TSTP Solution File: COM163^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : COM163^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.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 19:09:13 EDT 2024

% Result   : Theorem 33.00s 16.22s
% Output   : Refutation 33.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  329
% Syntax   : Number of formulae    :  609 ( 103 unt;  51 typ;   0 def)
%            Number of atoms       : 1869 ( 434 equ;   2 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives : 6904 ( 190   ~;  49   |; 110   &;5503   @)
%                                         (   0 <=>;1052  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   8 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  397 ( 397   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   54 (  50 usr;   9 con; 0-4 aty)
%            Number of variables   : 1875 (  58   ^1701   !;  74   ?;1875   :)
%                                         (  42  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(binDag_Mirabelle_dag_type,type,
    binDag_Mirabelle_dag: $tType ).

thf(simpl_ref_type,type,
    simpl_ref: $tType ).

thf(nat_type,type,
    nat: $tType ).

thf(field_type,type,
    field: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

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

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

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

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

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

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

thf(zero_neq_one_type,type,
    zero_neq_one: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

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

thf(zero_less_one_type,type,
    zero_less_one: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(division_ring_type,type,
    division_ring: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(semidom_divide_type,type,
    semidom_divide: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

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

thf(linordered_idom_type,type,
    linordered_idom: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(linordered_field_type,type,
    linordered_field: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

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

thf(linordered_semidom_type,type,
    linordered_semidom: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(ordered_ab_group_add_type,type,
    ordered_ab_group_add: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(linord219039673up_add_type,type,
    linord219039673up_add: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(linord1659791738miring_type,type,
    linord1659791738miring: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(canoni770627133id_add_type,type,
    canoni770627133id_add: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

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

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

thf(binDag_Mirabelle_DAG_type,type,
    binDag_Mirabelle_DAG: binDag_Mirabelle_dag > $o ).

thf(binDag476092410e_Node_type,type,
    binDag476092410e_Node: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > binDag_Mirabelle_dag ).

thf(binDag_Mirabelle_Tip_type,type,
    binDag_Mirabelle_Tip: binDag_Mirabelle_dag ).

thf(binDag1297733282se_dag_type,type,
    binDag1297733282se_dag: 
      !>[TA: $tType] : ( TA > ( binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > TA ) > binDag_Mirabelle_dag > TA ) ).

thf(binDag1442713106ec_dag_type,type,
    binDag1442713106ec_dag: 
      !>[TA: $tType] : ( TA > ( binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > TA > TA > TA ) > binDag_Mirabelle_dag > TA ) ).

thf(binDag1924123185ze_dag_type,type,
    binDag1924123185ze_dag: binDag_Mirabelle_dag > nat ).

thf(binDag786255756subdag_type,type,
    binDag786255756subdag: binDag_Mirabelle_dag > binDag_Mirabelle_dag > $o ).

thf(one_one_type,type,
    one_one: 
      !>[TA: $tType] : TA ).

thf(sgn_sgn_type,type,
    sgn_sgn: 
      !>[TA: $tType] : ( TA > TA ) ).

thf(uminus_uminus_type,type,
    uminus_uminus: 
      !>[TA: $tType] : ( TA > TA ) ).

thf(zero_zero_type,type,
    zero_zero: 
      !>[TA: $tType] : TA ).

thf(if_type,type,
    if: 
      !>[TA: $tType] : ( $o > TA > TA > TA ) ).

thf(size_size_type,type,
    size_size: 
      !>[TA: $tType] : ( TA > nat ) ).

thf(ord_Least_type,type,
    ord_Least: 
      !>[TA: $tType] : ( ( TA > $o ) > 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(order_antimono_type,type,
    order_antimono: 
      !>[TA: $tType,TB: $tType] : ( ( TB > TA ) > $o ) ).

thf(order_strict_mono_type,type,
    order_strict_mono: 
      !>[TA: $tType,TB: $tType] : ( ( TB > TA ) > $o ) ).

thf(ordering_type,type,
    ordering: 
      !>[TA: $tType] : ( ( TA > TA > $o ) > ( TA > TA > $o ) > $o ) ).

thf(type2_type,type,
    type2: 
      !>[TA: $tType] : ( itself @ TA ) ).

thf(divide_divide_type,type,
    divide_divide: 
      !>[TA: $tType] : ( TA > TA > TA ) ).

thf(zero_neq_one_of_bool_type,type,
    zero_neq_one_of_bool: 
      !>[TA: $tType] : ( $o > TA ) ).

thf(x_type,type,
    x: binDag_Mirabelle_dag ).

thf(y_type,type,
    y: binDag_Mirabelle_dag ).

thf(z_type,type,
    z: binDag_Mirabelle_dag ).

thf(239,axiom,
    ! [TA: $tType] :
      ( ( dense_linorder @ TA @ ( type2 @ 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_100_dense__ge) ).

thf(1036,plain,
    ! [TA: $tType] :
      ( ( dense_linorder @ TA @ ( type2 @ 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)],[239]) ).

thf(171,axiom,
    ( ( binDag1924123185ze_dag @ binDag_Mirabelle_Tip )
    = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_dag_Osize__gen_I1_J) ).

thf(809,plain,
    ( ( binDag1924123185ze_dag @ binDag_Mirabelle_Tip )
    = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(28,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_less__imp__not__less) ).

thf(347,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(123,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( A
           != ( zero_zero @ TA ) )
         => ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_gr__zeroI) ).

thf(666,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( A
           != ( zero_zero @ TA ) )
         => ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(30,axiom,
    ! [A: binDag_Mirabelle_dag] :
      ~ ( binDag786255756subdag @ binDag_Mirabelle_Tip @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_subdag_Osimps_I1_J) ).

thf(352,plain,
    ! [A: binDag_Mirabelle_dag] :
      ~ ( binDag786255756subdag @ binDag_Mirabelle_Tip @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(206,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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_110_dual__order_Ostrict__trans1) ).

thf(909,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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)],[206]) ).

thf(23,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ 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_59_less__trans) ).

thf(333,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ 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)],[23]) ).

thf(237,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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_14_antisym) ).

thf(1031,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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)],[237]) ).

thf(255,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ B @ A ) )
            = ( ord_less_eq @ TA @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_le__divide__eq__1__pos) ).

thf(1083,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ B @ A ) )
            = ( ord_less_eq @ TA @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(216,axiom,
    ord_less_eq @ binDag_Mirabelle_dag @ y @ z,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_y__z) ).

thf(962,plain,
    ord_less_eq @ binDag_Mirabelle_dag @ y @ z,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(146,axiom,
    ! [TA: $tType] :
      ( ( zero_less_one @ TA @ ( type2 @ TA ) )
     => ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_zero__less__one) ).

thf(730,plain,
    ! [TA: $tType] :
      ( ( zero_less_one @ TA @ ( type2 @ TA ) )
     => ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(249,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_le__zero__eq) ).

thf(1068,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(251,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ 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_98_le__less__trans) ).

thf(1073,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ 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)],[251]) ).

thf(193,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_121_pinf_I8_J) ).

thf(873,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[193]) ).

thf(120,axiom,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA] :
      ( ( ordering @ TA @ A @ B )
     => ~ ( B @ C @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_ordering_Oirrefl) ).

thf(655,plain,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA] :
      ( ( ordering @ TA @ A @ B )
     => ~ ( B @ C @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(102,axiom,
    ! [TA: $tType] :
      ( ( semidom_divide @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( divide_divide @ TA @ A @ ( one_one @ TA ) )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_divide__1) ).

thf(597,plain,
    ! [TA: $tType] :
      ( ( semidom_divide @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( divide_divide @ TA @ A @ ( one_one @ TA ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(51,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA @ ( type2 @ TA ) )
        & ( ord @ TB @ ( type2 @ 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_40_ord__less__eq__subst) ).

thf(408,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA @ ( type2 @ TA ) )
        & ( ord @ TB @ ( type2 @ 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)],[51]) ).

thf(222,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) )
            = ( ord_less_eq @ TA @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_divide__le__eq__1__neg) ).

thf(977,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) )
            = ( ord_less_eq @ TA @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(253,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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_16_dual__order_Oantisym) ).

