TSTP Solution File: ITP033^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP033^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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 22:22:15 EDT 2024

% Result   : Theorem 33.17s 17.67s
% Output   : Refutation 34.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  304
% Syntax   : Number of formulae    :  570 ( 155 unt;  40 typ;   0 def)
%            Number of atoms       : 1878 ( 387 equ;  10 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives : 6716 ( 195   ~;  38   |; 131   &;5473   @)
%                                         (   0 <=>; 879  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   9 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  490 ( 490   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   46 (  42 usr;  10 con; 0-5 aty)
%            Number of variables   : 2149 ( 200   ^1844   !;  64   ?;2149   :)
%                                         (  41  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(int_type,type,
    int: $tType ).

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

thf(bot_type,type,
    bot: 
      !>[TA: $tType] : $o ).

thf(ord_type,type,
    ord: 
      !>[TA: $tType] : $o ).

thf(order_type,type,
    order: 
      !>[TA: $tType] : $o ).

thf(no_bot_type,type,
    no_bot: 
      !>[TA: $tType] : $o ).

thf(no_top_type,type,
    no_top: 
      !>[TA: $tType] : $o ).

thf(linorder_type,type,
    linorder: 
      !>[TA: $tType] : $o ).

thf(preorder_type,type,
    preorder: 
      !>[TA: $tType] : $o ).

thf(wellorder_type,type,
    wellorder: 
      !>[TA: $tType] : $o ).

thf(dense_order_type,type,
    dense_order: 
      !>[TA: $tType] : $o ).

thf(dense_linorder_type,type,
    dense_linorder: 
      !>[TA: $tType] : $o ).

thf(condit1656338222tinuum_type,type,
    condit1656338222tinuum: 
      !>[TA: $tType] : $o ).

thf(condit1037483654norder_type,type,
    condit1037483654norder: 
      !>[TA: $tType] : $o ).

thf(bNF_Ca1785829860lChain_type,type,
    bNF_Ca1785829860lChain: 
      !>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TB ) ) > ( TB > TA ) > $o ) ).

thf(binary210054475elle_T_type,type,
    binary210054475elle_T: 
      !>[TA: $tType] : ( ( binary1291135688e_Tree @ TA ) > TA > ( binary1291135688e_Tree @ TA ) > ( binary1291135688e_Tree @ TA ) ) ).

thf(binary1746293266le_Tip_type,type,
    binary1746293266le_Tip: 
      !>[TA: $tType] : ( binary1291135688e_Tree @ TA ) ).

thf(binary536355927e_Tree_type,type,
    binary536355927e_Tree: 
      !>[TA: $tType,TB: $tType] : ( TB > ( ( binary1291135688e_Tree @ TA ) > TA > ( binary1291135688e_Tree @ TA ) > TB ) > ( binary1291135688e_Tree @ TA ) > TB ) ).

thf(binary1929596613c_Tree_type,type,
    binary1929596613c_Tree: 
      !>[TA: $tType,TB: $tType] : ( TB > ( ( binary1291135688e_Tree @ TA ) > TA > ( binary1291135688e_Tree @ TA ) > TB > TB > TB ) > ( binary1291135688e_Tree @ TA ) > TB ) ).

thf(binary1830089824insert_type,type,
    binary1830089824insert: 
      !>[TA: $tType] : ( ( TA > int ) > TA > ( binary1291135688e_Tree @ TA ) > ( binary1291135688e_Tree @ TA ) ) ).

thf(binary827270440e_memb_type,type,
    binary827270440e_memb: 
      !>[TA: $tType] : ( ( TA > int ) > TA > ( binary1291135688e_Tree @ TA ) > $o ) ).

thf(binary997842527remove_type,type,
    binary997842527remove: 
      !>[TA: $tType] : ( ( TA > int ) > TA > ( binary1291135688e_Tree @ TA ) > ( binary1291135688e_Tree @ TA ) ) ).

thf(binary576689334lle_rm_type,type,
    binary576689334lle_rm: 
      !>[TA: $tType] : ( ( TA > int ) > ( binary1291135688e_Tree @ TA ) > TA ) ).

thf(binary1653327646_setOf_type,type,
    binary1653327646_setOf: 
      !>[TA: $tType] : ( ( binary1291135688e_Tree @ TA ) > ( set @ TA ) ) ).

thf(binary1610619414edTree_type,type,
    binary1610619414edTree: 
      !>[TA: $tType] : ( ( TA > int ) > ( binary1291135688e_Tree @ TA ) > $o ) ).

thf(binary231205461t_pred_type,type,
    binary231205461t_pred: 
      !>[TA: $tType] : ( ( TA > int ) > TA > TA > ( binary1291135688e_Tree @ TA ) > $o ) ).

thf(binary213313527le_wrm_type,type,
    binary213313527le_wrm: 
      !>[TA: $tType] : ( ( TA > int ) > ( binary1291135688e_Tree @ TA ) > ( binary1291135688e_Tree @ TA ) ) ).

thf(binary1271298290_wrmrm_type,type,
    binary1271298290_wrmrm: 
      !>[TA: $tType] : ( ( TA > int ) > ( binary1291135688e_Tree @ TA ) > ( product_prod @ ( binary1291135688e_Tree @ TA ) @ TA ) ) ).

thf(bot_bot_type,type,
    bot_bot: 
      !>[TA: $tType] : TA ).

thf(ord_less_type,type,
    ord_less: 
      !>[TA: $tType] : ( TA > TA > $o ) ).

thf(ord_less_eq_type,type,
    ord_less_eq: 
      !>[TA: $tType] : ( TA > TA > $o ) ).

thf(product_Pair_type,type,
    product_Pair: 
      !>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).

thf(product_case_prod_type,type,
    product_case_prod: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).

thf(inv_image_type,type,
    inv_image: 
      !>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TB ) ) > ( TA > TB ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).

thf(collect_type,type,
    collect: 
      !>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).

thf(member_type,type,
    member: 
      !>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).

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

thf(t1_type,type,
    t1: binary1291135688e_Tree @ a ).

thf(t2_type,type,
    t2: binary1291135688e_Tree @ a ).

thf(x_type,type,
    x: a ).

thf(240,axiom,
    ! [TA: $tType,A: set @ TA,B: TA] :
      ( ( A
        = ( bot_bot @ ( set @ TA ) ) )
     => ~ ( member @ TA @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_equals0D) ).

thf(1024,plain,
    ! [TA: $tType,A: set @ TA,B: TA] :
      ( ( A
        = ( bot_bot @ ( set @ TA ) ) )
     => ~ ( member @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(152,axiom,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ord_less_eq @ ( TA > $o )
            @ ^ [C: TA] : ( member @ TA @ C @ A )
            @ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_less__eq__set__def) ).

thf(760,plain,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ord_less_eq @ ( TA > $o )
            @ ^ [C: TA] : ( member @ TA @ C @ A )
            @ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(178,axiom,
    ! [TA: $tType,A: binary1291135688e_Tree @ TA,B: TA > int,C: binary1291135688e_Tree @ TA,D: TA] :
      ( ( ( A
          = ( binary1746293266le_Tip @ TA ) )
       => ( ( binary213313527le_wrm @ TA @ B @ ( binary210054475elle_T @ TA @ C @ D @ A ) )
          = C ) )
      & ( ( A
         != ( binary1746293266le_Tip @ TA ) )
       => ( ( binary213313527le_wrm @ TA @ B @ ( binary210054475elle_T @ TA @ C @ D @ A ) )
          = ( binary210054475elle_T @ TA @ C @ D @ ( binary213313527le_wrm @ TA @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_wrm_Osimps) ).

thf(846,plain,
    ! [TA: $tType,A: binary1291135688e_Tree @ TA,B: TA > int,C: binary1291135688e_Tree @ TA,D: TA] :
      ( ( ( A
          = ( binary1746293266le_Tip @ TA ) )
       => ( ( binary213313527le_wrm @ TA @ B @ ( binary210054475elle_T @ TA @ C @ D @ A ) )
          = C ) )
      & ( ( A
         != ( binary1746293266le_Tip @ TA ) )
       => ( ( binary213313527le_wrm @ TA @ B @ ( binary210054475elle_T @ TA @ C @ D @ A ) )
          = ( binary210054475elle_T @ TA @ C @ D @ ( binary213313527le_wrm @ TA @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(265,axiom,
    ! [TA: $tType,A: TA > int,B: binary1291135688e_Tree @ TA,C: TA,D: binary1291135688e_Tree @ TA] :
      ( ( binary1610619414edTree @ TA @ A @ ( binary210054475elle_T @ TA @ B @ C @ D ) )
      = ( ( binary1610619414edTree @ TA @ A @ B )
        & ! [E: TA] :
            ( ( member @ TA @ E @ ( binary1653327646_setOf @ TA @ B ) )
           => ( ord_less @ int @ ( A @ E ) @ ( A @ C ) ) )
        & ! [E: TA] :
            ( ( member @ TA @ E @ ( binary1653327646_setOf @ TA @ D ) )
           => ( ord_less @ int @ ( A @ C ) @ ( A @ E ) ) )
        & ( binary1610619414edTree @ TA @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_sortedTree_Osimps_I2_J) ).

thf(1083,plain,
    ! [TA: $tType,A: TA > int,B: binary1291135688e_Tree @ TA,C: TA,D: binary1291135688e_Tree @ TA] :
      ( ( binary1610619414edTree @ TA @ A @ ( binary210054475elle_T @ TA @ B @ C @ D ) )
      = ( ( binary1610619414edTree @ TA @ A @ B )
        & ! [E: TA] :
            ( ( member @ TA @ E @ ( binary1653327646_setOf @ TA @ B ) )
           => ( ord_less @ int @ ( A @ E ) @ ( A @ C ) ) )
        & ! [E: TA] :
            ( ( member @ TA @ E @ ( binary1653327646_setOf @ TA @ D ) )
           => ( ord_less @ int @ ( A @ C ) @ ( A @ E ) ) )
        & ( binary1610619414edTree @ TA @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(66,axiom,
    ord @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_13) ).

thf(468,plain,
    ord @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(45,axiom,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( collect @ TA @ A )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( A
        = ( bot_bot @ ( TA > $o ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_Collect__empty__eq__bot) ).

thf(408,plain,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( collect @ TA @ A )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( A
        = ( bot_bot @ ( TA > $o ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(150,axiom,
    ! [TA: $tType] :
      ( ( condit1037483654norder @ TA )
     => ! [A: TA,B: TA,C: TA > $o] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( C @ A )
           => ( ~ ( C @ B )
             => ? [D: TA] :
                  ( ( ord_less_eq @ TA @ A @ D )
                  & ( ord_less_eq @ TA @ D @ B )
                  & ! [E: TA] :
                      ( ( ( ord_less_eq @ TA @ A @ E )
                        & ( ord_less @ TA @ E @ D ) )
                     => ( C @ E ) )
                  & ! [E: TA] :
                      ( ! [F: TA] :
                          ( ( ( ord_less_eq @ TA @ A @ F )
                            & ( ord_less @ TA @ F @ E ) )
                         => ( C @ F ) )
                     => ( ord_less_eq @ TA @ E @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_complete__interval) ).

thf(730,plain,
    ! [TA: $tType] :
      ( ( condit1037483654norder @ TA )
     => ! [A: TA,B: TA,C: TA > $o] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( C @ A )
           => ( ~ ( C @ B )
             => ? [D: TA] :
                  ( ( ord_less_eq @ TA @ A @ D )
                  & ( ord_less_eq @ TA @ D @ B )
                  & ! [E: TA] :
                      ( ( ( ord_less_eq @ TA @ A @ E )
                        & ( ord_less @ TA @ E @ D ) )
                     => ( C @ E ) )
                  & ! [E: TA] :
                      ( ! [F: TA] :
                          ( ( ( ord_less_eq @ TA @ A @ F )
                            & ( ord_less @ TA @ F @ E ) )
                         => ( C @ F ) )
                     => ( ord_less_eq @ TA @ E @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(15,axiom,
    preorder @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_10) ).

thf(308,plain,
    preorder @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(187,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( ! [B: TA] :
            ~ ( member @ TA @ B @ A ) )
      = ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_all__not__in__conv) ).

thf(873,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( ! [B: TA] :
            ~ ( member @ TA @ B @ A ) )
      = ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(189,axiom,
    ! [TA: $tType,A: set @ TA,B: TA > $o] :
      ( ord_less_eq @ ( set @ TA )
      @ ( collect @ TA
        @ ^ [C: TA] :
            ( ( member @ TA @ C @ A )
            & ( B @ C ) ) )
      @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_Collect__restrict) ).

thf(878,plain,
    ! [TA: $tType,A: set @ TA,B: TA > $o] :
      ( ord_less_eq @ ( set @ TA )
      @ ( collect @ TA
        @ ^ [C: TA] :
            ( ( member @ TA @ C @ A )
            & ( B @ C ) ) )
      @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(131,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( ord_less @ TA @ C @ A )
           => ( ord_less @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_dual__order_Ostrict__trans) ).

thf(677,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( ord_less @ TA @ C @ A )
           => ( ord_less @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(108,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less @ TA @ A @ B )
         => ( ( ~ ( ord_less @ TA @ B @ A ) )
            = ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_antisym__conv3) ).

thf(597,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less @ TA @ A @ B )
         => ( ( ~ ( ord_less @ TA @ B @ A ) )
            = ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(85,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
         => ( B @ C ) )
     => ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_predicate1I) ).

