( binary945792244etOf_a @ t1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_bdef1) ).

thf(409,plain,
    member_a @ b @ ( binary945792244etOf_a @ t1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(61,axiom,
    ! [A: int] :
    ? [B: int] :
    ! [C: int] :
      ( ( ord_less_int @ B @ C )
     => ~ ( ord_less_int @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_pinf_I5_J) ).

thf(310,plain,
    ! [A: int] :
    ? [B: int] :
    ! [C: int] :
      ( ( ord_less_int @ B @ C )
     => ~ ( ord_less_int @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(26,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_int @ C @ A )
       => ( ord_less_int @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_dual__order_Ostrict__trans) ).

thf(182,plain,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_int @ C @ A )
       => ( ord_less_int @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(73,axiom,
    ! [A: a,B: binary1439146945Tree_a] :
      ( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
     => ( ! [C: binary1439146945Tree_a] :
            ( ? [D: a,E: binary1439146945Tree_a] :
                ( B
                = ( binary717961607le_T_a @ C @ D @ E ) )
           => ~ ( member_a @ A @ ( binary256242811Tree_a @ C ) ) )
       => ( ! [C: binary1439146945Tree_a,D: binary1439146945Tree_a] :
              ( B
             != ( binary717961607le_T_a @ C @ A @ D ) )
         => ~ ! [C: binary1439146945Tree_a,D: a,E: binary1439146945Tree_a] :
                ( ( B
                  = ( binary717961607le_T_a @ C @ D @ E ) )
               => ~ ( member_a @ A @ ( binary256242811Tree_a @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Tree_Oset__cases) ).

thf(370,plain,
    ! [A: a,B: binary1439146945Tree_a] :
      ( ( member_a @ A @ ( binary256242811Tree_a @ B ) )
     => ( ! [C: binary1439146945Tree_a] :
            ( ? [D: a,E: binary1439146945Tree_a] :
                ( B
                = ( binary717961607le_T_a @ C @ D @ E ) )
           => ~ ( member_a @ A @ ( binary256242811Tree_a @ C ) ) )
       => ( ! [C: binary1439146945Tree_a,D: binary1439146945Tree_a] :
              ( B
             != ( binary717961607le_T_a @ C @ A @ D ) )
         => ~ ! [C: binary1439146945Tree_a,D: a,E: binary1439146945Tree_a] :
                ( ( B
                  = ( binary717961607le_T_a @ C @ D @ E ) )
               => ~ ( member_a @ A @ ( binary256242811Tree_a @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(14,axiom,
    ! [A: binary1439146945Tree_a,B: a,C: binary1439146945Tree_a] :
      ( binary476621312_Tip_a
     != ( binary717961607le_T_a @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Tree_Odistinct_I1_J) ).

thf(127,plain,
    ! [A: binary1439146945Tree_a,B: a,C: binary1439146945Tree_a] :
      ( binary476621312_Tip_a
     != ( binary717961607le_T_a @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(47,axiom,
    ! [A: int,B: int > int,C: int,D: int] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_int @ C @ D )
       => ( ! [E: int,F: int] :
              ( ( ord_less_int @ E @ F )
             => ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_ord__eq__less__subst) ).

thf(258,plain,
    ! [A: int,B: int > int,C: int,D: int] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_int @ C @ D )
       => ( ! [E: int,F: int] :
              ( ( ord_less_int @ E @ F )
             => ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(79,axiom,
    ( ( member_a @ b @ ( binary945792244etOf_a @ t1 ) )
    | ( b = x )
    | ( member_a @ b @ ( binary945792244etOf_a @ t2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_calculation) ).

thf(390,plain,
    ( ( member_a @ b @ ( binary945792244etOf_a @ t1 ) )
    | ( b = x )
    | ( member_a @ b @ ( binary945792244etOf_a @ t2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(10,axiom,
    ! [A: a] :
      ~ ( member_a @ A @ bot_bot_set_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_emptyE) ).

thf(114,plain,
    ! [A: a] :
      ~ ( member_a @ A @ bot_bot_set_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(75,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ~ ( ord_less_int @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_less__not__sym) ).

thf(383,plain,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ~ ( ord_less_int @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(40,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_less__imp__not__eq2) ).

thf(235,plain,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(43,axiom,
    ! [A: int] :
      ~ ( ord_less_int @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_dual__order_Oirrefl) ).

thf(246,plain,
    ! [A: int] :
      ~ ( ord_less_int @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(92,axiom,
    ord_less_int @ ( h @ b ) @ ( h @ a2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062h_Ab_A_060_Ah_Aa_092_060close_062) ).

thf(410,plain,
    ord_less_int @ ( h @ b ) @ ( h @ a2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(51,axiom,
    ! [A: int] :
      ~ ( ord_less_int @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_verit__comp__simplify1_I1_J) ).