thf(1078,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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)],[253]) ).

thf(43,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_133_minf_I5_J) ).

thf(384,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[43]) ).

thf(79,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) )
          = ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_zero__less__divide__1__iff) ).

thf(533,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) )
          = ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(173,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ B @ A ) )
            = ( ord_less @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_less__divide__eq__1__neg) ).

thf(814,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ B @ A ) )
            = ( ord_less @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(136,axiom,
    ! [A: binDag_Mirabelle_dag,B: simpl_ref,C: binDag_Mirabelle_dag] :
      ( binDag_Mirabelle_Tip
     != ( binDag476092410e_Node @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_dag_Odistinct_I1_J) ).

thf(698,plain,
    ! [A: binDag_Mirabelle_dag,B: simpl_ref,C: binDag_Mirabelle_dag] :
      ( binDag_Mirabelle_Tip
     != ( binDag476092410e_Node @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(247,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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_24_antisym__conv) ).

thf(1063,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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)],[247]) ).

thf(81,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ A )
          = ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_neg__less__pos) ).

thf(538,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ A )
          = ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(125,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_74_linorder__cases) ).

thf(670,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[125]) ).

thf(202,axiom,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
          = ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_neg__le__iff__le) ).

thf(898,plain,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
          = ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(162,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ B @ C )
         => ( C != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_pinf_I3_J) ).

thf(782,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ B @ C )
         => ( C != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(54,axiom,
    ! [TA: $tType] :
      ( ( division_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
          = ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_division__ring__divide__zero) ).

thf(417,plain,
    ! [TA: $tType] :
      ( ( division_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
          = ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(6,axiom,
    ! [TA: $tType,A: TA,B: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > TA > TA > TA,C: binDag_Mirabelle_dag,D: simpl_ref,E: binDag_Mirabelle_dag] :
      ( ( binDag1442713106ec_dag @ TA @ A @ B @ ( binDag476092410e_Node @ C @ D @ E ) )
      = ( B @ C @ D @ E @ ( binDag1442713106ec_dag @ TA @ A @ B @ C ) @ ( binDag1442713106ec_dag @ TA @ A @ B @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_dag_Osimps_I7_J) ).

thf(288,plain,
    ! [TA: $tType,A: TA,B: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > TA > TA > TA,C: binDag_Mirabelle_dag,D: simpl_ref,E: binDag_Mirabelle_dag] :
      ( ( binDag1442713106ec_dag @ TA @ A @ B @ ( binDag476092410e_Node @ C @ D @ E ) )
      = ( B @ C @ D @ E @ ( binDag1442713106ec_dag @ TA @ A @ B @ C ) @ ( binDag1442713106ec_dag @ TA @ A @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(89,axiom,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
          = ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_neg__less__iff__less) ).

thf(565,plain,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
          = ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(178,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ 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_88_order__le__less__subst1) ).

thf(829,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ 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)],[178]) ).

thf(260,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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_107_order_Ostrict__trans2) ).

thf(1095,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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)],[260]) ).

thf(144,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TA > TB] :
          ( ! [B: TA,C: TA] :
              ( ( ord_less @ TA @ B @ C )
             => ( ord_less @ TB @ ( A @ B ) @ ( A @ C ) ) )
         => ( order_strict_mono @ TA @ TB @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_strict__monoI) ).

thf(724,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TA > TB] :
          ( ! [B: TA,C: TA] :
              ( ( ord_less @ TA @ B @ C )
             => ( ord_less @ TB @ ( A @ B ) @ ( A @ C ) ) )
         => ( order_strict_mono @ TA @ TB @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(91,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_order_Oasym) ).

thf(570,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(70,axiom,
    ! [A: binDag_Mirabelle_dag > $o,B: binDag_Mirabelle_dag] :
      ( ( A @ binDag_Mirabelle_Tip )
     => ( ! [C: binDag_Mirabelle_dag,D: simpl_ref,E: binDag_Mirabelle_dag] :
            ( ( A @ C )
           => ( ( A @ E )
             => ( A @ ( binDag476092410e_Node @ C @ D @ E ) ) ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_dag_Oinduct) ).

thf(460,plain,
    ! [A: binDag_Mirabelle_dag > $o,B: binDag_Mirabelle_dag] :
      ( ( A @ binDag_Mirabelle_Tip )
     => ( ! [C: binDag_Mirabelle_dag,D: simpl_ref,E: binDag_Mirabelle_dag] :
            ( ( A @ C )
           => ( ( A @ E )
             => ( A @ ( binDag476092410e_Node @ C @ D @ E ) ) ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(209,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ B @ A ) )
            = ( ord_less_eq @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_le__divide__eq__1__neg) ).

thf(917,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ B @ A ) )
            = ( ord_less_eq @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(137,axiom,
    linorder @ $o @ ( type2 @ $o ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_8) ).

thf(702,plain,
    linorder @ $o @ ( type2 @ $o ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(168,axiom,
    ! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag,C: binDag_Mirabelle_dag] :
      ( ( binDag786255756subdag @ A @ B )
     => ( ( binDag786255756subdag @ B @ C )
       => ( binDag786255756subdag @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_subdag__trans) ).

thf(802,plain,
    ! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag,C: binDag_Mirabelle_dag] :
      ( ( binDag786255756subdag @ A @ B )
     => ( ( binDag786255756subdag @ B @ C )
       => ( binDag786255756subdag @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(27,axiom,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( C != D )
       => ( ( A @ C @ D )
         => ( B @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_ordering_Onot__eq__order__implies__strict) ).

thf(344,plain,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( C != D )
       => ( ( A @ C @ D )
         => ( B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(215,axiom,
    ! [TA: $tType] :
      ( ( condit1037483654norder @ TA @ ( type2 @ 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_123_complete__interval) ).

thf(934,plain,
    ! [TA: $tType] :
      ( ( condit1037483654norder @ TA @ ( type2 @ 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)],[215]) ).

thf(32,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_61_less__linear) ).

thf(357,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[32]) ).

thf(174,axiom,
    ! [A: binDag_Mirabelle_dag] :
      ( ( A != binDag_Mirabelle_Tip )
     => ~ ! [B: binDag_Mirabelle_dag,C: simpl_ref,D: binDag_Mirabelle_dag] :
            ( A
           != ( binDag476092410e_Node @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_dag_Oexhaust) ).

thf(817,plain,
    ! [A: binDag_Mirabelle_dag] :
      ( ( A != binDag_Mirabelle_Tip )
     => ~ ! [B: binDag_Mirabelle_dag,C: simpl_ref,D: binDag_Mirabelle_dag] :
            ( A
           != ( binDag476092410e_Node @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(114,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_50_neq__iff) ).

thf(638,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[114]) ).

thf(104,axiom,
    ! [TA: $tType] :
      ( ( zero_neq_one @ TA @ ( type2 @ TA ) )
     => ( ( zero_neq_one_of_bool @ TA )
        = ( ^ [A: $o] : ( if @ TA @ A @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_of__bool__def) ).

thf(606,plain,
    ! [TA: $tType] :
      ( ( zero_neq_one @ TA @ ( type2 @ TA ) )
     => ( ( zero_neq_one_of_bool @ TA )
        = ( ^ [A: $o] : ( if @ TA @ A @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(65,axiom,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA,E: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( A @ C @ D )
       => ( ( A @ D @ E )
         => ( A @ C @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_ordering_Otrans) ).

thf(448,plain,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA,E: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( A @ C @ D )
       => ( ( A @ D @ E )
         => ( A @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(16,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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_79_dual__order_Ostrict__trans) ).

thf(316,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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)],[16]) ).

thf(262,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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_106_order_Ostrict__trans1) ).

thf(1100,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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)],[262]) ).

thf(4,axiom,
    ! [A: $o] :
      ( ( A = $true )
      | ( A = $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).

thf(284,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(158,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ( sgn_sgn @ TA @ A )
            = ( one_one @ TA ) )
          = ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_sgn__1__pos) ).

thf(770,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ( sgn_sgn @ TA @ A )
            = ( one_one @ TA ) )
          = ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(196,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ A )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_neg__less__eq__nonneg) ).