thf(523,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
         => ( B @ C ) )
     => ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(104,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ B @ C )
         => ( C != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_pinf_I3_J) ).

thf(582,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ B @ C )
         => ( C != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(35,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less @ TB @ A @ B )
         => ( ( ord_less @ TA @ ( C @ B ) @ D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less @ TB @ E @ F )
                 => ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_order__less__subst2) ).

thf(384,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less @ TB @ A @ B )
         => ( ( ord_less @ TA @ ( C @ B ) @ D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less @ TB @ E @ F )
                 => ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(144,axiom,
    ! [TA: $tType,A: TA > int,B: TA] :
      ( ( binary1830089824insert @ TA @ A @ B @ ( binary1746293266le_Tip @ TA ) )
      = ( binary210054475elle_T @ TA @ ( binary1746293266le_Tip @ TA ) @ B @ ( binary1746293266le_Tip @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_binsert_Osimps_I1_J) ).

thf(715,plain,
    ! [TA: $tType,A: TA > int,B: TA] :
      ( ( binary1830089824insert @ TA @ A @ B @ ( binary1746293266le_Tip @ TA ) )
      = ( binary210054475elle_T @ TA @ ( binary1746293266le_Tip @ TA ) @ B @ ( binary1746293266le_Tip @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(139,axiom,
    ! [TA: $tType,A: TA > int,B: TA] :
      ( ( binary997842527remove @ TA @ A @ B @ ( binary1746293266le_Tip @ TA ) )
      = ( binary1746293266le_Tip @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_remove_Osimps_I1_J) ).

thf(698,plain,
    ! [TA: $tType,A: TA > int,B: TA] :
      ( ( binary997842527remove @ TA @ A @ B @ ( binary1746293266le_Tip @ TA ) )
      = ( binary1746293266le_Tip @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(20,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA > $o,B: product_prod @ TB @ TC,C: TA] :
      ( ( product_case_prod @ TB @ TC @ ( TA > $o ) @ A @ B @ C )
     => ~ ! [D: TB,E: TC] :
            ( ( B
              = ( product_Pair @ TB @ TC @ D @ E ) )
           => ~ ( A @ D @ E @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_case__prodE_H) ).

thf(340,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA > $o,B: product_prod @ TB @ TC,C: TA] :
      ( ( product_case_prod @ TB @ TC @ ( TA > $o ) @ A @ B @ C )
     => ~ ! [D: TB,E: TC] :
            ( ( B
              = ( product_Pair @ TB @ TC @ D @ E ) )
           => ~ ( A @ D @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(90,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ( ( ord_less_eq @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB] :
            ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_le__fun__def) ).

thf(538,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ( ( ord_less_eq @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB] :
            ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(159,axiom,
    ! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
      ( ! [C: TA,D: TB] :
          ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
         => ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
     => ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_subrelI) ).

thf(782,plain,
    ! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
      ( ! [C: TA,D: TB] :
          ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
         => ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
     => ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(192,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
      = ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_subset__empty) ).

thf(885,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
      = ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(9,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
          ( ? [E: TA] :
            ! [F: TA] :
              ( ( ord_less @ TA @ E @ F )
             => ( ( A @ F )
                = ( B @ F ) ) )
         => ( ? [E: TA] :
              ! [F: TA] :
                ( ( ord_less @ TA @ E @ F )
               => ( ( C @ F )
                  = ( D @ F ) ) )
           => ? [E: TA] :
              ! [F: TA] :
                ( ( ord_less @ TA @ E @ F )
               => ( ( ( A @ F )
                    | ( C @ F ) )
                  = ( ( B @ F )
                    | ( D @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_pinf_I2_J) ).

thf(288,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
          ( ? [E: TA] :
            ! [F: TA] :
              ( ( ord_less @ TA @ E @ F )
             => ( ( A @ F )
                = ( B @ F ) ) )
         => ( ? [E: TA] :
              ! [F: TA] :
                ( ( ord_less @ TA @ E @ F )
               => ( ( C @ F )
                  = ( D @ F ) ) )
           => ? [E: TA] :
              ! [F: TA] :
                ( ( ord_less @ TA @ E @ F )
               => ( ( ( A @ F )
                    | ( C @ F ) )
                  = ( ( B @ F )
                    | ( D @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(12,axiom,
    linorder @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Olinorder) ).

thf(301,plain,
    linorder @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(125,axiom,
    ! [TA: $tType] :
      ( ( bot_bot @ ( TA > $o ) )
      = ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_bot__empty__eq) ).

thf(651,plain,
    ! [TA: $tType] :
      ( ( bot_bot @ ( TA > $o ) )
      = ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(18,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA > TA > $o,B: TA,C: TA] :
          ( ! [D: TA,E: TA] :
              ( ( ord_less @ TA @ D @ E )
             => ( A @ D @ E ) )
         => ( ! [D: TA] : ( A @ D @ D )
           => ( ! [D: TA,E: TA] :
                  ( ( A @ E @ D )
                 => ( A @ D @ E ) )
             => ( A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_linorder__less__wlog) ).

thf(320,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA > TA > $o,B: TA,C: TA] :
          ( ! [D: TA,E: TA] :
              ( ( ord_less @ TA @ D @ E )
             => ( A @ D @ E ) )
         => ( ! [D: TA] : ( A @ D @ D )
           => ( ! [D: TA,E: TA] :
                  ( ( A @ E @ D )
                 => ( A @ D @ E ) )
             => ( A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(98,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_order__refl) ).

thf(565,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(100,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA )
        & ( ord @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( A
            = ( B @ C ) )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less_eq @ TA @ E @ F )
                 => ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_ord__eq__le__subst) ).

thf(570,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA )
        & ( ord @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( A
            = ( B @ C ) )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less_eq @ TA @ E @ F )
                 => ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(160,axiom,
    ! [TA: $tType] : ( bot @ ( set @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_8) ).

thf(785,plain,
    ! [TA: $tType] : ( bot @ ( set @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(33,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
          ( ? [E: TA] :
            ! [F: TA] :
              ( ( ord_less @ TA @ F @ E )
             => ( ( A @ F )
                = ( B @ F ) ) )
         => ( ? [E: TA] :
              ! [F: TA] :
                ( ( ord_less @ TA @ F @ E )
               => ( ( C @ F )
                  = ( D @ F ) ) )
           => ? [E: TA] :
              ! [F: TA] :
                ( ( ord_less @ TA @ F @ E )
               => ( ( ( A @ F )
                    & ( C @ F ) )
                  = ( ( B @ F )
                    & ( D @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_minf_I1_J) ).

thf(372,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
          ( ? [E: TA] :
            ! [F: TA] :
              ( ( ord_less @ TA @ F @ E )
             => ( ( A @ F )
                = ( B @ F ) ) )
         => ( ? [E: TA] :
              ! [F: TA] :
                ( ( ord_less @ TA @ F @ E )
               => ( ( C @ F )
                  = ( D @ F ) ) )
           => ? [E: TA] :
              ! [F: TA] :
                ( ( ord_less @ TA @ F @ E )
               => ( ( ( A @ F )
                    & ( C @ F ) )
                  = ( ( B @ F )
                    & ( D @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(115,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( A = B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_ord__eq__le__trans) ).

thf(619,plain,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( A = B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(21,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
      ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
     => ( ( D = B )
       => ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_ssubst__Pair__rhs) ).

thf(344,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
      ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
     => ( ( D = B )
       => ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(210,axiom,
    ! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_subset__refl) ).

thf(934,plain,
    ! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(256,axiom,
    ( ( ( t2
       != ( binary1746293266le_Tip @ a ) )
      & ( binary1610619414edTree @ a @ h @ t2 ) )
   => ( binary1610619414edTree @ a @ h @ ( binary213313527le_wrm @ a @ h @ t2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_h2) ).

thf(1059,plain,
    ( ( ( t2
       != ( binary1746293266le_Tip @ a ) )
      & ( binary1610619414edTree @ a @ h @ t2 ) )
   => ( binary1610619414edTree @ a @ h @ ( binary213313527le_wrm @ a @ h @ t2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(63,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA] :
      ( ( product_case_prod @ TB @ TA @ $o @ A @ ( product_Pair @ TB @ TA @ B @ C ) )
     => ( A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_case__prodD) ).

thf(460,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA] :
      ( ( product_case_prod @ TB @ TA @ $o @ A @ ( product_Pair @ TB @ TA @ B @ C ) )
     => ( A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(96,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TB )
     => ( ( bot_bot @ ( TA > TB ) )
        = ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_bot__apply) ).

thf(559,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TB )
     => ( ( bot_bot @ ( TA > TB ) )
        = ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(111,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( B != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_less__imp__not__eq2) ).

thf(606,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( B != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(156,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ~ ( ord_less_eq @ TA @ A @ B ) )
          = ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_not__le) ).

thf(770,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ~ ( ord_less_eq @ TA @ A @ B ) )
          = ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(206,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_psubset__subset__trans) ).

thf(924,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(77,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ C @ B )
         => ~ ( ord_less @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_minf_I7_J) ).

thf(492,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ C @ B )
         => ~ ( ord_less @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(58,axiom,
    bot @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_14) ).

thf(443,plain,
    bot @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(247,axiom,
    ! [TA: $tType] :
      ( ( dense_order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ? [C: TA] :
              ( ( ord_less @ TA @ A @ C )
              & ( ord_less @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_dense) ).

thf(1040,plain,
    ! [TA: $tType] :
      ( ( dense_order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ? [C: TA] :
              ( ( ord_less @ TA @ A @ C )
              & ( ord_less @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(116,axiom,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).

thf(623,plain,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(174,axiom,
    ! [TA: $tType] :
      ( ( ord_less @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ord_less @ ( TA > $o )
            @ ^ [C: TA] : ( member @ TA @ C @ A )
            @ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_less__set__def) ).

thf(834,plain,
    ! [TA: $tType] :
      ( ( ord_less @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ord_less @ ( TA > $o )
            @ ^ [C: TA] : ( member @ TA @ C @ A )
            @ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(22,axiom,
    ! [TA: $tType] :
      ( ( bot_bot @ ( set @ TA ) )
      = ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_bot__set__def) ).

thf(348,plain,
    ! [TA: $tType] :
      ( ( bot_bot @ ( set @ TA ) )
      = ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(165,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_subsetD) ).

thf(806,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(24,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_order_Oasym) ).

thf(353,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(171,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( ord_less @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( A != B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_order_Ostrict__iff__order) ).

thf(821,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( ord_less @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( A != B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(199,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
      = ( ! [C: TA] :
            ( ( A @ C )
           => ( B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_Collect__mono__iff) ).

thf(905,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
      = ( ! [C: TA] :
            ( ( A @ C )
           => ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(71,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB,C: TA] :
          ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
         => ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_le__funE) ).

thf(480,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB,C: TA] :
          ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
         => ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(224,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( TA > $o )
        @ ^ [C: TA] : ( member @ TA @ C @ A )
        @ ^ [C: TA] : ( member @ TA @ C @ B ) )
      = ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_pred__subset__eq) ).

thf(981,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( TA > $o )
        @ ^ [C: TA] : ( member @ TA @ C @ A )
        @ ^ [C: TA] : ( member @ TA @ C @ B ) )
      = ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(137,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
      ( ( ord_less_eq @ ( TA > TB > $o ) @ A @ B )
     => ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ A ) ) @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_Collect__case__prod__mono) ).

thf(692,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
      ( ( ord_less_eq @ ( TA > TB > $o ) @ A @ B )
     => ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ A ) ) @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(184,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_subset__antisym) ).

thf(866,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(40,axiom,
    ! [TA: $tType] :
      ( ( bot_bot @ ( set @ TA ) )
      = ( collect @ TA
        @ ^ [A: TA] : $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_empty__def) ).

thf(396,plain,
    ! [TA: $tType] :
      ( ( bot_bot @ ( set @ TA ) )
      = ( collect @ TA
        @ ^ [A: TA] : $false ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(46,axiom,
    ! [TA: $tType] : ( order @ ( set @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_6) ).

thf(411,plain,
    ! [TA: $tType] : ( order @ ( set @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(261,axiom,
    ! [TA: $tType,A: TA > int,B: binary1291135688e_Tree @ TA,C: TA,D: binary1291135688e_Tree @ TA] :
      ( ( binary1610619414edTree @ TA @ A @ ( binary210054475elle_T @ TA @ B @ C @ D ) )
     => ( binary1610619414edTree @ TA @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_sortLemmaL) ).

thf(1072,plain,
    ! [TA: $tType,A: TA > int,B: binary1291135688e_Tree @ TA,C: TA,D: binary1291135688e_Tree @ TA] :
      ( ( binary1610619414edTree @ TA @ A @ ( binary210054475elle_T @ TA @ B @ C @ D ) )
     => ( binary1610619414edTree @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(60,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_order__class_Oorder_Oantisym) ).

thf(453,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(262,axiom,
    ! [TA: $tType,A: TA > int,B: binary1291135688e_Tree @ TA,C: TA] :
      ( ( binary1610619414edTree @ TA @ A @ B )
     => ( ( binary827270440e_memb @ TA @ A @ C @ B )
        = ( member @ TA @ C @ ( binary1653327646_setOf @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_memb__spec) ).

thf(1074,plain,
    ! [TA: $tType,A: TA > int,B: binary1291135688e_Tree @ TA,C: TA] :
      ( ( binary1610619414edTree @ TA @ A @ B )
     => ( ( binary827270440e_memb @ TA @ A @ C @ B )
        = ( member @ TA @ C @ ( binary1653327646_setOf @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(57,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( B = C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_ord__le__eq__trans) ).