thf(273,plain,
    ! [A: int] :
      ~ ( ord_less_int @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(59,axiom,
    ( binary670562003pred_a
    = ( ^ [A: a > int,B: a,C: a,D: binary1439146945Tree_a] :
          ( ( ( binary1721989714Tree_a @ A @ D )
            & ( member_a @ B @ ( binary945792244etOf_a @ D ) )
            & ( member_a @ C @ ( binary945792244etOf_a @ D ) )
            & ( ( A @ B )
              = ( A @ C ) ) )
         => ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_sorted__distinct__pred__def) ).

thf(305,plain,
    ( binary670562003pred_a
    = ( ^ [A: a > int,B: a,C: a,D: binary1439146945Tree_a] :
          ( ( ( binary1721989714Tree_a @ A @ D )
            & ( member_a @ B @ ( binary945792244etOf_a @ D ) )
            & ( member_a @ C @ ( binary945792244etOf_a @ D ) )
            & ( ( A @ B )
              = ( A @ C ) ) )
         => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(8,axiom,
    ! [A: set_a,B: a] :
      ( ( A = bot_bot_set_a )
     => ~ ( member_a @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_equals0D) ).

thf(107,plain,
    ! [A: set_a,B: a] :
      ( ( A = bot_bot_set_a )
     => ~ ( member_a @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(41,axiom,
    ! [A: int] :
    ? [B: int] :
    ! [C: int] :
      ( ( ord_less_int @ B @ C )
     => ( C != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_pinf_I4_J) ).

thf(239,plain,
    ! [A: int] :
    ? [B: int] :
    ! [C: int] :
      ( ( ord_less_int @ B @ C )
     => ( C != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(16,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ~ ( ord_less_int @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_less__asym_H) ).

thf(136,plain,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ~ ( ord_less_int @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(86,axiom,
    ( ( a2 = x )
   => ( a2 = b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062a_A_061_Ax_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062) ).

thf(400,plain,
    ( ( a2 = x )
   => ( a2 = b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(1,conjecture,
    a2 = b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    a2 != b,
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(94,plain,
    a2 != b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(82,axiom,
    ord_less_int @ ( h @ b ) @ ( h @ x ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_o1) ).

thf(395,plain,
    ord_less_int @ ( h @ b ) @ ( h @ x ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(15,axiom,
    ! [A: int,B: int,C: int] :
      ( ( A = B )
     => ( ( ord_less_int @ B @ C )
       => ( ord_less_int @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_ord__eq__less__trans) ).

thf(131,plain,
    ! [A: int,B: int,C: int] :
      ( ( A = B )
     => ( ( ord_less_int @ B @ C )
       => ( ord_less_int @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(22,axiom,
    ! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
      ( ? [E: int] :
        ! [F: int] :
          ( ( ord_less_int @ E @ F )
         => ( ( A @ F )
            = ( B @ F ) ) )
     => ( ? [E: int] :
          ! [F: int] :
            ( ( ord_less_int @ E @ F )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ? [E: int] :
          ! [F: int] :
            ( ( ord_less_int @ E @ F )
           => ( ( ( A @ F )
                & ( C @ F ) )
              = ( ( B @ F )
                & ( D @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_pinf_I1_J) ).

thf(163,plain,
    ! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
      ( ? [E: int] :
        ! [F: int] :
          ( ( ord_less_int @ E @ F )
         => ( ( A @ F )
            = ( B @ F ) ) )
     => ( ? [E: int] :
          ! [F: int] :
            ( ( ord_less_int @ E @ F )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ? [E: int] :
          ! [F: int] :
            ( ( ord_less_int @ E @ F )
           => ( ( ( A @ F )
                & ( C @ F ) )
              = ( ( B @ F )
                & ( D @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(38,axiom,
    ! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
      ( ? [E: int] :
        ! [F: int] :
          ( ( ord_less_int @ F @ E )
         => ( ( A @ F )
            = ( B @ F ) ) )
     => ( ? [E: int] :
          ! [F: int] :
            ( ( ord_less_int @ F @ E )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ? [E: int] :
          ! [F: int] :
            ( ( ord_less_int @ F @ E )
           => ( ( ( A @ F )
                & ( C @ F ) )
              = ( ( B @ F )
                & ( D @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_minf_I1_J) ).

thf(222,plain,
    ! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
      ( ? [E: int] :
        ! [F: int] :
          ( ( ord_less_int @ F @ E )
         => ( ( A @ F )
            = ( B @ F ) ) )
     => ( ? [E: int] :
          ! [F: int] :
            ( ( ord_less_int @ F @ E )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ? [E: int] :
          ! [F: int] :
            ( ( ord_less_int @ F @ E )
           => ( ( ( A @ F )
                & ( C @ F ) )
              = ( ( B @ F )
                & ( D @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(39,axiom,
    ! [A: int] :
      ~ ( ord_less_int @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_less__irrefl) ).

thf(232,plain,
    ! [A: int] :
      ~ ( ord_less_int @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(5,axiom,
    ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_order__refl) ).