thf(881,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ A )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(53,axiom,
    wellorder @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).

thf(416,plain,
    wellorder @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(212,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TA > TB] :
          ( ! [B: TA,C: TA] :
              ( ( ord_less_eq @ TA @ B @ C )
             => ( ord_less_eq @ TB @ ( A @ C ) @ ( A @ B ) ) )
         => ( order_antimono @ TA @ TB @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_antimonoI) ).

thf(924,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TA > TB] :
          ( ! [B: TA,C: TA] :
              ( ( ord_less_eq @ TA @ B @ C )
             => ( ord_less_eq @ TB @ ( A @ C ) @ ( A @ B ) ) )
         => ( order_antimono @ TA @ TB @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(100,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ A ) )
          = ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_less__neg__neg) ).

thf(591,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ A ) )
          = ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(62,axiom,
    ! [TA: $tType] :
      ( ( field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( divide_divide @ TA @ A @ B )
            = ( divide_divide @ TA @ A @ C ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            | ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_divide__cancel__left) ).

thf(443,plain,
    ! [TA: $tType] :
      ( ( field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( divide_divide @ TA @ A @ B )
            = ( divide_divide @ TA @ A @ C ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            | ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(266,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( ( ord_less_eq @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less @ TA @ A @ B )
              | ( B = A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_dual__order_Oorder__iff__strict) ).

thf(1109,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( ( ord_less_eq @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less @ TA @ A @ B )
              | ( B = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(40,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA @ ( type2 @ 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_65_ord__less__eq__trans) ).

thf(376,plain,
    ! [TA: $tType] :
      ( ( ord @ TA @ ( type2 @ 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)],[40]) ).

thf(117,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( A != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_less__imp__neq) ).

thf(646,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(93,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ B @ A ) )
            = ( ord_less @ TA @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_less__divide__eq__1__pos) ).

thf(574,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ B @ A ) )
            = ( ord_less @ TA @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(218,axiom,
    ! [TA: $tType] :
      ( ( dense_linorder @ TA @ ( type2 @ 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_113_dense__le__bounded) ).

thf(966,plain,
    ! [TA: $tType] :
      ( ( dense_linorder @ TA @ ( type2 @ 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)],[218]) ).

thf(175,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_15_linear) ).

thf(821,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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(276,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_96_antisym__conv1) ).

thf(1136,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[276]) ).

thf(180,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ~ ( ord_less @ TA @ A @ B ) )
          = ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_not__less) ).

thf(834,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ~ ( ord_less @ TA @ A @ B ) )
          = ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(1,conjecture,
    ord_less_eq @ binDag_Mirabelle_dag @ x @ z,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( ord_less_eq @ binDag_Mirabelle_dag @ x @ z ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(280,plain,
    ~ ( ord_less_eq @ binDag_Mirabelle_dag @ x @ z ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(148,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( one_one @ TA )
            = ( divide_divide @ TA @ A @ B ) )
          = ( ( B
             != ( zero_zero @ TA ) )
            & ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_eq__divide__eq__1) ).

thf(734,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( one_one @ TA )
            = ( divide_divide @ TA @ A @ B ) )
          = ( ( B
             != ( zero_zero @ TA ) )
            & ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(46,axiom,
    ! [TA: $tType] :
      ( ( wellorder @ TA @ ( type2 @ 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_70_less__induct) ).

thf(396,plain,
    ! [TA: $tType] :
      ( ( wellorder @ TA @ ( type2 @ 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)],[46]) ).

thf(121,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( divide_divide @ TA @ A @ B )
            = ( one_one @ TA ) )
          = ( ( B
             != ( zero_zero @ TA ) )
            & ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_divide__eq__eq__1) ).

thf(660,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( divide_divide @ TA @ A @ B )
            = ( one_one @ TA ) )
          = ( ( B
             != ( zero_zero @ TA ) )
            & ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(264,axiom,
    ! [TA: $tType] :
      ( ( linord1659791738miring @ TA @ ( type2 @ TA ) )
     => ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_zero__le__one) ).

thf(1104,plain,
    ! [TA: $tType] :
      ( ( linord1659791738miring @ TA @ ( type2 @ TA ) )
     => ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(67,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).

thf(452,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(210,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_dual__order_Ostrict__implies__order) ).

thf(920,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(41,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_49_neqE) ).

thf(380,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[41]) ).

thf(61,axiom,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( B @ C @ D )
       => ( C != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_ordering_Ostrict__implies__not__eq) ).

thf(439,plain,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( B @ C @ D )
       => ( C != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(76,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_not__less__zero) ).

thf(529,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(84,axiom,
    linorder @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).

thf(546,plain,
    linorder @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(242,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( ( ord_less_eq @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less @ TA @ A @ B )
              | ( A = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_le__less) ).

thf(1047,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( ( ord_less_eq @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less @ TA @ A @ B )
              | ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(201,axiom,
    ! [TA: $tType] :
      ( ( dense_linorder @ TA @ ( type2 @ 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_112_dense__ge__bounded) ).

thf(894,plain,
    ! [TA: $tType] :
      ( ( dense_linorder @ TA @ ( type2 @ 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)],[201]) ).

thf(152,axiom,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ A ) )
          = ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_neg__0__less__iff__less) ).

thf(746,plain,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ A ) )
          = ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(241,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o,B: TA] :
          ( ( A @ B )
         => ( ! [C: TA] :
                ( ( A @ C )
               => ( ord_less_eq @ TA @ B @ C ) )
           => ( ( ord_Least @ TA @ A )
              = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Least__equality) ).

thf(1042,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o,B: TA] :
          ( ( A @ B )
         => ( ! [C: TA] :
                ( ( A @ C )
               => ( ord_less_eq @ TA @ B @ C ) )
           => ( ( ord_Least @ TA @ A )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(9,axiom,
    ! [A: binDag_Mirabelle_dag,B: simpl_ref,C: binDag_Mirabelle_dag,D: binDag_Mirabelle_dag,E: simpl_ref,F: binDag_Mirabelle_dag] :
      ( ( ( binDag476092410e_Node @ A @ B @ C )
        = ( binDag476092410e_Node @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_dag_Oinject) ).

thf(297,plain,
    ! [A: binDag_Mirabelle_dag,B: simpl_ref,C: binDag_Mirabelle_dag,D: binDag_Mirabelle_dag,E: simpl_ref,F: binDag_Mirabelle_dag] :
      ( ( ( binDag476092410e_Node @ A @ B @ C )
        = ( binDag476092410e_Node @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(134,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_less__asym_H) ).

thf(693,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(57,axiom,
    ! [TA: $tType] :
      ( ( semidom_divide @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( divide_divide @ TA @ ( zero_zero @ TA ) @ A )
          = ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_divide__zero__left) ).

thf(429,plain,
    ! [TA: $tType] :
      ( ( semidom_divide @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( divide_divide @ TA @ ( zero_zero @ TA ) @ A )
          = ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(165,axiom,
    ! [TA: $tType] :
      ( ( no_bot @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] : ( ord_less @ TA @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_lt__ex) ).

thf(788,plain,
    ! [TA: $tType] :
      ( ( no_bot @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] : ( ord_less @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(271,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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_103_le__imp__less__or__eq) ).

thf(1123,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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)],[271]) ).

thf(190,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_order_Ostrict__implies__order) ).

thf(862,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(29,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) )
            = ( ord_less @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_divide__less__eq__1__pos) ).

thf(349,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) )
            = ( ord_less @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(195,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ 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_99_less__le__trans) ).

thf(879,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ 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(130,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ 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_41_order__less__subst1) ).

thf(682,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ 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)],[130]) ).

thf(183,axiom,
    ! [TA: $tType] :
      ( ( dense_linorder @ TA @ ( type2 @ 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_101_dense__le) ).

thf(842,plain,
    ! [TA: $tType] :
      ( ( dense_linorder @ TA @ ( type2 @ 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)],[183]) ).