thf(439,plain,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( B = C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(93,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA )
        & ( ord @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( A
            = ( B @ C ) )
         => ( ( ord_less @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less @ TA @ E @ F )
                 => ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_ord__eq__less__subst) ).

thf(546,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA )
        & ( ord @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( A
            = ( B @ C ) )
         => ( ( ord_less @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less @ TA @ E @ F )
                 => ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(34,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ B )
         => ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less_eq @ TB @ E @ F )
                 => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_order__subst2) ).

thf(381,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ B )
         => ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less_eq @ TB @ E @ F )
                 => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(30,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_less__asym) ).

thf(366,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(259,axiom,
    ! [TA: $tType,A: TA > int,B: binary1291135688e_Tree @ TA,C: TA] :
      ( ( binary1610619414edTree @ TA @ A @ B )
     => ( binary1610619414edTree @ TA @ A @ ( binary1830089824insert @ TA @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_binsert__sorted) ).

thf(1067,plain,
    ! [TA: $tType,A: TA > int,B: binary1291135688e_Tree @ TA,C: TA] :
      ( ( binary1610619414edTree @ TA @ A @ B )
     => ( binary1610619414edTree @ TA @ A @ ( binary1830089824insert @ TA @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(250,axiom,
    ! [TA: $tType] :
      ( ( dense_linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ! [C: TA] :
              ( ( ord_less @ TA @ C @ A )
             => ( ord_less_eq @ TA @ C @ B ) )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_dense__le) ).

thf(1047,plain,
    ! [TA: $tType] :
      ( ( dense_linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ! [C: TA] :
              ( ( ord_less @ TA @ C @ A )
             => ( ord_less_eq @ TA @ C @ B ) )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(239,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ~ ( ord_less @ TA @ A @ B ) )
          = ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_not__less) ).

thf(1021,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ~ ( ord_less @ TA @ A @ B ) )
          = ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(13,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( A != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_less__imp__not__eq) ).

thf(302,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(38,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB] :
          ( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
         => ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_le__funI) ).

thf(392,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB] :
          ( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
         => ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(10,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_order__trans) ).

thf(297,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(51,axiom,
    ! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
      ( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
        = ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_pred__equals__eq2) ).

thf(424,plain,
    ! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
      ( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
        = ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(118,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: TB > TA > $o] :
      ( ( A @ B @ C )
     => ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ D )
       => ( D @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_rev__predicate2D) ).

thf(630,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: TB > TA > $o] :
      ( ( A @ B @ C )
     => ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ D )
       => ( D @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(53,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ~ ( ord_less @ TA @ A @ B ) )
          = ( ( ord_less @ TA @ B @ A )
            | ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_not__less__iff__gr__or__eq) ).

thf(429,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ~ ( ord_less @ TA @ A @ B ) )
          = ( ( ord_less @ TA @ B @ A )
            | ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(5,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
      ( ( product_case_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
      = ( A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_case__prod__conv) ).

thf(275,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
      ( ( product_case_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
      = ( A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(203,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( ord_less_eq @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less @ TA @ A @ B )
              | ( B = A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_dual__order_Oorder__iff__strict) ).

thf(916,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( ord_less_eq @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less @ TA @ A @ B )
              | ( B = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(73,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA,C: $o] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( ord_less @ TA @ B @ A )
           => C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_less__imp__triv) ).

thf(484,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA,C: $o] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( ord_less @ TA @ B @ A )
           => C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(179,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less @ TB @ A @ B )
         => ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less @ TB @ E @ F )
                 => ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_order__less__le__subst2) ).

thf(852,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less @ TB @ A @ B )
         => ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less @ TB @ E @ F )
                 => ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(84,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA] :
        ? [B: TB] :
        ! [C: TB] :
          ( ( ord_less @ TB @ B @ C )
         => ( A = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_pinf_I11_J) ).

thf(522,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(142,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ! [C: TA] :
          ( ( member @ TA @ C @ A )
         => ( member @ TA @ C @ B ) )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_subsetI) ).

thf(710,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ! [C: TA] :
          ( ( member @ TA @ C @ A )
         => ( member @ TA @ C @ B ) )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(61,axiom,
    ! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
      ( ( product_case_prod @ TA @ TB @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_case__prod__Pair__iden) ).

thf(456,plain,
    ! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
      ( ( product_case_prod @ TA @ TB @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(8,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TB )
     => ( ( bot_bot @ ( TA > TB ) )
        = ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_bot__fun__def) ).

thf(285,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TB )
     => ( ( bot_bot @ ( TA > TB ) )
        = ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(238,axiom,
    ! [TA: $tType] :
      ( ( dense_linorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ! [D: TA] :
                ( ( ord_less @ TA @ A @ D )
               => ( ( ord_less @ TA @ D @ B )
                 => ( ord_less_eq @ TA @ D @ C ) ) )
           => ( ord_less_eq @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_dense__le__bounded) ).

thf(1017,plain,
    ! [TA: $tType] :
      ( ( dense_linorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ! [D: TA] :
                ( ( ord_less @ TA @ A @ D )
               => ( ( ord_less @ TA @ D @ B )
                 => ( ord_less_eq @ TA @ D @ C ) ) )
           => ( ord_less_eq @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(258,axiom,
    ! [TA: $tType] :
      ( ( binary231205461t_pred @ TA )
      = ( ^ [A: TA > int,B: TA,C: TA,D: binary1291135688e_Tree @ TA] :
            ( ( ( binary1610619414edTree @ TA @ A @ D )
              & ( member @ TA @ B @ ( binary1653327646_setOf @ TA @ D ) )
              & ( member @ TA @ C @ ( binary1653327646_setOf @ TA @ D ) )
              & ( ( A @ B )
                = ( A @ C ) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_sorted__distinct__pred__def) ).

thf(1064,plain,
    ! [TA: $tType] :
      ( ( binary231205461t_pred @ TA )
      = ( ^ [A: TA > int,B: TA,C: TA,D: binary1291135688e_Tree @ TA] :
            ( ( ( binary1610619414edTree @ TA @ A @ D )
              & ( member @ TA @ B @ ( binary1653327646_setOf @ TA @ D ) )
              & ( member @ TA @ C @ ( binary1653327646_setOf @ TA @ D ) )
              & ( ( A @ B )
                = ( A @ C ) ) )
           => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(148,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_dual__order_Ostrict__implies__order) ).

thf(725,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(43,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( ord_less @ TA @ B @ C )
           => ( ord_less @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_less__trans) ).

thf(403,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( ord_less @ TA @ B @ C )
           => ( ord_less @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(234,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
          | ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_le__less__linear) ).

thf(1006,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
          | ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(185,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA,D: TA > $o] :
      ( ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B
          @ ( collect @ TA
            @ ^ [E: TA] :
                ( ( member @ TA @ E @ C )
                & ( D @ E ) ) ) )
       => ( D @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_prop__restrict) ).

thf(869,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA,D: TA > $o] :
      ( ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B
          @ ( collect @ TA
            @ ^ [E: TA] :
                ( ( member @ TA @ E @ C )
                & ( D @ E ) ) ) )
       => ( D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(112,axiom,
    ! [TA: $tType,TB: $tType,A: $o,B: TA > TB > $o] :
      ( ( product_case_prod @ TA @ TB @ $o
        @ ^ [C: TA,D: TB] :
            ( A
            & ( B @ C @ D ) ) )
      = ( ^ [C: product_prod @ TA @ TB] :
            ( A
            & ( product_case_prod @ TA @ TB @ $o @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_split__part) ).

thf(610,plain,
    ! [TA: $tType,TB: $tType,A: $o,B: TA > TB > $o] :
      ( ( product_case_prod @ TA @ TB @ $o
        @ ^ [C: TA,D: TB] :
            ( A
            & ( B @ C @ D ) ) )
      = ( ^ [C: product_prod @ TA @ TB] :
            ( A
            & ( product_case_prod @ TA @ TB @ $o @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(227,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: ( binary1291135688e_Tree @ TB ) > TB > ( binary1291135688e_Tree @ TB ) > TA > TA > TA] :
      ( ( binary1929596613c_Tree @ TA @ TB @ A @ B @ ( binary1746293266le_Tip @ TB ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_Tree_Osimps_I6_J) ).

thf(989,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: ( binary1291135688e_Tree @ TB ) > TB > ( binary1291135688e_Tree @ TB ) > TA > TA > TA] :
      ( ( binary1929596613c_Tree @ TA @ TB @ A @ B @ ( binary1746293266le_Tip @ TB ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(83,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( A = B )
          | ~ ( ord_less_eq @ TA @ A @ B )
          | ~ ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_verit__la__disequality) ).

thf(519,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( A = B )
          | ~ ( ord_less_eq @ TA @ A @ B )
          | ~ ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(102,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ B @ C )
         => ( ord_less @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_pinf_I7_J) ).

thf(578,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ B @ C )
         => ( ord_less @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(68,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
         => ( ~ ( ord_less @ TA @ A @ B )
           => ( ord_less @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_neqE) ).

thf(471,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
         => ( ~ ( ord_less @ TA @ A @ B )
           => ( ord_less @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(241,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_psubsetD) ).

thf(1028,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(75,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA] :
          ~ ( ord_less @ TA @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_verit__comp__simplify1_I1_J) ).

thf(488,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA] :
          ~ ( ord_less @ TA @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(86,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( A = B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_eq__refl) ).

thf(526,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( A = B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(121,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TB,B: TC > TB > TA > $o,C: TA] :
      ( ! [D: TC,E: TB] :
          ( ( ( product_Pair @ TC @ TB @ D @ E )
            = A )
         => ( B @ D @ E @ C ) )
     => ( product_case_prod @ TC @ TB @ ( TA > $o ) @ B @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_case__prodI2_H) ).

thf(637,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TB,B: TC > TB > TA > $o,C: TA] :
      ( ! [D: TC,E: TB] :
          ( ( ( product_Pair @ TC @ TB @ D @ E )
            = A )
         => ( B @ D @ E @ C ) )
     => ( product_case_prod @ TC @ TB @ ( TA > $o ) @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(106,axiom,
    ! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: TA > TB > $o] :
      ( ! [C: TA,D: TB] :
          ( ( A
            = ( product_Pair @ TA @ TB @ C @ D ) )
         => ( B @ C @ D ) )
     => ( product_case_prod @ TA @ TB @ $o @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_case__prodI2) ).

thf(590,plain,
    ! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: TA > TB > $o] :
      ( ! [C: TA,D: TB] :
          ( ( A
            = ( product_Pair @ TA @ TB @ C @ D ) )
         => ( B @ C @ D ) )
     => ( product_case_prod @ TA @ TB @ $o @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(132,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ A )
           => ( ord_less_eq @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_dual__order_Otrans) ).

thf(679,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ A )
           => ( ord_less_eq @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(220,axiom,
    ! [TA: $tType] :
      ( ( no_bot @ TA )
     => ! [A: TA] :
        ? [B: TA] : ( ord_less @ TA @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_lt__ex) ).

thf(970,plain,
    ! [TA: $tType] :
      ( ( no_bot @ TA )
     => ! [A: TA] :
        ? [B: TA] : ( ord_less @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(175,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ( ( ord_less @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ~ ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_less__le__not__le) ).

thf(837,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ( ( ord_less @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ~ ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(230,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less @ ( set @ TA ) @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_psubset__imp__subset) ).

thf(997,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less @ ( set @ TA ) @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(140,axiom,
    ! [TA: $tType,A: binary1291135688e_Tree @ TA,B: TA,C: binary1291135688e_Tree @ TA] :
      ( ( binary1746293266le_Tip @ TA )
     != ( binary210054475elle_T @ TA @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Tree_Odistinct_I1_J) ).

thf(701,plain,
    ! [TA: $tType,A: binary1291135688e_Tree @ TA,B: TA,C: binary1291135688e_Tree @ TA] :
      ( ( binary1746293266le_Tip @ TA )
     != ( binary210054475elle_T @ TA @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(126,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( A = B )
         => ( ( ord_less @ TA @ B @ C )
           => ( ord_less @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_ord__eq__less__trans) ).

thf(654,plain,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( A = B )
         => ( ( ord_less @ TA @ B @ C )
           => ( ord_less @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(251,axiom,
    ! [TA: $tType,A: TA > int] : ( binary1610619414edTree @ TA @ A @ ( binary1746293266le_Tip @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_sortedTree_Osimps_I1_J) ).

thf(1050,plain,
    ! [TA: $tType,A: TA > int] : ( binary1610619414edTree @ TA @ A @ ( binary1746293266le_Tip @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(232,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ B @ C )
         => ~ ( ord_less_eq @ TA @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_pinf_I6_J) ).

thf(1002,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ B @ C )
         => ~ ( ord_less_eq @ TA @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(225,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ B @ C )
         => ( ord_less_eq @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_pinf_I8_J) ).

thf(984,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ B @ C )
         => ( ord_less_eq @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(201,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: ( binary1291135688e_Tree @ TA ) > TA > ( binary1291135688e_Tree @ TA ) > TB > TB > TB,C: binary1291135688e_Tree @ TA,D: TA,E: binary1291135688e_Tree @ TA] :
      ( ( binary1929596613c_Tree @ TB @ TA @ A @ B @ ( binary210054475elle_T @ TA @ C @ D @ E ) )
      = ( B @ C @ D @ E @ ( binary1929596613c_Tree @ TB @ TA @ A @ B @ C ) @ ( binary1929596613c_Tree @ TB @ TA @ A @ B @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_Tree_Osimps_I7_J) ).