thf(100,plain,
    ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(475,plain,
    $false,
    inference(cvc4,[status(thm)],[385,185,189,348,403,406,314,138,249,352,408,276,120,202,389,196,396,411,243,312,206,307,292,270,102,380,117,220,366,302,192,407,361,97,324,328,124,212,96,393,173,105,266,398,298,148,279,180,149,176,204,144,350,387,140,251,198,330,399,394,267,255,209,112,355,295,282,409,310,182,370,127,258,390,114,383,235,246,410,273,305,107,239,136,400,94,395,131,163,222,232,100]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ITP029^1 : TPTP v8.2.0. Released v7.5.0.
% 0.03/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n025.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sat May 18 15:24:09 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.96/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.90/1.15  % [INFO] 	 Parsing done (269ms). 
% 1.90/1.16  % [INFO] 	 Running in sequential loop mode. 
% 2.71/1.39  % [INFO] 	 eprover registered as external prover. 
% 2.71/1.40  % [INFO] 	 cvc4 registered as external prover. 
% 2.71/1.40  % [INFO] 	 Scanning for conjecture ... 
% 2.95/1.49  % [INFO] 	 Found a conjecture (or negated_conjecture) and 350 axioms. Running axiom selection ... 
% 3.20/1.56  % [INFO] 	 Axiom selection finished. Selected 91 axioms (removed 259 axioms). 
% 3.59/1.68  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.59/1.70  % [INFO] 	 Type checking passed. 
% 3.59/1.71  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 9.04/3.38  % External prover 'cvc4' found a proof!
% 9.04/3.38  % [INFO] 	 Killing All external provers ... 
% 9.04/3.38  % Time passed: 2853ms (effective reasoning time: 2221ms)
% 9.04/3.38  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 9.04/3.38  % Axioms used in derivation (91): fact_347_subset__antisym, fact_99_order_Oasym, fact_29_minf_I3_J, fact_26_minf_I7_J, fact_22_sortedTree_Osimps_I2_J, fact_134_less__imp__not__eq2, fact_191_Tree_Oset__intros_I1_J, fact_115_less__irrefl, fact_20_s2, fact_141_dual__order_Oirrefl, fact_193_Tree_Oset__intros_I2_J, fact_138_linorder__cases, fact_0_hahb, fact_173_equals0I, fact_4_bdef1, fact_121_ord__less__eq__trans, fact_19_Tree_Oexhaust, fact_111_less__trans, fact_6_o1, fact_346_order__refl, fact_53_not__less__iff__gr__or__eq, fact_44_dual__order_Ostrict__implies__not__eq, fact_30_minf_I2_J, fact_15_adef, fact_18_Tree_Oinduct, fact_24_sorted__distinct__pred__def, fact_118_ord__eq__less__trans, fact_335_chain__mono, fact_333_pred__on_Ochain__empty, fact_162_all__not__in__conv, fact_21_s1, fact_102_less__imp__neq, fact_108_less__asym_H, fact_40_minf_I1_J, fact_34_pinf_I1_J, fact_151_verit__comp__simplify1_I1_J, fact_3_adef1, fact_38_pinf_I5_J, fact_36_pinf_I3_J, fact_147_less__imp__not__less, fact_2__092_060open_062a_A_061_Ax_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062, fact_52_order_Ostrict__implies__not__eq, fact_83_order__less__subst1, fact_175_ex__in__conv, fact_95_neqE, fact_27_minf_I5_J, fact_12__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060or_062_Aa_A_061_Ax_A_092_060or_062_Aa_A_092_060in_062_AsetOf_At2_092_060close_062, fact_10__092_060open_062sorted__distinct__pred_Ah_Aa_Ab_ATip_092_060close_062, fact_9_h1, fact_56_dual__order_Ostrict__trans, fact_112_less__linear, fact_148_linorder__less__wlog, fact_195_Tree_Oset__intros_I3_J, fact_152_setOf_Osimps_I1_J, fact_11_calculation, fact_37_pinf_I4_J, fact_94_gt__ex, fact_32_sortLemmaL, fact_96_neq__iff, fact_127_less__imp__not__eq, fact_35_pinf_I2_J, fact_8_h2, fact_16_s, fact_171_equals0D, fact_130_less__not__sym, fact_7_o2, fact_336_pred__on_Ochain_Ocong, fact_33_sortedTree_Osimps_I1_J, fact_124_dual__order_Oasym, fact_41_linorder__neqE__linordered__idom, fact_92_order__less__subst2, fact_137_less__imp__triv, fact_14_Tree_Oinject, fact_105_less__asym, fact_348_subsetI, fact_74_ord__less__eq__subst, fact_93_lt__ex, fact_169_emptyE, fact_13_bdef, fact_17_Tree_Odistinct_I1_J, fact_39_pinf_I7_J, fact_189_Tree_Oset__cases, fact_28_minf_I4_J, fact_164_empty__iff, fact_1__092_060open_062h_Ab_A_060_Ah_Aa_092_060close_062, fact_5__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062, fact_65_ord__eq__less__subst, fact_131_antisym__conv3, fact_180_Tree_Osimps_I14_J, fact_31_sortLemmaR, fact_144_order_Ostrict__trans
% 9.04/3.38  % No. of inferences in proof: 186
% 9.04/3.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2853 ms resp. 2221 ms w/o parsing
% 9.04/3.44  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.04/3.44  % [INFO] 	 Killing All external provers ... 
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