thf(97,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ( ( order_strict_mono @ TA @ TB )
        = ( ^ [A: TA > TB] :
            ! [B: TA,C: TA] :
              ( ( ord_less @ TA @ B @ C )
             => ( ord_less @ TB @ ( A @ B ) @ ( A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_strict__mono__def) ).

thf(583,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ( ( order_strict_mono @ TA @ TB )
        = ( ^ [A: TA > TB] :
            ! [B: TA,C: TA] :
              ( ( ord_less @ TA @ B @ C )
             => ( ord_less @ TB @ ( A @ B ) @ ( A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(73,axiom,
    ! [A: binDag_Mirabelle_dag,B: simpl_ref,C: binDag_Mirabelle_dag,D: binDag_Mirabelle_dag] :
      ( ( binDag786255756subdag @ ( binDag476092410e_Node @ A @ B @ C ) @ D )
      = ( ( D = A )
        | ( D = C )
        | ( binDag786255756subdag @ A @ D )
        | ( binDag786255756subdag @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_subdag_Osimps_I2_J) ).

thf(522,plain,
    ! [A: binDag_Mirabelle_dag,B: simpl_ref,C: binDag_Mirabelle_dag,D: binDag_Mirabelle_dag] :
      ( ( binDag786255756subdag @ ( binDag476092410e_Node @ A @ B @ C ) @ D )
      = ( ( D = A )
        | ( D = C )
        | ( binDag786255756subdag @ A @ D )
        | ( binDag786255756subdag @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(86,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_137_minf_I1_J) ).

thf(551,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[86]) ).

thf(273,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ( ( order_antimono @ TA @ TB )
        = ( ^ [A: TA > TB] :
            ! [B: TA,C: TA] :
              ( ( ord_less_eq @ TA @ B @ C )
             => ( ord_less_eq @ TB @ ( A @ C ) @ ( A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_antimono__def) ).

thf(1128,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ( ( order_antimono @ TA @ TB )
        = ( ^ [A: TA > TB] :
            ! [B: TA,C: TA] :
              ( ( ord_less_eq @ TA @ B @ C )
             => ( ord_less_eq @ TB @ ( A @ C ) @ ( A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(5,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).

thf(285,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(265,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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_118_order_Onot__eq__order__implies__strict) ).

thf(1106,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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)],[265]) ).

thf(279,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ 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_5_le__funD) ).

thf(1143,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ 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)],[279]) ).

thf(118,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TA @ ( type2 @ TA ) )
     => ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).

thf(650,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TA @ ( type2 @ TA ) )
     => ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(107,axiom,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( zero_zero @ TA ) )
          = ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_neg__less__0__iff__less) ).

thf(615,plain,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( zero_zero @ TA ) )
          = ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(232,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_zero__le__divide__1__iff) ).

thf(1006,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(188,axiom,
    ! [TA: $tType] :
      ( ( linordered_semidom @ TA @ ( type2 @ TA ) )
     => ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_le__numeral__extra_I4_J) ).

thf(857,plain,
    ! [TA: $tType] :
      ( ( linordered_semidom @ TA @ ( type2 @ TA ) )
     => ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(223,axiom,
    x = y,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_True) ).

thf(980,plain,
    x = y,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(49,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] : ( ord_less @ TA @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_linordered__field__no__lb) ).

thf(403,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] : ( ord_less @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(55,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_less__asym) ).

thf(420,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(269,axiom,
    ! [TA: $tType] :
      ( ( linordered_semidom @ TA @ ( type2 @ TA ) )
     => ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_le__numeral__extra_I1_J) ).

thf(1118,plain,
    ! [TA: $tType] :
      ( ( linordered_semidom @ TA @ ( type2 @ TA ) )
     => ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(197,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ~ ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_le__minus__one__simps_I4_J) ).

thf(884,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ~ ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(236,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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_94_le__neq__trans) ).

thf(1028,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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)],[236]) ).

thf(25,axiom,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( A @ C @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_ordering_Orefl) ).

thf(339,plain,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( A @ C @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(154,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_132_minf_I7_J) ).

thf(753,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[154]) ).

thf(124,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ TB ) )
     => ! [A: TA] :
        ? [B: TB] :
        ! [C: TB] :
          ( ( ord_less @ TB @ C @ B )
         => ( A = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_minf_I11_J) ).

thf(669,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(85,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( A != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__imp__not__eq) ).

thf(547,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(203,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_leD) ).

thf(901,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(252,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ 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_90_order__less__le__subst1) ).

thf(1075,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ 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)],[252]) ).

thf(72,axiom,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o] :
      ( ! [C: TA,D: TA] :
          ( ( A @ C @ D )
          = ( ( B @ C @ D )
            & ( C != D ) ) )
     => ( ! [C: TA] : ( B @ C @ C )
       => ( ! [C: TA,D: TA] :
              ( ( B @ C @ D )
             => ( ( B @ D @ C )
               => ( C = D ) ) )
         => ( ! [C: TA,D: TA,E: TA] :
                ( ( B @ C @ D )
               => ( ( B @ D @ E )
                 => ( B @ C @ E ) ) )
           => ( ordering @ TA @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_ordering_Ointro) ).

thf(476,plain,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o] :
      ( ! [C: TA,D: TA] :
          ( ( A @ C @ D )
          = ( ( B @ C @ D )
            & ( C != D ) ) )
     => ( ! [C: TA] : ( B @ C @ C )
       => ( ! [C: TA,D: TA] :
              ( ( B @ C @ D )
             => ( ( B @ D @ C )
               => ( C = D ) ) )
         => ( ! [C: TA,D: TA,E: TA] :
                ( ( B @ C @ D )
               => ( ( B @ D @ E )
                 => ( B @ C @ E ) ) )
           => ( ordering @ TA @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(128,axiom,
    ! [TA: $tType] :
      ( ( condit1656338222tinuum @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] :
          ( ( ord_less @ TA @ A @ B )
          | ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_ex__gt__or__lt) ).

thf(679,plain,
    ! [TA: $tType] :
      ( ( condit1656338222tinuum @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] :
          ( ( ord_less @ TA @ A @ B )
          | ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(240,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( ( ord_less @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( A != B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_order_Ostrict__iff__order) ).

thf(1039,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( ( ord_less @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( A != B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(219,axiom,
    ( ( ord_less_eq @ binDag_Mirabelle_dag )
    = ( ^ [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag] :
          ( ( A = B )
          | ( ord_less @ binDag_Mirabelle_dag @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_le__dag__def) ).

thf(970,plain,
    ( ( ord_less_eq @ binDag_Mirabelle_dag )
    = ( ^ [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag] :
          ( ( A = B )
          | ( ord_less @ binDag_Mirabelle_dag @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(268,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA @ ( type2 @ 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_22_ord__le__eq__trans) ).

thf(1114,plain,
    ! [TA: $tType] :
      ( ( ord @ TA @ ( type2 @ 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)],[268]) ).

thf(228,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) @ ( zero_zero @ TA ) )
          = ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_divide__le__0__1__iff) ).

thf(997,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) @ ( zero_zero @ TA ) )
          = ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(274,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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_13_eq__iff) ).

thf(1131,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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)],[274]) ).

thf(207,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ 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_91_order__less__le__subst2) ).

thf(911,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ 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)],[207]) ).

thf(230,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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_111_dual__order_Ostrict__trans2) ).

thf(1002,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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)],[230]) ).

thf(38,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).

thf(371,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(109,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TA > TB,B: TA,C: TA] :
          ( ( order_strict_mono @ TA @ TB @ A )
         => ( ( ord_less @ TA @ B @ C )
           => ( ord_less @ TB @ ( A @ B ) @ ( A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_strict__monoD) ).

thf(622,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TA > TB,B: TA,C: TA] :
          ( ( order_strict_mono @ TA @ TB @ A )
         => ( ( ord_less @ TA @ B @ C )
           => ( ord_less @ TB @ ( A @ B ) @ ( A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(181,axiom,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( zero_zero @ TA ) )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_neg__le__0__iff__le) ).

thf(837,plain,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( zero_zero @ TA ) )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(243,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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_17_dual__order_Otrans) ).

thf(1050,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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)],[243]) ).