thf(911,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: ( binary1291135688e_Tree @ TA ) > TA > ( binary1291135688e_Tree @ TA ) > TB > TB > TB,C: binary1291135688e_Tree @ TA,D: TA,E: binary1291135688e_Tree @ TA] :
      ( ( binary1929596613c_Tree @ TB @ TA @ A @ B @ ( binary210054475elle_T @ TA @ C @ D @ E ) )
      = ( B @ C @ D @ E @ ( binary1929596613c_Tree @ TB @ TA @ A @ B @ C ) @ ( binary1929596613c_Tree @ TB @ TA @ A @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(1,conjecture,
    binary1610619414edTree @ a @ h @ t1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( binary1610619414edTree @ a @ h @ t1 ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(266,plain,
    ~ ( binary1610619414edTree @ a @ h @ t1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(27,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TB > TA > ( set @ TC ),C: TB,D: TA] :
      ( ( member @ TC @ A @ ( B @ C @ D ) )
     => ( member @ TC @ A @ ( product_case_prod @ TB @ TA @ ( set @ TC ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_mem__case__prodI) ).

thf(360,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TB > TA > ( set @ TC ),C: TB,D: TA] :
      ( ( member @ TC @ A @ ( B @ C @ D ) )
     => ( member @ TC @ A @ ( product_case_prod @ TB @ TA @ ( set @ TC ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(91,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ TB ) > TC] :
      ( ( product_case_prod @ TA @ TB @ TC
        @ ^ [B: TA,C: TB] : ( A @ ( product_Pair @ TA @ TB @ B @ C ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_case__prod__eta) ).

thf(541,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ TB ) > TC] :
      ( ( product_case_prod @ TA @ TB @ TC
        @ ^ [B: TA,C: TB] : ( A @ ( product_Pair @ TA @ TB @ B @ C ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(244,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_less__imp__le) ).

thf(1035,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(87,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_dual__order_Oasym) ).

thf(530,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(207,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ( ( ord_less @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB] :
              ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
              & ~ ( ord_less_eq @ ( TA > TB ) @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_less__fun__def) ).

thf(926,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ( ( ord_less @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB] :
              ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
              & ~ ( ord_less_eq @ ( TA > TB ) @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(154,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
         => ( B @ C ) )
     => ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Collect__mono) ).

thf(765,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
         => ( B @ C ) )
     => ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(254,axiom,
    ! [TA: $tType,A: TA > int,B: binary1291135688e_Tree @ TA,C: TA,D: binary1291135688e_Tree @ TA] :
      ( ( binary1610619414edTree @ TA @ A @ ( binary210054475elle_T @ TA @ B @ C @ D ) )
     => ( binary1610619414edTree @ TA @ A @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_sortLemmaR) ).

thf(1054,plain,
    ! [TA: $tType,A: TA > int,B: binary1291135688e_Tree @ TA,C: TA,D: binary1291135688e_Tree @ TA] :
      ( ( binary1610619414edTree @ TA @ A @ ( binary210054475elle_T @ TA @ B @ C @ D ) )
     => ( binary1610619414edTree @ TA @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(157,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
         => ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_equalityE) ).

thf(773,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
         => ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(105,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA > $o,B: product_prod @ TB @ TA] :
      ( ( product_case_prod @ TB @ TA @ $o @ A @ B )
     => ~ ! [C: TB,D: TA] :
            ( ( B
              = ( product_Pair @ TB @ TA @ C @ D ) )
           => ~ ( A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_case__prodE) ).

thf(586,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA > $o,B: product_prod @ TB @ TA] :
      ( ( product_case_prod @ TB @ TA @ $o @ A @ B )
     => ~ ! [C: TB,D: TA] :
            ( ( B
              = ( product_Pair @ TB @ TA @ C @ D ) )
           => ~ ( A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(145,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_order_Ostrict__trans2) ).

thf(718,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(193,axiom,
    ! [TA: $tType,A: binary1291135688e_Tree @ TA,B: TA,C: binary1291135688e_Tree @ TA,D: binary1291135688e_Tree @ TA,E: TA,F: binary1291135688e_Tree @ TA] :
      ( ( ( binary210054475elle_T @ TA @ A @ B @ C )
        = ( binary210054475elle_T @ TA @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_Tree_Oinject) ).

thf(888,plain,
    ! [TA: $tType,A: binary1291135688e_Tree @ TA,B: TA,C: binary1291135688e_Tree @ TA,D: binary1291135688e_Tree @ TA,E: TA,F: binary1291135688e_Tree @ TA] :
      ( ( ( binary210054475elle_T @ TA @ A @ B @ C )
        = ( binary210054475elle_T @ TA @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(172,axiom,
    ! [TA: $tType,A: TA > int,B: TA,C: TA,D: binary1291135688e_Tree @ TA,E: binary1291135688e_Tree @ TA] :
      ( ( ( ord_less @ int @ ( A @ B ) @ ( A @ C ) )
       => ( ( binary1830089824insert @ TA @ A @ B @ ( binary210054475elle_T @ TA @ D @ C @ E ) )
          = ( binary210054475elle_T @ TA @ ( binary1830089824insert @ TA @ A @ B @ D ) @ C @ E ) ) )
      & ( ~ ( ord_less @ int @ ( A @ B ) @ ( A @ C ) )
       => ( ( ( ord_less @ int @ ( A @ C ) @ ( A @ B ) )
           => ( ( binary1830089824insert @ TA @ A @ B @ ( binary210054475elle_T @ TA @ D @ C @ E ) )
              = ( binary210054475elle_T @ TA @ D @ C @ ( binary1830089824insert @ TA @ A @ B @ E ) ) ) )
          & ( ~ ( ord_less @ int @ ( A @ C ) @ ( A @ B ) )
           => ( ( binary1830089824insert @ TA @ A @ B @ ( binary210054475elle_T @ TA @ D @ C @ E ) )
              = ( binary210054475elle_T @ TA @ D @ B @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_binsert_Osimps_I2_J) ).

thf(824,plain,
    ! [TA: $tType,A: TA > int,B: TA,C: TA,D: binary1291135688e_Tree @ TA,E: binary1291135688e_Tree @ TA] :
      ( ( ( ord_less @ int @ ( A @ B ) @ ( A @ C ) )
       => ( ( binary1830089824insert @ TA @ A @ B @ ( binary210054475elle_T @ TA @ D @ C @ E ) )
          = ( binary210054475elle_T @ TA @ ( binary1830089824insert @ TA @ A @ B @ D ) @ C @ E ) ) )
      & ( ~ ( ord_less @ int @ ( A @ B ) @ ( A @ C ) )
       => ( ( ( ord_less @ int @ ( A @ C ) @ ( A @ B ) )
           => ( ( binary1830089824insert @ TA @ A @ B @ ( binary210054475elle_T @ TA @ D @ C @ E ) )
              = ( binary210054475elle_T @ TA @ D @ C @ ( binary1830089824insert @ TA @ A @ B @ E ) ) ) )
          & ( ~ ( ord_less @ int @ ( A @ C ) @ ( A @ B ) )
           => ( ( binary1830089824insert @ TA @ A @ B @ ( binary210054475elle_T @ TA @ D @ C @ E ) )
              = ( binary210054475elle_T @ TA @ D @ B @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(59,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
          ( ? [E: TA] :
            ! [F: TA] :
              ( ( ord_less @ TA @ F @ E )
             => ( ( A @ F )
                = ( B @ F ) ) )
         => ( ? [E: TA] :
              ! [F: TA] :
                ( ( ord_less @ TA @ F @ E )
               => ( ( C @ F )
                  = ( D @ F ) ) )
           => ? [E: TA] :
              ! [F: TA] :
                ( ( ord_less @ TA @ F @ E )
               => ( ( ( A @ F )
                    | ( C @ F ) )
                  = ( ( B @ F )
                    | ( D @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_minf_I2_J) ).

thf(444,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
          ( ? [E: TA] :
            ! [F: TA] :
              ( ( ord_less @ TA @ F @ E )
             => ( ( A @ F )
                = ( B @ F ) ) )
         => ( ? [E: TA] :
              ! [F: TA] :
                ( ( ord_less @ TA @ F @ E )
               => ( ( C @ F )
                  = ( D @ F ) ) )
           => ? [E: TA] :
              ! [F: TA] :
                ( ( ord_less @ TA @ F @ E )
               => ( ( ( A @ F )
                    | ( C @ F ) )
                  = ( ( B @ F )
                    | ( D @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(138,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_equalityD2) ).

thf(694,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(177,axiom,
    ! [TA: $tType] :
      ( ( dense_linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ! [C: TA] :
              ( ( ord_less @ TA @ A @ C )
             => ( ord_less_eq @ TA @ B @ C ) )
         => ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_dense__ge) ).

thf(843,plain,
    ! [TA: $tType] :
      ( ( dense_linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ! [C: TA] :
              ( ( ord_less @ TA @ A @ C )
             => ( ord_less_eq @ TA @ B @ C ) )
         => ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(101,axiom,
    preorder @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Opreorder_1) ).

thf(577,plain,
    preorder @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(47,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB,C: TA] :
          ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
         => ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_le__funD) ).

thf(413,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB,C: TA] :
          ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
         => ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(97,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: $o,D: TB,E: TA] :
      ( ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
        & C )
     => ( C
        & ( ( A @ D @ E )
         => ( B @ D @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_predicate2D__conj) ).

thf(562,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: $o,D: TB,E: TA] :
      ( ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
        & C )
     => ( C
        & ( ( A @ D @ E )
         => ( B @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(222,axiom,
    ! [TA: $tType,A: binary1291135688e_Tree @ TA] :
      ( ( A
       != ( binary1746293266le_Tip @ TA ) )
     => ~ ! [B: binary1291135688e_Tree @ TA,C: TA,D: binary1291135688e_Tree @ TA] :
            ( A
           != ( binary210054475elle_T @ TA @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Tree_Oexhaust) ).

thf(975,plain,
    ! [TA: $tType,A: binary1291135688e_Tree @ TA] :
      ( ( A
       != ( binary1746293266le_Tip @ TA ) )
     => ~ ! [B: binary1291135688e_Tree @ TA,C: TA,D: binary1291135688e_Tree @ TA] :
            ( A
           != ( binary210054475elle_T @ TA @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(122,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_antisym) ).

thf(641,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(37,axiom,
    ord @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oord_3) ).

thf(391,plain,
    ord @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(211,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( A != B )
           => ( ord_less @ TA @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_le__neq__trans) ).

thf(936,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( A != B )
           => ( ord_less @ TA @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(17,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA )
        & ( ord @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ B )
         => ( ( ( C @ B )
              = D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less_eq @ TB @ E @ F )
                 => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_ord__le__eq__subst) ).

thf(313,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA )
        & ( ord @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ B )
         => ( ( ( C @ B )
              = D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less_eq @ TB @ E @ F )
                 => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(161,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( A != B )
       => ( ord_less @ ( set @ TA ) @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_psubsetI) ).

thf(787,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( A != B )
       => ( ord_less @ ( set @ TA ) @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(204,axiom,
    ! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ A
        @ ( collect @ TA
          @ ^ [D: TA] :
              ( ( B @ D )
              & ( C @ D ) ) ) )
      = ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
        & ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_conj__subset__def) ).

thf(919,plain,
    ! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ A
        @ ( collect @ TA
          @ ^ [D: TA] :
              ( ( B @ D )
              & ( C @ D ) ) ) )
      = ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
        & ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(141,axiom,
    ! [TA: $tType,A: binary1291135688e_Tree @ TA,B: TA > int,C: binary1291135688e_Tree @ TA,D: TA] :
      ( ( ( A
          = ( binary1746293266le_Tip @ TA ) )
       => ( ( binary576689334lle_rm @ TA @ B @ ( binary210054475elle_T @ TA @ C @ D @ A ) )
          = D ) )
      & ( ( A
         != ( binary1746293266le_Tip @ TA ) )
       => ( ( binary576689334lle_rm @ TA @ B @ ( binary210054475elle_T @ TA @ C @ D @ A ) )
          = ( binary576689334lle_rm @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_rm_Osimps) ).

thf(704,plain,
    ! [TA: $tType,A: binary1291135688e_Tree @ TA,B: TA > int,C: binary1291135688e_Tree @ TA,D: TA] :
      ( ( ( A
          = ( binary1746293266le_Tip @ TA ) )
       => ( ( binary576689334lle_rm @ TA @ B @ ( binary210054475elle_T @ TA @ C @ D @ A ) )
          = D ) )
      & ( ( A
         != ( binary1746293266le_Tip @ TA ) )
       => ( ( binary576689334lle_rm @ TA @ B @ ( binary210054475elle_T @ TA @ C @ D @ A ) )
          = ( binary576689334lle_rm @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(129,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( B != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_dual__order_Ostrict__implies__not__eq) ).

thf(672,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( B != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(143,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_subset__trans) ).

thf(713,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(80,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ C @ B )
         => ( C != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_minf_I4_J) ).

thf(498,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ C @ B )
         => ( C != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(197,axiom,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
          ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( member @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_subset__iff) ).

thf(900,plain,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
          ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( member @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(173,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ~ ( ord_less_eq @ TA @ A @ B ) )
          = ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_verit__comp__simplify1_I3_J) ).

thf(831,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ~ ( ord_less_eq @ TA @ A @ B ) )
          = ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(133,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( A != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_less__imp__neq) ).

thf(681,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(4,axiom,
    linorder @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_11) ).

thf(274,plain,
    linorder @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(236,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( ord_less @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( B != A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_dual__order_Ostrict__iff__order) ).