thf(69,axiom,
    ! [TA: $tType] :
      ( ( field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( divide_divide @ TA @ A @ B )
            = ( divide_divide @ TA @ C @ B ) )
          = ( ( B
              = ( zero_zero @ TA ) )
            | ( A = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_divide__cancel__right) ).

thf(457,plain,
    ! [TA: $tType] :
      ( ( field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( divide_divide @ TA @ A @ B )
            = ( divide_divide @ TA @ C @ B ) )
          = ( ( B
              = ( zero_zero @ TA ) )
            | ( A = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(256,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TA > TB,B: TA,C: TA] :
          ( ( order_antimono @ TA @ TB @ A )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TB @ ( A @ C ) @ ( A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_antimonoD) ).

thf(1086,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TA > TB,B: TA,C: TA] :
          ( ( order_antimono @ TA @ TB @ A )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TB @ ( A @ C ) @ ( A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(33,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ~ ( ord_less @ TA @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_dual__order_Oirrefl) ).

thf(360,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ~ ( ord_less @ TA @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(169,axiom,
    ! [TA: $tType] :
      ( ( linordered_semidom @ TA @ ( type2 @ TA ) )
     => ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_less__numeral__extra_I4_J) ).

thf(805,plain,
    ! [TA: $tType] :
      ( ( linordered_semidom @ TA @ ( type2 @ TA ) )
     => ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(14,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ( ord_less @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( one_one @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_less__minus__one__simps_I2_J) ).

thf(311,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ( ord_less @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( one_one @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(82,axiom,
    ! [TA: $tType,A: TA,B: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > TA] :
      ( ( binDag1297733282se_dag @ TA @ A @ B @ binDag_Mirabelle_Tip )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_dag_Osimps_I4_J) ).

thf(541,plain,
    ! [TA: $tType,A: TA,B: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > TA] :
      ( ( binDag1297733282se_dag @ TA @ A @ B @ binDag_Mirabelle_Tip )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(245,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA @ ( type2 @ TA ) )
        & ( ord @ TB @ ( type2 @ 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_11_ord__eq__le__subst) ).

thf(1054,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA @ ( type2 @ TA ) )
        & ( ord @ TB @ ( type2 @ 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)],[245]) ).

thf(250,axiom,
    ! [TA: $tType] :
      ( ( linordered_semidom @ TA @ ( type2 @ TA ) )
     => ~ ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_le__numeral__extra_I2_J) ).

thf(1071,plain,
    ! [TA: $tType] :
      ( ( linordered_semidom @ TA @ ( type2 @ TA ) )
     => ~ ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(235,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_27_le__cases) ).

thf(1026,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[235]) ).

thf(199,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ 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_8_le__fun__def) ).

thf(888,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ 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)],[199]) ).

thf(159,axiom,
    ! [TA: $tType,A: TA,B: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > TA > TA > TA] :
      ( ( binDag1442713106ec_dag @ TA @ A @ B @ binDag_Mirabelle_Tip )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_dag_Osimps_I6_J) ).

thf(773,plain,
    ! [TA: $tType,A: TA,B: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > TA > TA > TA] :
      ( ( binDag1442713106ec_dag @ TA @ A @ B @ binDag_Mirabelle_Tip )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(98,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_dual__order_Oasym) ).

thf(586,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(108,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( B != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_less__imp__not__eq2) ).

thf(618,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( B != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(133,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( B != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_dual__order_Ostrict__implies__not__eq) ).

thf(689,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( B != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(147,axiom,
    ! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_4) ).

thf(732,plain,
    ! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(151,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( sgn_sgn @ TA @ ( sgn_sgn @ TA @ A ) )
          = ( sgn_sgn @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_sgn__sgn) ).

thf(743,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( sgn_sgn @ TA @ ( sgn_sgn @ TA @ A ) )
          = ( sgn_sgn @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(3,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).

thf(281,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(88,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( linorder @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TA > TB,B: TA,C: TA] :
          ( ( order_strict_mono @ TA @ TB @ A )
         => ( ( ( A @ B )
              = ( A @ C ) )
            = ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_strict__mono__eq) ).

thf(562,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( linorder @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TA > TB,B: TA,C: TA] :
          ( ( order_strict_mono @ TA @ TB @ A )
         => ( ( ( A @ B )
              = ( A @ C ) )
            = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(221,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_order__refl) ).

thf(975,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(194,axiom,
    ! [TA: $tType] :
      ( ( wellorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o,B: TA,C: TA > $o] :
          ( ( A @ B )
         => ( ! [D: TA] :
                ( ( A @ D )
               => ( ! [E: TA] :
                      ( ( A @ E )
                     => ( ord_less_eq @ TA @ D @ E ) )
                 => ( C @ D ) ) )
           => ( C @ ( ord_Least @ TA @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_LeastI2__wellorder) ).

thf(875,plain,
    ! [TA: $tType] :
      ( ( wellorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o,B: TA,C: TA > $o] :
          ( ( A @ B )
         => ( ! [D: TA] :
                ( ( A @ D )
               => ( ! [E: TA] :
                      ( ( A @ E )
                     => ( ord_less_eq @ TA @ D @ E ) )
                 => ( C @ D ) ) )
           => ( C @ ( ord_Least @ TA @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(177,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_97_antisym__conv2) ).

thf(826,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[177]) ).

thf(94,axiom,
    ! [TA: $tType] :
      ( ( linordered_semidom @ TA @ ( type2 @ TA ) )
     => ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_less__numeral__extra_I2_J) ).

thf(577,plain,
    ! [TA: $tType] :
      ( ( linordered_semidom @ TA @ ( type2 @ TA ) )
     => ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(95,axiom,
    order @ $o @ ( type2 @ $o ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_9) ).

thf(579,plain,
    order @ $o @ ( type2 @ $o ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(7,axiom,
    ! [TA: $tType] :
      ( ( zero_neq_one @ TA @ ( type2 @ TA ) )
     => ( ( zero_neq_one_of_bool @ TA @ $false )
        = ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_of__bool__eq_I1_J) ).

thf(291,plain,
    ! [TA: $tType] :
      ( ( zero_neq_one @ TA @ ( type2 @ TA ) )
     => ( ( zero_neq_one_of_bool @ TA @ $false )
        = ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(115,axiom,
    ! [TA: $tType] :
      ( ( linordered_semidom @ TA @ ( type2 @ TA ) )
     => ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_less__numeral__extra_I1_J) ).

thf(641,plain,
    ! [TA: $tType] :
      ( ( linordered_semidom @ TA @ ( type2 @ TA ) )
     => ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(277,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_zero__le) ).

thf(1139,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(92,axiom,
    ! [TA: $tType] :
      ( ( no_top @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] : ( ord_less @ TA @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_gt__ex) ).

thf(572,plain,
    ! [TA: $tType] :
      ( ( no_top @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] : ( ord_less @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(15,axiom,
    ! [TA: $tType] :
      ( ( zero_neq_one @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o,B: $o] :
          ( ( A @ ( zero_neq_one_of_bool @ TA @ B ) )
          = ( ( B
             => ( A @ ( one_one @ TA ) ) )
            & ( ~ B
             => ( A @ ( zero_zero @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_split__of__bool) ).

thf(313,plain,
    ! [TA: $tType] :
      ( ( zero_neq_one @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o,B: $o] :
          ( ( A @ ( zero_neq_one_of_bool @ TA @ B ) )
          = ( ( B
             => ( A @ ( one_one @ TA ) ) )
            & ( ~ B
             => ( A @ ( zero_zero @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(164,axiom,
    binDag_Mirabelle_DAG @ binDag_Mirabelle_Tip,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_DAG_Osimps_I1_J) ).

thf(787,plain,
    binDag_Mirabelle_DAG @ binDag_Mirabelle_Tip,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(24,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ C @ B )
         => ( C != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_minf_I4_J) ).

thf(335,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ C @ B )
         => ( C != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(258,axiom,
    ! [TA: $tType] :
      ( ( wellorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o,B: TA > $o] :
          ( ? [C: TA] : ( A @ C )
         => ( ! [C: TA] :
                ( ( A @ C )
               => ( ! [D: TA] :
                      ( ( A @ D )
                     => ( ord_less_eq @ TA @ C @ D ) )
                 => ( B @ C ) ) )
           => ( B @ ( ord_Least @ TA @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_LeastI2__wellorder__ex) ).

thf(1090,plain,
    ! [TA: $tType] :
      ( ( wellorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o,B: TA > $o] :
          ( ? [C: TA] : ( A @ C )
         => ( ! [C: TA] :
                ( ( A @ C )
               => ( ! [D: TA] :
                      ( ( A @ D )
                     => ( ord_less_eq @ TA @ C @ D ) )
                 => ( B @ C ) ) )
           => ( B @ ( ord_Least @ TA @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(156,axiom,
    ! [TA: $tType] :
      ( ( field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( one_one @ TA )
            = ( divide_divide @ TA @ A @ B ) )
          = ( ( B
             != ( zero_zero @ TA ) )
            & ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_one__eq__divide__iff) ).

thf(764,plain,
    ! [TA: $tType] :
      ( ( field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( one_one @ TA )
            = ( divide_divide @ TA @ A @ B ) )
          = ( ( B
             != ( zero_zero @ TA ) )
            & ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(129,axiom,
    zero_less_one @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ozero__less__one) ).

thf(681,plain,
    zero_less_one @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(34,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_less__not__sym) ).

thf(362,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ~ ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(59,axiom,
    ! [TA: $tType] :
      ( ( field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( divide_divide @ TA @ A @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
          = ( uminus_uminus @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_divide__minus1) ).

thf(434,plain,
    ! [TA: $tType] :
      ( ( field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( divide_divide @ TA @ A @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
          = ( uminus_uminus @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(11,axiom,
    ! [TA: $tType,A: TA,B: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > TA,C: binDag_Mirabelle_dag,D: simpl_ref,E: binDag_Mirabelle_dag] :
      ( ( binDag1297733282se_dag @ TA @ A @ B @ ( binDag476092410e_Node @ C @ D @ E ) )
      = ( B @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_dag_Osimps_I5_J) ).

thf(303,plain,
    ! [TA: $tType,A: TA,B: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > TA,C: binDag_Mirabelle_dag,D: simpl_ref,E: binDag_Mirabelle_dag] :
      ( ( binDag1297733282se_dag @ TA @ A @ B @ ( binDag476092410e_Node @ C @ D @ E ) )
      = ( B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(149,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
          = ( A
           != ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_zero__less__iff__neq__zero) ).

thf(737,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
          = ( A
           != ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(17,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( B
           != ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_gr__implies__not__zero) ).

thf(318,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( B
           != ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(112,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ B @ C )
         => ( C != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_pinf_I4_J) ).

thf(631,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ B @ C )
         => ( C != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(36,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) @ ( zero_zero @ TA ) )
          = ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_divide__less__0__1__iff) ).

thf(367,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) @ ( zero_zero @ TA ) )
          = ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(105,axiom,
    ! [TA: $tType] :
      ( ( semidom_divide @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( A
           != ( zero_zero @ TA ) )
         => ( ( divide_divide @ TA @ A @ A )
            = ( one_one @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_div__self) ).

thf(609,plain,
    ! [TA: $tType] :
      ( ( semidom_divide @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( A
           != ( zero_zero @ TA ) )
         => ( ( divide_divide @ TA @ A @ A )
            = ( one_one @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(19,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( sgn_sgn @ TA @ A ) @ ( zero_zero @ TA ) )
          = ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_sgn__less) ).

thf(323,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( sgn_sgn @ TA @ A ) @ ( zero_zero @ TA ) )
          = ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(101,axiom,
    ! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag,C: simpl_ref,D: binDag_Mirabelle_dag] :
      ( ( binDag786255756subdag @ A @ ( binDag476092410e_Node @ B @ C @ D ) )
     => ( ( binDag786255756subdag @ A @ B )
        & ( binDag786255756subdag @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_subdag__NodeD) ).

thf(594,plain,
    ! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag,C: simpl_ref,D: binDag_Mirabelle_dag] :
      ( ( binDag786255756subdag @ A @ ( binDag476092410e_Node @ B @ C @ D ) )
     => ( ( binDag786255756subdag @ A @ B )
        & ( binDag786255756subdag @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(167,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( sgn_sgn @ TA @ A )
            = ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_sgn__neg) ).

thf(799,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( sgn_sgn @ TA @ A )
            = ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(185,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ 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_89_order__le__less__subst2) ).

thf(848,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ 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)],[185]) ).

thf(22,axiom,
    ! [TA: $tType] :
      ( ( dense_order @ TA @ ( type2 @ 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_52_dense) ).

thf(330,plain,
    ! [TA: $tType] :
      ( ( dense_order @ TA @ ( type2 @ 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)],[22]) ).

thf(267,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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_26_order_Otrans) ).

thf(1112,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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)],[267]) ).

thf(172,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( sgn_sgn @ TA @ A ) )
          = ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_sgn__greater) ).

thf(811,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( sgn_sgn @ TA @ A ) )
          = ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(45,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_136_minf_I2_J) ).

thf(387,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[45]) ).

thf(214,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ 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_6_le__funE) ).

thf(932,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ 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)],[214]) ).

thf(246,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less @ TA @ A @ B )
         => ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_leI) ).

thf(1061,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less @ TA @ A @ B )
         => ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(131,axiom,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( A @ C @ D )
        = ( ( B @ C @ D )
          | ( C = D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_ordering_Oorder__iff__strict) ).

thf(685,plain,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( A @ C @ D )
        = ( ( B @ C @ D )
          | ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(47,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_139_pinf_I7_J) ).

thf(399,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[47]) ).

thf(135,axiom,
    ! [TA: $tType] :
      ( ( field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( divide_divide @ TA @ A @ B )
            = ( zero_zero @ TA ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            | ( B
              = ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_divide__eq__0__iff) ).

thf(695,plain,
    ! [TA: $tType] :
      ( ( field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( divide_divide @ TA @ A @ B )
            = ( zero_zero @ TA ) )
          = ( ( A
              = ( zero_zero @ TA ) )
            | ( B
              = ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(248,axiom,
    ! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag] :
      ( ( binDag786255756subdag @ A @ B )
     => ( ord_less @ nat @ ( size_size @ binDag_Mirabelle_dag @ B ) @ ( size_size @ binDag_Mirabelle_dag @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_subdag__size) ).

thf(1066,plain,
    ! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag] :
      ( ( binDag786255756subdag @ A @ B )
     => ( ord_less @ nat @ ( size_size @ binDag_Mirabelle_dag @ B ) @ ( size_size @ binDag_Mirabelle_dag @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(161,axiom,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( B @ C @ D )
       => ~ ( B @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_ordering_Oasym) ).

thf(780,plain,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( B @ C @ D )
       => ~ ( B @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(229,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
          | ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_le__less__linear) ).

thf(1000,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
          | ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(211,axiom,
    ! [TA: $tType] :
      ( ( linord1659791738miring @ TA @ ( type2 @ TA ) )
     => ~ ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_not__one__le__zero) ).

thf(922,plain,
    ! [TA: $tType] :
      ( ( linord1659791738miring @ TA @ ( type2 @ TA ) )
     => ~ ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(225,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o,B: TA,C: TA > $o] :
          ( ( A @ B )
         => ( ! [D: TA] :
                ( ( A @ D )
               => ( ord_less_eq @ TA @ B @ D ) )
           => ( ! [D: TA] :
                  ( ( A @ D )
                 => ( ! [E: TA] :
                        ( ( A @ E )
                       => ( ord_less_eq @ TA @ D @ E ) )
                   => ( C @ D ) ) )
             => ( C @ ( ord_Least @ TA @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_LeastI2__order) ).