thf(1011,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( ord_less @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( B != A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(49,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > TC,B: ( product_prod @ TA @ TB ) > TC] :
      ( ! [C: TA,D: TB] :
          ( ( A @ C @ D )
          = ( B @ ( product_Pair @ TA @ TB @ C @ D ) ) )
     => ( ( product_case_prod @ TA @ TB @ TC @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_cond__case__prod__eta) ).

thf(419,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > TC,B: ( product_prod @ TA @ TB ) > TC] :
      ( ! [C: TA,D: TB] :
          ( ( A @ C @ D )
          = ( B @ ( product_Pair @ TA @ TB @ C @ D ) ) )
     => ( ( product_case_prod @ TA @ TB @ TC @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(28,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( ord_less @ TA @ B @ C )
           => ( ord_less @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_order_Ostrict__trans) ).

thf(362,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( ord_less @ TA @ B @ C )
           => ( ord_less @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(99,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ B @ A )
              & ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_dual__order_Oeq__iff) ).

thf(567,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ B @ A )
              & ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(190,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( ord_less_eq @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less @ TA @ A @ B )
              | ( A = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_le__less) ).

thf(880,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( ord_less_eq @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less @ TA @ A @ B )
              | ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(248,axiom,
    no_top @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Ono__top) ).

thf(1043,plain,
    no_top @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(55,axiom,
    ! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
      ( ( ord_less_eq @ ( TA > TB > $o )
        @ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
        @ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
      = ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_pred__subset__eq2) ).

thf(434,plain,
    ! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
      ( ( ord_less_eq @ ( TA > TB > $o )
        @ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
        @ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
      = ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(70,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
      ( ! [C: TA,D: TB] :
          ( ( A @ C @ D )
         => ( B @ C @ D ) )
     => ( ord_less_eq @ ( TA > TB > $o ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_predicate2I) ).

thf(477,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
      ( ! [C: TA,D: TB] :
          ( ( A @ C @ D )
         => ( B @ C @ D ) )
     => ( ord_less_eq @ ( TA > TB > $o ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(151,axiom,
    ! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_empty__subsetI) ).

thf(758,plain,
    ! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(181,axiom,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_emptyE) ).

thf(858,plain,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(89,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less @ TA @ A @ B )
         => ( ( A != B )
           => ( ord_less @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_linorder__cases) ).

thf(535,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less @ TA @ A @ B )
         => ( ( A != B )
           => ( ord_less @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(169,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ A )
           => ( ord_less @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_dual__order_Ostrict__trans2) ).

thf(816,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ A )
           => ( ord_less @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(107,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
            = ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_antisym__conv) ).

thf(594,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
            = ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(195,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_less__le__trans) ).

thf(895,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(218,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ! [E: TA] :
            ( ( member @ TA @ E @ A )
           => ( ( C @ E )
             => ( D @ E ) ) )
       => ( ord_less_eq @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [E: TA] :
                ( ( member @ TA @ E @ A )
                & ( C @ E ) ) )
          @ ( collect @ TA
            @ ^ [E: TA] :
                ( ( member @ TA @ E @ B )
                & ( D @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_subset__CollectI) ).

thf(964,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ! [E: TA] :
            ( ( member @ TA @ E @ A )
           => ( ( C @ E )
             => ( D @ E ) ) )
       => ( ord_less_eq @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [E: TA] :
                ( ( member @ TA @ E @ A )
                & ( C @ E ) ) )
          @ ( collect @ TA
            @ ^ [E: TA] :
                ( ( member @ TA @ E @ B )
                & ( D @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(117,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > $o,B: TC > TA > TB,C: product_prod @ TC @ TA] :
      ( ( A @ ( product_case_prod @ TC @ TA @ TB @ B @ C ) )
     => ~ ! [D: TC,E: TA] :
            ( ( C
              = ( product_Pair @ TC @ TA @ D @ E ) )
           => ~ ( A @ ( B @ D @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_case__prodE2) ).

thf(626,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > $o,B: TC > TA > TB,C: product_prod @ TC @ TA] :
      ( ( A @ ( product_case_prod @ TC @ TA @ TB @ B @ C ) )
     => ~ ! [D: TC,E: TA] :
            ( ( C
              = ( product_Pair @ TC @ TA @ D @ E ) )
           => ~ ( A @ ( B @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(214,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less @ TA @ A @ B )
            | ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_le__imp__less__or__eq) ).

thf(943,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less @ TA @ A @ B )
            | ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(64,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_dual__order_Oantisym) ).

thf(462,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(167,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ! [B: TA] :
          ~ ( member @ TA @ B @ A )
     => ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_subset__emptyI) ).

thf(811,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ! [B: TA] :
          ~ ( member @ TA @ B @ A )
     => ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(36,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ C @ B )
         => ( C != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_minf_I3_J) ).

thf(387,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ C @ B )
         => ( C != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(78,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA] :
        ? [B: TB] :
        ! [C: TB] :
          ( ( ord_less @ TB @ C @ B )
         => ( A = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_minf_I11_J) ).

thf(494,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(264,axiom,
    ! [TA: $tType,A: binary1291135688e_Tree @ TA,B: TA > int] :
      ( ( ( A
         != ( binary1746293266le_Tip @ TA ) )
        & ( binary1610619414edTree @ TA @ B @ A ) )
     => ( member @ TA @ ( binary576689334lle_rm @ TA @ B @ A ) @ ( binary1653327646_setOf @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_rm__set) ).

thf(1080,plain,
    ! [TA: $tType,A: binary1291135688e_Tree @ TA,B: TA > int] :
      ( ( ( A
         != ( binary1746293266le_Tip @ TA ) )
        & ( binary1610619414edTree @ TA @ B @ A ) )
     => ( member @ TA @ ( binary576689334lle_rm @ TA @ B @ A ) @ ( binary1653327646_setOf @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(134,axiom,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( collect @ TA @ A )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ! [B: TA] :
            ~ ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Collect__empty__eq) ).

thf(685,plain,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( collect @ TA @ A )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ! [B: TA] :
            ~ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(41,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TA )
     => ( bot @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).

thf(399,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TA )
     => ( bot @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(216,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less @ TA @ A @ B )
         => ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_leI) ).

thf(959,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less @ TA @ A @ B )
         => ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(155,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_order_Ostrict__implies__order) ).

thf(768,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(249,axiom,
    ! [TA: $tType] :
      ( ( ord_less @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
            & ( A != B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_psubset__eq) ).

thf(1044,plain,
    ! [TA: $tType] :
      ( ( ord_less @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
            & ( A != B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(6,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( B = C )
           => ( ord_less @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_ord__less__eq__trans) ).

thf(278,plain,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ( B = C )
           => ( ord_less @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(158,axiom,
    ! [TA: $tType] :
      ( ( no_top @ TA )
     => ! [A: TA] :
        ? [B: TA] : ( ord_less @ TA @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_gt__ex) ).

thf(780,plain,
    ! [TA: $tType] :
      ( ( no_top @ TA )
     => ! [A: TA] :
        ? [B: TA] : ( ord_less @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(191,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less @ TA @ B @ C )
           => ( ord_less @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_le__less__trans) ).

thf(883,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less @ TA @ B @ C )
           => ( ord_less @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(11,axiom,
    ! [TA: $tType] : ( preorder @ ( set @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_5) ).

thf(299,plain,
    ! [TA: $tType] : ( preorder @ ( set @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(3,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA )
        & ( ord @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less @ TB @ A @ B )
         => ( ( ( C @ B )
              = D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less @ TB @ E @ F )
                 => ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_ord__less__eq__subst) ).

thf(267,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA )
        & ( ord @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less @ TB @ A @ B )
         => ( ( ( C @ B )
              = D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less @ TB @ E @ F )
                 => ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(205,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less @ ( set @ TA ) @ B @ C )
       => ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_subset__psubset__trans) ).

thf(922,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less @ ( set @ TA ) @ B @ C )
       => ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(127,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
          ( ? [E: TA] :
            ! [F: TA] :
              ( ( ord_less @ TA @ E @ F )
             => ( ( A @ F )
                = ( B @ F ) ) )
         => ( ? [E: TA] :
              ! [F: TA] :
                ( ( ord_less @ TA @ E @ F )
               => ( ( C @ F )
                  = ( D @ F ) ) )
           => ? [E: TA] :
              ! [F: TA] :
                ( ( ord_less @ TA @ E @ F )
               => ( ( ( A @ F )
                    & ( C @ F ) )
                  = ( ( B @ F )
                    & ( D @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_pinf_I1_J) ).

thf(658,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
          ( ? [E: TA] :
            ! [F: TA] :
              ( ( ord_less @ TA @ E @ F )
             => ( ( A @ F )
                = ( B @ F ) ) )
         => ( ? [E: TA] :
              ! [F: TA] :
                ( ( ord_less @ TA @ E @ F )
               => ( ( C @ F )
                  = ( D @ F ) ) )
           => ? [E: TA] :
              ! [F: TA] :
                ( ( ord_less @ TA @ E @ F )
               => ( ( ( A @ F )
                    & ( C @ F ) )
                  = ( ( B @ F )
                    & ( D @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(39,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ C @ B )
         => ( ord_less @ TA @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_minf_I5_J) ).

thf(394,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ C @ B )
         => ( ord_less @ TA @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(226,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ~ ( ord_less @ TA @ A @ B ) )
            = ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_antisym__conv2) ).

thf(986,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ~ ( ord_less @ TA @ A @ B ) )
            = ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(14,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_less__imp__not__less) ).

thf(306,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(147,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ ( B @ C ) )
         => ( ( ord_less @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less @ TA @ E @ F )
                 => ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_order__le__less__subst1) ).

thf(722,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ ( B @ C ) )
         => ( ( ord_less @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less @ TA @ E @ F )
                 => ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(76,axiom,
    ! [TA: $tType,A: TA > TA > $o] :
      ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA )
      @ ^ [B: TA,C: TA] :
          ( ( A @ B @ C )
          | ( B = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_eq__subset) ).

thf(490,plain,
    ! [TA: $tType,A: TA > TA > $o] :
      ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA )
      @ ^ [B: TA,C: TA] :
          ( ( A @ B @ C )
          | ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(124,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TB,C: ( binary1291135688e_Tree @ TA ) > TA > ( binary1291135688e_Tree @ TA ) > TB,D: binary1291135688e_Tree @ TA] :
      ( ( A @ ( binary536355927e_Tree @ TB @ TA @ B @ C @ D ) )
      = ( binary536355927e_Tree @ TC @ TA @ ( A @ B )
        @ ^ [E: binary1291135688e_Tree @ TA,F: TA,G: binary1291135688e_Tree @ TA] : ( A @ ( C @ E @ F @ G ) )
        @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Tree_Ocase__distrib) ).

thf(648,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TB,C: ( binary1291135688e_Tree @ TA ) > TA > ( binary1291135688e_Tree @ TA ) > TB,D: binary1291135688e_Tree @ TA] :
      ( ( A @ ( binary536355927e_Tree @ TB @ TA @ B @ C @ D ) )
      = ( binary536355927e_Tree @ TC @ TA @ ( A @ B )
        @ ^ [E: binary1291135688e_Tree @ TA,F: TA,G: binary1291135688e_Tree @ TA] : ( A @ ( C @ E @ F @ G ) )
        @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(212,axiom,
    no_bot @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Ono__bot) ).

thf(939,plain,
    no_bot @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(25,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( product_case_prod @ TA @ TB @ ( TC > TD ) )
      = ( ^ [A: TA > TB > TC > TD,B: product_prod @ TA @ TB,C: TC] :
            ( product_case_prod @ TA @ TB @ TD
            @ ^ [D: TA,E: TB] : ( A @ D @ E @ C )
            @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_case__prod__app) ).

thf(355,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( product_case_prod @ TA @ TB @ ( TC > TD ) )
      = ( ^ [A: TA > TB > TC > TD,B: product_prod @ TA @ TB,C: TC] :
            ( product_case_prod @ TA @ TB @ TD
            @ ^ [D: TA,E: TB] : ( A @ D @ E @ C )
            @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(94,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( ord_less @ TB @ A @ ( B @ C ) )
         => ( ( ord_less @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less @ TA @ E @ F )
                 => ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_order__less__subst1) ).

thf(553,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( ord_less @ TB @ A @ ( B @ C ) )
         => ( ( ord_less @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less @ TA @ E @ F )
                 => ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(219,axiom,
    ! [TA: $tType] :
      ( ( condit1656338222tinuum @ TA )
     => ! [A: TA] :
        ? [B: TA] :
          ( ( ord_less @ TA @ A @ B )
          | ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_ex__gt__or__lt) ).

thf(968,plain,
    ! [TA: $tType] :
      ( ( condit1656338222tinuum @ TA )
     => ! [A: TA] :
        ? [B: TA] :
          ( ( ord_less @ TA @ A @ B )
          | ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(114,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
      ( ( ord_less_eq @ ( TA > $o ) @ A @ B )
     => ( ( A @ C )
       => ( B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_predicate1D) ).

thf(617,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
      ( ( ord_less_eq @ ( TA > $o ) @ A @ B )
     => ( ( A @ C )
       => ( B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(82,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_eq__iff) ).

thf(516,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(136,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ B @ C )
         => ~ ( ord_less @ TA @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_pinf_I5_J) ).

thf(690,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ B @ C )
         => ~ ( ord_less @ TA @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(7,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ( ( bNF_Ca1785829860lChain @ TA @ TB )
        = ( ^ [A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
            ! [C: TA,D: TA] :
              ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
             => ( ord_less_eq @ TB @ ( B @ C ) @ ( B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_relChain__def) ).