thf(986,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o,B: TA,C: TA > $o] :
          ( ( A @ B )
         => ( ! [D: TA] :
                ( ( A @ D )
               => ( ord_less_eq @ TA @ B @ D ) )
           => ( ! [D: TA] :
                  ( ( A @ D )
                 => ( ! [E: TA] :
                        ( ( A @ E )
                       => ( ord_less_eq @ TA @ D @ E ) )
                   => ( C @ D ) ) )
             => ( C @ ( ord_Least @ TA @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(12,axiom,
    ! [TA: $tType] :
      ( ( wellorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o,B: TA > $o] :
          ( ? [C: TA] : ( A @ C )
         => ( ! [C: TA] :
                ( ( A @ C )
               => ( B @ C ) )
           => ( B @ ( ord_Least @ TA @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_LeastI2__ex) ).

thf(306,plain,
    ! [TA: $tType] :
      ( ( wellorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o,B: TA > $o] :
          ( ? [C: TA] : ( A @ C )
         => ( ! [C: TA] :
                ( ( A @ C )
               => ( B @ C ) )
           => ( B @ ( ord_Least @ TA @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(186,axiom,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ A ) )
          = ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_neg__0__le__iff__le) ).

thf(851,plain,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ A ) )
          = ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(263,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_120_minf_I6_J) ).

thf(1102,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[263]) ).

thf(143,axiom,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA,E: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( B @ C @ D )
       => ( ( A @ D @ E )
         => ( B @ C @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_ordering_Ostrict__trans2) ).

thf(722,plain,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA,E: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( B @ C @ D )
       => ( ( A @ D @ E )
         => ( B @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(238,axiom,
    ! [TA: $tType] :
      ( ( linordered_semidom @ TA @ ( type2 @ TA ) )
     => ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_le__numeral__extra_I3_J) ).

thf(1034,plain,
    ! [TA: $tType] :
      ( ( linordered_semidom @ TA @ ( type2 @ TA ) )
     => ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(127,axiom,
    ! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag] :
      ( ( binDag786255756subdag @ A @ B )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_subdag__neq) ).

thf(675,plain,
    ! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag] :
      ( ( binDag786255756subdag @ A @ B )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(77,axiom,
    condit1037483654norder @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder) ).

thf(531,plain,
    condit1037483654norder @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(122,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ 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_126_linorder__neqE__linordered__idom) ).

thf(663,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ 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)],[122]) ).

thf(213,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_18_linorder__wlog) ).

thf(927,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[213]) ).

thf(275,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ 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_7_le__funI) ).

thf(1134,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ 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)],[275]) ).

thf(31,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_less__minus__one__simps_I4_J) ).

thf(355,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(176,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ A ) )
          = ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_less__eq__neg__nonpos) ).

thf(823,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ A ) )
          = ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(254,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_119_minf_I8_J) ).

thf(1081,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[254]) ).

thf(153,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA @ ( type2 @ 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_64_ord__eq__less__trans) ).

thf(749,plain,
    ! [TA: $tType] :
      ( ( ord @ TA @ ( type2 @ 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)],[153]) ).

thf(160,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( A != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_order_Ostrict__implies__not__eq) ).

thf(776,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(74,axiom,
    ! [TA: $tType] :
      ( ( zero_neq_one @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o,B: $o] :
          ( ( A @ ( zero_neq_one_of_bool @ TA @ B ) )
          = ( ~ ( ( B
                  & ~ ( A @ ( one_one @ TA ) ) )
                | ( ~ B
                  & ~ ( A @ ( zero_zero @ TA ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_split__of__bool__asm) ).

thf(525,plain,
    ! [TA: $tType] :
      ( ( zero_neq_one @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o,B: $o] :
          ( ( A @ ( zero_neq_one_of_bool @ TA @ B ) )
          = ( ~ ( ( B
                  & ~ ( A @ ( one_one @ TA ) ) )
                | ( ~ B
                  & ~ ( A @ ( zero_zero @ TA ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(96,axiom,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( A @ C @ D )
       => ( ( A @ D @ C )
         => ( C = D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_ordering_Oantisym) ).

thf(580,plain,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( A @ C @ D )
       => ( ( A @ D @ C )
         => ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(139,axiom,
    ! [TA: $tType] :
      ( ( wellorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o,B: TA,C: TA > $o] :
          ( ( A @ B )
         => ( ! [D: TA] :
                ( ( A @ D )
               => ( C @ D ) )
           => ( C @ ( ord_Least @ TA @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_LeastI2) ).

thf(705,plain,
    ! [TA: $tType] :
      ( ( wellorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o,B: TA,C: TA > $o] :
          ( ( A @ B )
         => ( ! [D: TA] :
                ( ( A @ D )
               => ( C @ D ) )
           => ( C @ ( ord_Least @ TA @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(21,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ 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_42_order__less__subst2) ).

thf(327,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ 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)],[21]) ).

thf(126,axiom,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA,E: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( B @ C @ D )
       => ( ( B @ D @ E )
         => ( B @ C @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_ordering_Ostrict__trans) ).

thf(673,plain,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA,E: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( B @ C @ D )
       => ( ( B @ D @ E )
         => ( B @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(37,axiom,
    preorder @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_1) ).

thf(370,plain,
    preorder @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(141,axiom,
    ! [TA: $tType] :
      ( ( zero_neq_one @ TA @ ( type2 @ TA ) )
     => ( ( zero_zero @ TA )
       != ( one_one @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_zero__neq__one) ).

thf(717,plain,
    ! [TA: $tType] :
      ( ( zero_neq_one @ TA @ ( type2 @ TA ) )
     => ( ( zero_zero @ TA )
       != ( one_one @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(182,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_122_pinf_I6_J) ).

thf(840,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[182]) ).

thf(116,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ( divide_divide @ TA @ ( one_one @ TA ) @ A )
            = ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_one__divide__eq__0__iff) ).

thf(643,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ( divide_divide @ TA @ ( one_one @ TA ) @ A )
            = ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(83,axiom,
    ! [TA: $tType] :
      ( ( linordered_semidom @ TA @ ( type2 @ TA ) )
     => ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_less__numeral__extra_I3_J) ).

thf(544,plain,
    ! [TA: $tType] :
      ( ( linordered_semidom @ TA @ ( type2 @ TA ) )
     => ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(205,axiom,
    ! [A: binDag_Mirabelle_dag] : ( ord_less_eq @ binDag_Mirabelle_dag @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_le__dag__refl) ).

thf(907,plain,
    ! [A: binDag_Mirabelle_dag] : ( ord_less_eq @ binDag_Mirabelle_dag @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(138,axiom,
    ! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_6) ).

thf(703,plain,
    ! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(278,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ 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_20_order__trans) ).

thf(1141,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ 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)],[278]) ).

thf(234,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( ( ord_less @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( A != B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_less__le) ).

thf(1023,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( ( ord_less @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( A != B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(103,axiom,
    ! [TA: $tType] :
      ( ( division_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ( A
              = ( zero_zero @ TA ) )
           => ( ( divide_divide @ TA @ A @ A )
              = ( zero_zero @ TA ) ) )
          & ( ( A
             != ( zero_zero @ TA ) )
           => ( ( divide_divide @ TA @ A @ A )
              = ( one_one @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_divide__self__if) ).

thf(600,plain,
    ! [TA: $tType] :
      ( ( division_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ( A
              = ( zero_zero @ TA ) )
           => ( ( divide_divide @ TA @ A @ A )
              = ( zero_zero @ TA ) ) )
          & ( ( A
             != ( zero_zero @ TA ) )
           => ( ( divide_divide @ TA @ A @ A )
              = ( one_one @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(244,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TA > TB,B: TA,C: TA] :
          ( ( order_antimono @ TA @ TB @ A )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TB @ ( A @ C ) @ ( A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_antimonoE) ).

thf(1052,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TA > TB,B: TA,C: TA] :
          ( ( order_antimono @ TA @ TB @ A )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TB @ ( A @ C ) @ ( A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(191,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA @ ( type2 @ TA ) )
        & ( ord @ TB @ ( type2 @ 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_12_ord__le__eq__subst) ).

thf(864,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA @ ( type2 @ TA ) )
        & ( ord @ TB @ ( type2 @ 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)],[191]) ).

thf(145,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( linorder @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TA > TB,B: TA,C: TA] :
          ( ( order_strict_mono @ TA @ TB @ A )
         => ( ( ord_less @ TB @ ( A @ B ) @ ( A @ C ) )
            = ( ord_less @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_strict__mono__less) ).