thf(282,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ( ( bNF_Ca1785829860lChain @ TA @ TB )
        = ( ^ [A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
            ! [C: TA,D: TA] :
              ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
             => ( ord_less_eq @ TB @ ( B @ C ) @ ( B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(103,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA > $o,B: TB,C: TC,D: TA] :
      ( ( product_case_prod @ TB @ TC @ ( TA > $o ) @ A @ ( product_Pair @ TB @ TC @ B @ C ) @ D )
     => ( A @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_case__prodD_H) ).

thf(580,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA > $o,B: TB,C: TC,D: TA] :
      ( ( product_case_prod @ TB @ TC @ ( TA > $o ) @ A @ ( product_Pair @ TB @ TC @ B @ C ) @ D )
     => ( A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(180,axiom,
    ! [TA: $tType,A: binary1291135688e_Tree @ TA,B: TA > int] :
      ( ( A
       != ( binary1746293266le_Tip @ TA ) )
     => ( ( binary1271298290_wrmrm @ TA @ B @ A )
        = ( product_Pair @ ( binary1291135688e_Tree @ TA ) @ TA @ ( binary213313527le_wrm @ TA @ B @ A ) @ ( binary576689334lle_rm @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_wrmrm__decomp) ).

thf(855,plain,
    ! [TA: $tType,A: binary1291135688e_Tree @ TA,B: TA > int] :
      ( ( A
       != ( binary1746293266le_Tip @ TA ) )
     => ( ( binary1271298290_wrmrm @ TA @ B @ A )
        = ( product_Pair @ ( binary1291135688e_Tree @ TA ) @ TA @ ( binary213313527le_wrm @ TA @ B @ A ) @ ( binary576689334lle_rm @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(253,axiom,
    binary1610619414edTree @ a @ h @ ( binary210054475elle_T @ a @ t1 @ x @ t2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_s) ).

thf(1053,plain,
    binary1610619414edTree @ a @ h @ ( binary210054475elle_T @ a @ t1 @ x @ t2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(81,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( ord_less_eq @ TA @ A @ B )
           => ~ ( ord_less_eq @ TA @ B @ C ) )
         => ( ( ( ord_less_eq @ TA @ B @ A )
             => ~ ( ord_less_eq @ TA @ A @ C ) )
           => ( ( ( ord_less_eq @ TA @ A @ C )
               => ~ ( ord_less_eq @ TA @ C @ B ) )
             => ( ( ( ord_less_eq @ TA @ C @ B )
                 => ~ ( ord_less_eq @ TA @ B @ A ) )
               => ( ( ( ord_less_eq @ TA @ B @ C )
                   => ~ ( ord_less_eq @ TA @ C @ A ) )
                 => ~ ( ( ord_less_eq @ TA @ C @ A )
                     => ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_le__cases3) ).

thf(502,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( ord_less_eq @ TA @ A @ B )
           => ~ ( ord_less_eq @ TA @ B @ C ) )
         => ( ( ( ord_less_eq @ TA @ B @ A )
             => ~ ( ord_less_eq @ TA @ A @ C ) )
           => ( ( ( ord_less_eq @ TA @ A @ C )
               => ~ ( ord_less_eq @ TA @ C @ B ) )
             => ( ( ( ord_less_eq @ TA @ C @ B )
                 => ~ ( ord_less_eq @ TA @ B @ A ) )
               => ( ( ( ord_less_eq @ TA @ B @ C )
                   => ~ ( ord_less_eq @ TA @ C @ A ) )
                 => ~ ( ( ord_less_eq @ TA @ C @ A )
                     => ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(176,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
         => ( ( ord_less_eq @ TA @ A @ B )
           => ( ord_less @ TA @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_order_Onot__eq__order__implies__strict) ).

thf(840,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
         => ( ( ord_less_eq @ TA @ A @ B )
           => ( ord_less @ TA @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(166,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( ? [B: TA] : ( member @ TA @ B @ A ) )
      = ( A
       != ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_ex__in__conv) ).

thf(808,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( ? [B: TA] : ( member @ TA @ B @ A ) )
      = ( A
       != ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(92,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
          | ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_linear) ).

thf(544,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
          | ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(246,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less @ ( set @ TA ) @ A @ B )
     => ( ( ord_less @ ( set @ TA ) @ B @ C )
       => ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_psubset__trans) ).

thf(1038,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less @ ( set @ TA ) @ A @ B )
     => ( ( ord_less @ ( set @ TA ) @ B @ C )
       => ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(32,axiom,
    ! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
      ( product_case_prod @ TA @ TB @ $o
      @ ^ [B: TA,C: TB] : $true
      @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_prod_Odisc__eq__case) ).

thf(370,plain,
    ! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
      ( product_case_prod @ TA @ TB @ $o
      @ ^ [B: TA,C: TB] : $true
      @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(113,axiom,
    ! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
      ( ( A
        = ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) )
     => ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_less__by__empty) ).

thf(613,plain,
    ! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
      ( ( A
        = ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) )
     => ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(109,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
          = ( ( ord_less @ TA @ A @ B )
            | ( ord_less @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_neq__iff) ).

thf(600,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( A != B )
          = ( ( ord_less @ TA @ A @ B )
            | ( ord_less @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(252,axiom,
    ( ( ( ( binary1746293266le_Tip @ a )
       != ( binary1746293266le_Tip @ a ) )
      & ( binary1610619414edTree @ a @ h @ ( binary1746293266le_Tip @ a ) ) )
   => ( binary1610619414edTree @ a @ h @ ( binary213313527le_wrm @ a @ h @ ( binary1746293266le_Tip @ a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__092_060open_062Tip_A_092_060noteq_062_ATip_A_092_060and_062_AsortedTree_Ah_ATip_A_092_060longrightarrow_062_AsortedTree_Ah_A_Iwrm_Ah_ATip_J_092_060close_062) ).

thf(1052,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(183,axiom,
    ! [TA: $tType,A: set @ TA] :
      ~ ( ord_less @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_not__psubset__empty) ).

thf(864,plain,
    ! [TA: $tType,A: set @ TA] :
      ~ ( ord_less @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(149,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ B )
         => ( ( ord_less @ TA @ ( C @ B ) @ D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less_eq @ TB @ E @ F )
                 => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_order__le__less__subst2) ).

thf(727,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ B )
         => ( ( ord_less @ TA @ ( C @ B ) @ D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less_eq @ TB @ E @ F )
                 => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(223,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( ord_less @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( A != B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_less__le) ).

thf(978,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( ord_less @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( A != B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(235,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( ord_less_eq @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less @ TA @ A @ B )
              | ( A = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_order_Oorder__iff__strict) ).

thf(1008,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( ord_less_eq @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less @ TA @ A @ B )
              | ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(188,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less @ TA @ B @ C )
           => ( ord_less @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_order_Ostrict__trans1) ).

thf(876,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less @ TA @ B @ C )
           => ( ord_less @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(65,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_order__class_Oorder_Oeq__iff) ).

thf(465,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(95,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( bot_bot @ ( TA > TB > $o ) )
      = ( ^ [A: TA,B: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_bot__empty__eq2) ).

thf(556,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bot_bot @ ( TA > TB > $o ) )
      = ( ^ [A: TA,B: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(209,axiom,
    ! [TA: $tType] :
      ( ( (=) @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
            & ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_set__eq__subset) ).

thf(931,plain,
    ! [TA: $tType] :
      ( ( (=) @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
            & ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(72,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA] :
      ( ( A @ B @ C )
     => ( product_case_prod @ TB @ TA @ $o @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_case__prodI) ).

thf(482,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA] :
      ( ( A @ B @ C )
     => ( product_case_prod @ TB @ TA @ $o @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(79,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
          | ( A = B )
          | ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_less__linear) ).

thf(495,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
          | ( A = B )
          | ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(194,axiom,
    ! [TA: $tType] :
      ( ( dense_linorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ! [D: TA] :
                ( ( ord_less @ TA @ A @ D )
               => ( ( ord_less @ TA @ D @ B )
                 => ( ord_less_eq @ TA @ C @ D ) ) )
           => ( ord_less_eq @ TA @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_dense__ge__bounded) ).

thf(891,plain,
    ! [TA: $tType] :
      ( ( dense_linorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ! [D: TA] :
                ( ( ord_less @ TA @ A @ D )
               => ( ( ord_less @ TA @ D @ B )
                 => ( ord_less_eq @ TA @ C @ D ) ) )
           => ( ord_less_eq @ TA @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(31,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_less__asym_H) ).

thf(368,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(135,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less_eq @ TA @ A @ B )
         => ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_le__cases) ).

thf(688,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less_eq @ TA @ A @ B )
         => ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(198,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_in__mono) ).

thf(903,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(257,axiom,
    ( ( binary213313527le_wrm @ a @ h @ ( binary210054475elle_T @ a @ t1 @ x @ t2 ) )
    = ( binary210054475elle_T @ a @ t1 @ x @ ( binary213313527le_wrm @ a @ h @ t2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_res) ).

thf(1062,plain,
    ( ( binary213313527le_wrm @ a @ h @ ( binary210054475elle_T @ a @ t1 @ x @ t2 ) )
    = ( binary210054475elle_T @ a @ t1 @ x @ ( binary213313527le_wrm @ a @ h @ t2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(215,axiom,
    ! [TA: $tType,A: ( binary1291135688e_Tree @ TA ) > $o,B: binary1291135688e_Tree @ TA] :
      ( ( A @ ( binary1746293266le_Tip @ TA ) )
     => ( ! [C: binary1291135688e_Tree @ TA,D: TA,E: binary1291135688e_Tree @ TA] :
            ( ( A @ C )
           => ( ( A @ E )
             => ( A @ ( binary210054475elle_T @ TA @ C @ D @ E ) ) ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Tree_Oinduct) ).

thf(946,plain,
    ! [TA: $tType,A: ( binary1291135688e_Tree @ TA ) > $o,B: binary1291135688e_Tree @ TA] :
      ( ( A @ ( binary1746293266le_Tip @ TA ) )
     => ( ! [C: binary1291135688e_Tree @ TA,D: TA,E: binary1291135688e_Tree @ TA] :
            ( ( A @ C )
           => ( ( A @ E )
             => ( A @ ( binary210054475elle_T @ TA @ C @ D @ E ) ) ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(23,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( preorder @ TA )
     => ( preorder @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).

thf(351,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( preorder @ TA )
     => ( preorder @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(119,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ ( B @ C ) )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less_eq @ TA @ E @ F )
                 => ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_order__subst1) ).

thf(632,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ ( B @ C ) )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less_eq @ TA @ E @ F )
                 => ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(42,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_less__not__sym) ).

thf(401,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(229,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ C @ B )
         => ( ord_less_eq @ TA @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_minf_I6_J) ).

thf(995,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ C @ B )
         => ( ord_less_eq @ TA @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(217,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less @ ( set @ TA ) @ A @ B )
     => ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
         => ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_psubsetE) ).

thf(961,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less @ ( set @ TA ) @ A @ B )
     => ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
         => ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(168,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ A
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ B )
                & ( C @ D ) ) ) )
        = ( ! [D: TA] :
              ( ( member @ TA @ D @ A )
             => ( C @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_subset__Collect__iff) ).

thf(813,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ A
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ B )
                & ( C @ D ) ) ) )
        = ( ! [D: TA] :
              ( ( member @ TA @ D @ A )
             => ( C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(242,axiom,
    ! [TA: $tType] :
      ( ( ord_less @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
            & ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_subset__not__subset__eq) ).

thf(1030,plain,
    ! [TA: $tType] :
      ( ( ord_less @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
            & ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(202,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ C @ B )
         => ~ ( ord_less_eq @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_minf_I8_J) ).

thf(914,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ C @ B )
         => ~ ( ord_less_eq @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(128,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA > TA > $o,B: TA,C: TA] :
          ( ! [D: TA,E: TA] :
              ( ( ord_less_eq @ TA @ D @ E )
             => ( A @ D @ E ) )
         => ( ! [D: TA,E: TA] :
                ( ( A @ E @ D )
               => ( A @ D @ E ) )
           => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_linorder__wlog) ).

thf(667,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA > TA > $o,B: TA,C: TA] :
          ( ! [D: TA,E: TA] :
              ( ( ord_less_eq @ TA @ D @ E )
             => ( A @ D @ E ) )
         => ( ! [D: TA,E: TA] :
                ( ( A @ E @ D )
               => ( A @ D @ E ) )
           => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(208,axiom,
    ! [TA: $tType,A: TA > int,B: TA,C: TA,D: binary1291135688e_Tree @ TA] : ( binary231205461t_pred @ TA @ A @ B @ C @ D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_sorted__distinct) ).

thf(929,plain,
    ! [TA: $tType,A: TA > int,B: TA,C: TA,D: binary1291135688e_Tree @ TA] : ( binary231205461t_pred @ TA @ A @ B @ C @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(263,axiom,
    ( t2
   != ( binary1746293266le_Tip @ a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_t2nTip) ).

thf(1077,plain,
    ( t2
   != ( binary1746293266le_Tip @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(153,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_leD) ).

thf(763,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(163,axiom,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
          ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( member @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_subset__eq) ).

thf(800,plain,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
          ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( member @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(231,axiom,
    ! [TA: $tType] :
      ( ( wellorder @ TA )
     => ( ( '?' @ TA )
        = ( ^ [A: TA > $o] :
            ? [B: TA] :
              ( ( A @ B )
              & ! [C: TA] :
                  ( ( ord_less @ TA @ C @ B )
                 => ~ ( A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_exists__least__iff) ).

thf(999,plain,
    ! [TA: $tType] :
      ( ( wellorder @ TA )
     => ( ( '?' @ TA )
        = ( ^ [A: TA > $o] :
            ? [B: TA] :
              ( ( A @ B )
              & ! [C: TA] :
                  ( ( ord_less @ TA @ C @ B )
                 => ~ ( A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(54,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA] :
          ~ ( ord_less @ TA @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_dual__order_Oirrefl) ).

thf(432,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA] :
          ~ ( ord_less @ TA @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(170,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ A @ B )
            = ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_antisym__conv1) ).

thf(818,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ A @ B )
            = ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(44,axiom,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( bot_bot @ ( set @ TA ) )
        = ( collect @ TA @ A ) )
      = ( ! [B: TA] :
            ~ ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_empty__Collect__eq) ).

thf(405,plain,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( bot_bot @ ( set @ TA ) )
        = ( collect @ TA @ A ) )
      = ( ! [B: TA] :
            ~ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(110,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).

thf(603,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(50,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_order_Otrans) ).

thf(422,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(162,axiom,
    ! [TA: $tType,A: TA > int,B: TA,C: TA,D: binary1291135688e_Tree @ TA,E: binary1291135688e_Tree @ TA] :
      ( ( ( ord_less @ int @ ( A @ B ) @ ( A @ C ) )
       => ( ( binary997842527remove @ TA @ A @ B @ ( binary210054475elle_T @ TA @ D @ C @ E ) )
          = ( binary210054475elle_T @ TA @ ( binary997842527remove @ TA @ A @ B @ D ) @ C @ E ) ) )
      & ( ~ ( ord_less @ int @ ( A @ B ) @ ( A @ C ) )
       => ( ( ( ord_less @ int @ ( A @ C ) @ ( A @ B ) )
           => ( ( binary997842527remove @ TA @ A @ B @ ( binary210054475elle_T @ TA @ D @ C @ E ) )
              = ( binary210054475elle_T @ TA @ D @ C @ ( binary997842527remove @ TA @ A @ B @ E ) ) ) )
          & ( ~ ( ord_less @ int @ ( A @ C ) @ ( A @ B ) )
           => ( ( ( D
                  = ( binary1746293266le_Tip @ TA ) )
               => ( ( binary997842527remove @ TA @ A @ B @ ( binary210054475elle_T @ TA @ D @ C @ E ) )
                  = E ) )
              & ( ( D
                 != ( binary1746293266le_Tip @ TA ) )
               => ( ( binary997842527remove @ TA @ A @ B @ ( binary210054475elle_T @ TA @ D @ C @ E ) )
                  = ( product_case_prod @ ( binary1291135688e_Tree @ TA ) @ TA @ ( binary1291135688e_Tree @ TA )
                    @ ^ [F: binary1291135688e_Tree @ TA,G: TA] : ( binary210054475elle_T @ TA @ F @ G @ E )
                    @ ( binary1271298290_wrmrm @ TA @ A @ D ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_remove_Osimps_I2_J) ).

thf(790,plain,
    ! [TA: $tType,A: TA > int,B: TA,C: TA,D: binary1291135688e_Tree @ TA,E: binary1291135688e_Tree @ TA] :
      ( ( ( ord_less @ int @ ( A @ B ) @ ( A @ C ) )
       => ( ( binary997842527remove @ TA @ A @ B @ ( binary210054475elle_T @ TA @ D @ C @ E ) )
          = ( binary210054475elle_T @ TA @ ( binary997842527remove @ TA @ A @ B @ D ) @ C @ E ) ) )
      & ( ~ ( ord_less @ int @ ( A @ B ) @ ( A @ C ) )
       => ( ( ( ord_less @ int @ ( A @ C ) @ ( A @ B ) )
           => ( ( binary997842527remove @ TA @ A @ B @ ( binary210054475elle_T @ TA @ D @ C @ E ) )
              = ( binary210054475elle_T @ TA @ D @ C @ ( binary997842527remove @ TA @ A @ B @ E ) ) ) )
          & ( ~ ( ord_less @ int @ ( A @ C ) @ ( A @ B ) )
           => ( ( ( D
                  = ( binary1746293266le_Tip @ TA ) )
               => ( ( binary997842527remove @ TA @ A @ B @ ( binary210054475elle_T @ TA @ D @ C @ E ) )
                  = E ) )
              & ( ( D
                 != ( binary1746293266le_Tip @ TA ) )
               => ( ( binary997842527remove @ TA @ A @ B @ ( binary210054475elle_T @ TA @ D @ C @ E ) )
                  = ( product_case_prod @ ( binary1291135688e_Tree @ TA ) @ TA @ ( binary1291135688e_Tree @ TA )
                    @ ^ [F: binary1291135688e_Tree @ TA,G: TA] : ( binary210054475elle_T @ TA @ F @ G @ E )
                    @ ( binary1271298290_wrmrm @ TA @ A @ D ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(26,axiom,
    ! [TA: $tType] : ( ord @ ( set @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_7) ).

thf(358,plain,
    ! [TA: $tType] : ( ord @ ( set @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(56,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( order @ TA )
     => ( order @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).

thf(437,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( order @ TA )
     => ( order @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(255,axiom,
    ! [TA: $tType,A: binary1291135688e_Tree @ TA,B: TA > int] :
      ( ( ( A
         != ( binary1746293266le_Tip @ TA ) )
        & ( binary1610619414edTree @ TA @ B @ A ) )
     => ( ord_less_eq @ ( set @ TA ) @ ( binary1653327646_setOf @ TA @ ( binary213313527le_wrm @ TA @ B @ A ) ) @ ( binary1653327646_setOf @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_wrm__set1) ).

thf(1056,plain,
    ! [TA: $tType,A: binary1291135688e_Tree @ TA,B: TA > int] :
      ( ( ( A
         != ( binary1746293266le_Tip @ TA ) )
        & ( binary1610619414edTree @ TA @ B @ A ) )
     => ( ord_less_eq @ ( set @ TA ) @ ( binary1653327646_setOf @ TA @ ( binary213313527le_wrm @ TA @ B @ A ) ) @ ( binary1653327646_setOf @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(243,axiom,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_empty__iff) ).

thf(1033,plain,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(120,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_dual__order_Orefl) ).

thf(635,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(88,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( inv_image @ TA @ TB )
      = ( ^ [A: set @ ( product_prod @ TA @ TA ),B: TB > TA] :
            ( collect @ ( product_prod @ TB @ TB )
            @ ( product_case_prod @ TB @ TB @ $o
              @ ^ [C: TB,D: TB] : ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( B @ C ) @ ( B @ D ) ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_inv__image__def) ).

thf(532,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( inv_image @ TA @ TB )
      = ( ^ [A: set @ ( product_prod @ TA @ TA ),B: TB > TA] :
            ( collect @ ( product_prod @ TB @ TB )
            @ ( product_case_prod @ TB @ TB @ $o
              @ ^ [C: TB,D: TB] : ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( B @ C ) @ ( B @ D ) ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(146,axiom,
    ! [TA: $tType,A: set @ TA,B: TA > $o] :
      ( ord_less_eq @ ( set @ TA )
      @ ( collect @ TA
        @ ^ [C: TA] :
            ( ( member @ TA @ C @ A )
            & ( B @ C ) ) )
      @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_Collect__subset) ).

thf(720,plain,
    ! [TA: $tType,A: set @ TA,B: TA > $o] :
      ( ord_less_eq @ ( set @ TA )
      @ ( collect @ TA
        @ ^ [C: TA] :
            ( ( member @ TA @ C @ A )
            & ( B @ C ) ) )
      @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(48,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( A != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_order_Ostrict__implies__not__eq) ).

thf(415,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(196,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( ord_less @ TB @ A @ ( B @ C ) )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less_eq @ TA @ E @ F )
                 => ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_order__less__le__subst1) ).

thf(897,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( ord_less @ TB @ A @ ( B @ C ) )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less_eq @ TA @ E @ F )
                 => ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(69,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect @ TA @ A )
        = ( collect @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).

thf(474,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect @ TA @ A )
        = ( collect @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(52,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA] :
          ~ ( ord_less @ TA @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_less__irrefl) ).

thf(427,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA] :
          ~ ( ord_less @ TA @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(182,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_equalityD1) ).

thf(860,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(123,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: TC,C: TA > TB > ( set @ TC )] :
      ( ! [D: TA,E: TB] :
          ( ( A
            = ( product_Pair @ TA @ TB @ D @ E ) )
         => ( member @ TC @ B @ ( C @ D @ E ) ) )
     => ( member @ TC @ B @ ( product_case_prod @ TA @ TB @ ( set @ TC ) @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_mem__case__prodI2) ).

thf(644,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: TC,C: TA > TB > ( set @ TC )] :
      ( ! [D: TA,E: TB] :
          ( ( A
            = ( product_Pair @ TA @ TB @ D @ E ) )
         => ( member @ TC @ B @ ( C @ D @ E ) ) )
     => ( member @ TC @ B @ ( product_case_prod @ TA @ TB @ ( set @ TC ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(62,axiom,
    order @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_12) ).

thf(459,plain,
    order @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(233,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less_eq @ TA @ A @ B )
         => ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_not__le__imp__less) ).

thf(1004,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less_eq @ TA @ A @ B )
         => ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(186,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less @ TA @ C @ A )
           => ( ord_less @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_dual__order_Ostrict__trans1) ).

thf(871,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less @ TA @ C @ A )
           => ( ord_less @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(200,axiom,
    ! [TA: $tType] :
      ( ( wellorder @ TA )
     => ! [A: TA > $o,B: TA] :
          ( ! [C: TA] :
              ( ! [D: TA] :
                  ( ( ord_less @ TA @ D @ C )
                 => ( A @ D ) )
             => ( A @ C ) )
         => ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_less__induct) ).

thf(908,plain,
    ! [TA: $tType] :
      ( ( wellorder @ TA )
     => ! [A: TA > $o,B: TA] :
          ( ! [C: TA] :
              ( ! [D: TA] :
                  ( ( ord_less @ TA @ D @ C )
                 => ( A @ D ) )
             => ( A @ C ) )
         => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(228,axiom,
    ! [TA: $tType] :
      ( ( binary1653327646_setOf @ TA @ ( binary1746293266le_Tip @ TA ) )
      = ( bot_bot @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_setOf_Osimps_I1_J) ).

thf(992,plain,
    ! [TA: $tType] :
      ( ( binary1653327646_setOf @ TA @ ( binary1746293266le_Tip @ TA ) )
      = ( bot_bot @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(74,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: TB,D: TA] :
      ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
     => ( ( A @ C @ D )
       => ( B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_predicate2D) ).

thf(486,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: TB,D: TA] :
      ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
     => ( ( A @ C @ D )
       => ( B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(164,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ! [B: TA] :
          ~ ( member @ TA @ B @ A )
     => ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_equals0I) ).

thf(803,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ! [B: TA] :
          ~ ( member @ TA @ B @ A )
     => ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(19,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB > TD,C: product_prod @ TA @ TB] :
      ( ( A @ ( product_case_prod @ TA @ TB @ TD @ B @ C ) )
      = ( product_case_prod @ TA @ TB @ TC
        @ ^ [D: TA,E: TB] : ( A @ ( B @ D @ E ) )
        @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_prod_Ocase__distrib) ).

thf(337,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB > TD,C: product_prod @ TA @ TB] :
      ( ( A @ ( product_case_prod @ TA @ TB @ TD @ B @ C ) )
      = ( product_case_prod @ TA @ TB @ TC
        @ ^ [D: TA,E: TB] : ( A @ ( B @ D @ E ) )
        @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(16,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ B @ C )
         => ( C != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_pinf_I4_J) ).

thf(309,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ B @ C )
         => ( C != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(245,axiom,
    condit1037483654norder @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Conditionally__Complete__Lattices_Oconditionally__complete__linorder) ).

thf(1037,plain,
    condit1037483654norder @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(130,axiom,
    order @ int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oorder_2) ).

thf(676,plain,
    order @ int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(260,axiom,
    ( ( ( t1
       != ( binary1746293266le_Tip @ a ) )
      & ( binary1610619414edTree @ a @ h @ t1 ) )
   => ( binary1610619414edTree @ a @ h @ ( binary213313527le_wrm @ a @ h @ t1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_h1) ).

thf(1069,plain,
    ( ( ( t1
       != ( binary1746293266le_Tip @ a ) )
      & ( binary1610619414edTree @ a @ h @ t1 ) )
   => ( binary1610619414edTree @ a @ h @ ( binary213313527le_wrm @ a @ h @ t1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(29,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TA )
     => ( ord @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).

thf(364,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TA )
     => ( ord @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(67,axiom,
    ! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
      ( ( A @ B )
     => ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
       => ( C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_rev__predicate1D) ).

thf(469,plain,
    ! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
      ( ( A @ B )
     => ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
       => ( C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(213,axiom,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less @ ( set @ TA ) @ A @ B )
            | ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_subset__iff__psubset__eq) ).

thf(940,plain,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less @ ( set @ TA ) @ A @ B )
            | ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(237,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: ( binary1291135688e_Tree @ TA ) > TA > ( binary1291135688e_Tree @ TA ) > TB,C: binary1291135688e_Tree @ TA,D: TA,E: binary1291135688e_Tree @ TA] :
      ( ( binary536355927e_Tree @ TB @ TA @ A @ B @ ( binary210054475elle_T @ TA @ C @ D @ E ) )
      = ( B @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Tree_Osimps_I5_J) ).

thf(1014,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: ( binary1291135688e_Tree @ TA ) > TA > ( binary1291135688e_Tree @ TA ) > TB,C: binary1291135688e_Tree @ TA,D: TA,E: binary1291135688e_Tree @ TA] :
      ( ( binary536355927e_Tree @ TB @ TA @ A @ B @ ( binary210054475elle_T @ TA @ C @ D @ E ) )
      = ( B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(221,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: ( binary1291135688e_Tree @ TB ) > TB > ( binary1291135688e_Tree @ TB ) > TA] :
      ( ( binary536355927e_Tree @ TA @ TB @ A @ B @ ( binary1746293266le_Tip @ TB ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Tree_Osimps_I4_J) ).

thf(972,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: ( binary1291135688e_Tree @ TB ) > TB > ( binary1291135688e_Tree @ TB ) > TA] :
      ( ( binary536355927e_Tree @ TA @ TB @ A @ B @ ( binary1746293266le_Tip @ TB ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(1086,plain,
    $false,
    inference(e,[status(thm)],[1024,760,846,1083,468,408,730,308,873,878,677,597,523,582,384,715,698,340,538,782,885,288,301,651,320,565,570,785,372,619,344,934,1059,460,559,606,770,924,492,443,1040,623,834,348,806,353,821,905,480,981,692,866,396,411,1072,453,1074,439,546,381,366,1067,1047,1021,302,392,297,424,630,429,275,916,484,852,522,710,456,285,1017,1064,725,403,1006,869,610,989,519,578,471,1028,488,526,637,590,679,970,837,997,701,654,1050,1002,984,911,266,360,541,1035,530,926,765,1054,773,586,718,888,824,444,694,843,577,413,562,975,641,391,936,313,787,919,704,672,713,498,900,831,681,274,1011,419,362,567,880,1043,434,477,758,858,535,816,594,895,964,626,943,462,811,387,494,1080,685,399,959,768,1044,278,780,883,299,267,922,658,394,986,306,722,490,648,939,355,553,968,617,516,690,282,580,855,1053,502,840,808,544,1038,370,613,600,1052,864,727,978,1008,876,465,556,931,482,495,891,368,688,903,1062,946,351,632,401,995,961,813,1030,914,667,929,1077,763,800,999,432,818,405,603,422,790,358,437,1056,1033,635,532,720,415,897,474,427,860,644,459,1004,871,908,992,486,803,337,309,1037,676,1069,364,469,940,1014,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : ITP033^2 : TPTP v8.2.0. Released v7.5.0.
% 0.08/0.17  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n028.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Sat May 18 16:47:09 EDT 2024
% 0.25/0.38  % CPUTime  : 
% 0.92/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.84/1.17  % [INFO] 	 Parsing done (267ms). 
% 1.84/1.18  % [INFO] 	 Running in sequential loop mode. 
% 2.82/1.42  % [INFO] 	 eprover registered as external prover. 
% 2.82/1.43  % [INFO] 	 cvc4 registered as external prover. 
% 2.82/1.43  % [INFO] 	 Scanning for conjecture ... 
% 3.10/1.53  % [INFO] 	 Found a conjecture (or negated_conjecture) and 279 axioms. Running axiom selection ... 
% 3.25/1.64  % [INFO] 	 Axiom selection finished. Selected 263 axioms (removed 16 axioms). 
% 4.08/1.85  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 4.28/1.87  % [INFO] 	 Type checking passed. 
% 4.28/1.87  % [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 ... 
% 33.17/17.67  % External prover 'e' found a proof!
% 33.17/17.67  % [INFO] 	 Killing All external provers ... 
% 33.17/17.67  % Time passed: 17116ms (effective reasoning time: 16482ms)
% 33.17/17.67  % 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)>
% 33.17/17.67  % Axioms used in derivation (263): fact_158_dual__order_Ostrict__iff__order, tcon_fun___Orderings_Obot, fact_145_le__imp__less__or__eq, fact_34_subsetI, fact_52_ord__eq__le__subst, fact_73_ord__less__eq__subst, fact_26_binsert_Osimps_I2_J, fact_88_ord__eq__less__trans, fact_193_pinf_I1_J, fact_170_pinf_I6_J, fact_224_case__prod__app, fact_242_rev__predicate2D, fact_3_sortLemmaL, fact_32_subset__empty, fact_53_ord__le__eq__subst, fact_9_memb__spec, fact_37_all__not__in__conv, fact_92_less__not__sym, fact_226_bot__empty__eq2, fact_187_psubset__eq, tcon_HOL_Obool___Orderings_Olinorder_11, fact_43_le__funE, fact_38_empty__iff, fact_189_less__eq__set__def, fact_184_subset__not__subset__eq, fact_55_antisym, fact_195_pinf_I3_J, fact_12_sorted__distinct, fact_148_order_Ostrict__trans1, fact_248_case__prodE2, fact_197_pinf_I5_J, tcon_Int_Oint___Orderings_Oorder_2, fact_230_ssubst__Pair__rhs, fact_117_equalityD2, fact_220_subset__CollectI, fact_104_not__less__iff__gr__or__eq, fact_240_eq__subset, fact_250_cond__case__prod__eta, fact_0_t2nTip, fact_190_verit__la__disequality, fact_232_mem__case__prodI2, fact_8_sortedTree_Osimps_I1_J, fact_18_Tree_Oexhaust, fact_15_binsert_Osimps_I1_J, fact_152_dual__order_Ostrict__trans1, fact_130_order__le__less__subst1, tcon_fun___Orderings_Oord, fact_103_dual__order_Ostrict__trans, fact_244_case__prodE, fact_109_equals0D, fact_77_gt__ex, fact_141_less__le__trans, fact_185_psubset__subset__trans, tcon_Set_Oset___Orderings_Obot_8, fact_17_Tree_Oinduct, fact_1_s, fact_96_less__imp__triv, fact_202_minf_I3_J, fact_160_order_Onot__eq__order__implies__strict, fact_115_subset__eq, fact_132_order__less__le__subst1, fact_127_leI, fact_68_linorder__wlog, fact_172_complete__interval, fact_154_dense__ge__bounded, fact_39_bot__apply, fact_2_res, fact_40_order__refl, fact_50_order__subst1, fact_210_Collect__empty__eq__bot, fact_234_case__prodI, fact_13__092_060open_062Tip_A_092_060noteq_062_ATip_A_092_060and_062_AsortedTree_Ah_ATip_A_092_060longrightarrow_062_AsortedTree_Ah_A_Iwrm_Ah_ATip_J_092_060close_062, fact_87_less__irrefl, fact_200_minf_I1_J, fact_41_bot__set__def, fact_182_subset__iff__psubset__eq, fact_49_le__fun__def, fact_181_not__psubset__empty, fact_119_subset__refl, fact_58_le__cases, fact_156_order_Ostrict__implies__order, fact_106_dual__order_Ostrict__implies__not__eq, fact_140_le__less__trans, fact_110_equals0I, fact_192_verit__comp__simplify1_I1_J, fact_231_case__prod__conv, fact_254_prod_Odisc__eq__case, tcon_Int_Oint___Orderings_Opreorder_1, fact_46_Collect__mem__eq, fact_90_dual__order_Oasym, fact_23_remove_Osimps_I1_J, fact_228_pred__subset__eq2, fact_251_less__by__empty, fact_19_rm__set, fact_174_psubsetI, fact_75_order__less__subst2, fact_78_neqE, fact_85_less__trans, fact_121_subset__trans, fact_207_prop__restrict, fact_213_less__set__def, fact_95_less__imp__not__eq2, fact_139_less__imp__le, fact_35_empty__Collect__eq, fact_208_Collect__restrict, fact_235_case__prodI2, fact_63_ord__eq__le__trans, fact_105_order_Ostrict__implies__not__eq, fact_81_dense, tcon_Int_Oint___Conditionally__Complete__Lattices_Oconditionally__complete__linorder, fact_124_empty__def, fact_188_psubsetE, fact_255_inv__image__def, fact_241_predicate2D, fact_209_bot__empty__eq, fact_118_subset__iff, fact_67_dual__order_Orefl, fact_138_antisym__conv2, fact_83_less__asym, fact_44_le__funI, fact_11_h2, fact_107_bot__fun__def, fact_133_order__less__le__subst2, fact_70_dual__order_Oeq__iff, fact_125_Collect__subset, tcon_Set_Oset___Orderings_Oorder_6, fact_21_wrm__set1, tcon_Int_Oint___Orderings_Olinorder, fact_129_less__le, fact_5_Tree_Oinject, fact_31_empty__subsetI, tcon_HOL_Obool___Orderings_Oorder_12, fact_237_mem__case__prodI, fact_97_linorder__cases, fact_82_less__imp__neq, fact_36_Collect__empty__eq, fact_144_le__less__linear, fact_99_order_Ostrict__trans, tcon_Set_Oset___Orderings_Oord_7, fact_14_Tree_Odistinct_I1_J, fact_146_less__le__not__le, fact_91_less__imp__not__eq, fact_45_mem__Collect__eq, tcon_HOL_Obool___Orderings_Opreorder_10, fact_27_setOf_Osimps_I1_J, fact_243_case__prodD, fact_147_not__le__imp__less, fact_33_subset__antisym, fact_169_pinf_I8_J, fact_175_less__fun__def, fact_219_subset__Collect__iff, fact_171_verit__comp__simplify1_I3_J, fact_225_case__prod__Pair__iden, fact_196_pinf_I4_J, fact_7_h1, fact_222_remove_Osimps_I2_J, fact_89_ord__less__eq__trans, fact_217_psubsetD, fact_194_pinf_I2_J, fact_42_le__funD, fact_113_subsetD, fact_168_minf_I6_J, fact_203_minf_I4_J, fact_143_dense__le, fact_47_Collect__cong, fact_79_neq__iff, fact_150_order_Oorder__iff__strict, fact_236_case__prodI2_H, fact_80_order_Oasym, fact_84_less__asym_H, fact_214_rev__predicate1D, fact_102_linorder__less__wlog, fact_20_rm_Osimps, tcon_HOL_Obool___Orderings_Obot_14, fact_114_equalityE, fact_206_minf_I11_J, fact_167_minf_I8_J, fact_229_pred__equals__eq2, fact_60_le__cases3, fact_216_psubset__trans, fact_252_relChain__def, fact_94_antisym__conv3, fact_191_ex__gt__or__lt, tcon_HOL_Obool___Orderings_Oord_13, fact_25_Tree_Osimps_I5_J, tcon_fun___Orderings_Opreorder, fact_212_predicate1I, fact_51_order__subst2, fact_30_Tree_Ocase__distrib, fact_126_leD, fact_249_case__prod__eta, fact_61_antisym__conv, fact_122_set__eq__subset, fact_149_order_Ostrict__trans2, fact_4_sortLemmaR, fact_98_dual__order_Oirrefl, fact_247_prod_Ocase__distrib, fact_215_predicate1D, fact_6_binsert__sorted, fact_221_conj__subset__def, fact_116_equalityD1, fact_201_minf_I2_J, fact_120_Collect__mono, fact_159_dual__order_Ostrict__implies__order, fact_65_order__class_Oorder_Oantisym, fact_245_case__prodD_H, fact_10_sorted__distinct__pred__def, fact_101_exists__least__iff, fact_62_order__class_Oorder_Oeq__iff, fact_151_order_Ostrict__iff__order, fact_142_dense__ge, fact_123_Collect__mono__iff, tcon_fun___Orderings_Oorder, fact_198_pinf_I7_J, fact_100_less__imp__not__less, fact_108_emptyE, tcon_Int_Oint___Orderings_Ono__bot, fact_155_dense__le__bounded, fact_22_sortedTree_Osimps_I2_J, fact_28_Tree_Osimps_I6_J, fact_183_subset__psubset__trans, fact_153_dual__order_Ostrict__trans2, fact_71_dual__order_Oantisym, fact_72_ord__eq__less__subst, fact_86_less__linear, fact_131_order__le__less__subst2, fact_205_minf_I7_J, fact_246_case__prodE_H, fact_253_split__part, fact_134_not__le, fact_239_predicate2D__conj, tcon_Int_Oint___Orderings_Ono__top, fact_74_order__less__subst1, fact_128_le__less, fact_166_subset__emptyI, fact_199_pinf_I11_J, fact_29_Tree_Osimps_I7_J, fact_136_le__neq__trans, fact_59_order_Otrans, fact_24_Tree_Osimps_I4_J, fact_76_lt__ex, tcon_Set_Oset___Orderings_Opreorder_5, fact_54_eq__iff, fact_66_order__trans, fact_233_predicate2I, fact_186_psubset__imp__subset, fact_157_dual__order_Oorder__iff__strict, fact_137_antisym__conv1, fact_56_linear, tcon_Int_Oint___Orderings_Oord_3, fact_223_wrmrm__decomp, fact_16_wrm_Osimps, fact_57_eq__refl, fact_111_ex__in__conv, fact_64_ord__le__eq__trans, fact_112_in__mono, fact_93_less__induct, fact_69_dual__order_Otrans, fact_238_Collect__case__prod__mono, fact_135_not__less, fact_204_minf_I5_J, fact_227_subrelI, fact_218_pred__subset__eq
% 33.17/17.67  % No. of inferences in proof: 530
% 33.17/17.67  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 17116 ms resp. 16482 ms w/o parsing
% 34.12/17.82  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 34.12/17.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------