thf(727,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( linorder @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TA > TB,B: TA,C: TA] :
          ( ( order_strict_mono @ TA @ TB @ A )
         => ( ( ord_less @ TB @ ( A @ B ) @ ( A @ C ) )
            = ( ord_less @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(63,axiom,
    zero_neq_one @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ozero__neq__one) ).

thf(446,plain,
    zero_neq_one @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(106,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ( sgn_sgn @ TA @ A )
            = ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_sgn__0__0) ).

thf(612,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ( sgn_sgn @ TA @ A )
            = ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(189,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ~ ( ord_less_eq @ TA @ A @ B ) )
          = ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_not__le) ).

thf(859,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ~ ( ord_less_eq @ TA @ A @ B ) )
          = ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(259,axiom,
    ord_less_eq @ binDag_Mirabelle_dag @ x @ y,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_x__y) ).

thf(1094,plain,
    ord_less_eq @ binDag_Mirabelle_dag @ x @ y,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(44,axiom,
    preorder @ $o @ ( type2 @ $o ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_7) ).

thf(386,plain,
    preorder @ $o @ ( type2 @ $o ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(184,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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_21_order__class_Oorder_Oantisym) ).

thf(845,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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)],[184]) ).

thf(111,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ C @ B )
         => ( C != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_minf_I3_J) ).

thf(627,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] :
        ! [C: TA] :
          ( ( ord_less @ TA @ C @ B )
         => ( C != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(66,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ 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_73_less__imp__triv) ).

thf(450,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ 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)],[66]) ).

thf(200,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( ( ord_less_eq @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less @ TA @ A @ B )
              | ( A = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_order_Oorder__iff__strict) ).

thf(891,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( ( ord_less_eq @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less @ TA @ A @ B )
              | ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(272,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less_eq @ TA @ A @ B )
         => ( ord_less @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_not__le__imp__less) ).

thf(1126,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less_eq @ TA @ A @ B )
         => ( ord_less @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(132,axiom,
    no_top @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Ono__top) ).

thf(688,plain,
    no_top @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(204,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA @ ( type2 @ 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_23_ord__eq__le__trans) ).

thf(903,plain,
    ! [TA: $tType] :
      ( ( ord @ TA @ ( type2 @ 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)],[204]) ).

thf(99,axiom,
    ! [TA: $tType] :
      ( ( semidom_divide @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
          = ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_divide__zero) ).

thf(588,plain,
    ! [TA: $tType] :
      ( ( semidom_divide @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
          = ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(217,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) )
            = ( ord_less_eq @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_divide__le__eq__1__pos) ).

thf(963,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) )
            = ( ord_less_eq @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(119,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( sgn_sgn @ TA @ A )
            = ( one_one @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_sgn__pos) ).

thf(652,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( sgn_sgn @ TA @ A )
            = ( one_one @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(48,axiom,
    ! [TA: $tType] :
      ( ( wellorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o] :
          ( ? [B: TA] : ( A @ B )
         => ( A @ ( ord_Least @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_LeastI__ex) ).

thf(401,plain,
    ! [TA: $tType] :
      ( ( wellorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA > $o] :
          ( ? [B: TA] : ( A @ B )
         => ( A @ ( ord_Least @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(163,axiom,
    linordered_semidom @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semidom) ).

thf(786,plain,
    linordered_semidom @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(227,axiom,
    ( ( ord_less @ binDag_Mirabelle_dag )
    = ( ^ [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag] : ( binDag786255756subdag @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_less__dag__def) ).

thf(995,plain,
    ( ( ord_less @ binDag_Mirabelle_dag )
    = ( ^ [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag] : ( binDag786255756subdag @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(90,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] : ( ord_less @ TA @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_linordered__field__no__ub) ).

thf(568,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
        ? [B: TA] : ( ord_less @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(208,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( ( ord_less @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( B != A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_dual__order_Ostrict__iff__order) ).

thf(914,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( ( ord_less @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( B != A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(42,axiom,
    ord @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_3) ).

thf(383,plain,
    ord @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(179,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_less__imp__le) ).

thf(832,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(80,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ~ ( ord_less @ TA @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_less__irrefl) ).

thf(536,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ~ ( ord_less @ TA @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(10,axiom,
    ! [TA: $tType] :
      ( ( zero_neq_one @ TA @ ( type2 @ TA ) )
     => ! [A: $o,B: $o] :
          ( ( ( zero_neq_one_of_bool @ TA @ A )
            = ( zero_neq_one_of_bool @ TA @ B ) )
          = ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_of__bool__eq__iff) ).

thf(300,plain,
    ! [TA: $tType] :
      ( ( zero_neq_one @ TA @ ( type2 @ TA ) )
     => ! [A: $o,B: $o] :
          ( ( ( zero_neq_one_of_bool @ TA @ A )
            = ( zero_neq_one_of_bool @ TA @ B ) )
          = ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(64,axiom,
    order @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_2) ).

thf(447,plain,
    order @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(58,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_140_pinf_I5_J) ).

thf(432,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[58]) ).

thf(261,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( linorder @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TA > TB,B: TA,C: TA] :
          ( ( order_strict_mono @ TA @ TB @ A )
         => ( ( ord_less_eq @ TB @ ( A @ B ) @ ( A @ C ) )
            = ( ord_less_eq @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_strict__mono__less__eq) ).

thf(1097,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( linorder @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ TB ) ) )
     => ! [A: TA > TB,B: TA,C: TA] :
          ( ( order_strict_mono @ TA @ TB @ A )
         => ( ( ord_less_eq @ TB @ ( A @ B ) @ ( A @ C ) )
            = ( ord_less_eq @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(50,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = ( divide_divide @ TA @ ( one_one @ TA ) @ A ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_zero__eq__1__divide__iff) ).

thf(405,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = ( divide_divide @ TA @ ( one_one @ TA ) @ A ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(187,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ 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_10_order__subst2) ).

thf(854,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ 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)],[187]) ).

thf(39,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_not__gr__zero) ).

thf(373,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(56,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA @ ( type2 @ TA ) )
        & ( ord @ TB @ ( type2 @ 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_39_ord__eq__less__subst) ).

thf(422,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA @ ( type2 @ TA ) )
        & ( ord @ TB @ ( type2 @ 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)],[56]) ).

thf(166,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( wellorder @ TA @ ( type2 @ TA ) )
     => ! [A: ( TA > TB ) > TA > TB > $o] :
          ( ! [B: TB,C: TA > TB,D: TA > TB,E: TA] :
              ( ! [F: TA] :
                  ( ( ord_less @ TA @ F @ E )
                 => ( ( C @ F )
                    = ( D @ F ) ) )
             => ( ( A @ C @ E @ B )
                = ( A @ D @ E @ B ) ) )
         => ( ! [B: TA,C: TA > TB] :
                ( ! [D: TA] :
                    ( ( ord_less @ TA @ D @ B )
                   => ( A @ C @ D @ ( C @ D ) ) )
               => ? [D: TB] : ( A @ C @ B @ D ) )
           => ? [B: TA > TB] :
              ! [C: TA] : ( A @ B @ C @ ( B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_dependent__wellorder__choice) ).

thf(790,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( wellorder @ TA @ ( type2 @ TA ) )
     => ! [A: ( TA > TB ) > TA > TB > $o] :
          ( ! [B: TB,C: TA > TB,D: TA > TB,E: TA] :
              ( ! [F: TA] :
                  ( ( ord_less @ TA @ F @ E )
                 => ( ( C @ F )
                    = ( D @ F ) ) )
             => ( ( A @ C @ E @ B )
                = ( A @ D @ E @ B ) ) )
         => ( ! [B: TA,C: TA > TB] :
                ( ! [D: TA] :
                    ( ( ord_less @ TA @ D @ B )
                   => ( A @ C @ D @ ( C @ D ) ) )
               => ? [D: TB] : ( A @ C @ B @ D ) )
           => ? [B: TA > TB] :
              ! [C: TA] : ( A @ B @ C @ ( B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(20,axiom,
    canoni770627133id_add @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).

thf(326,plain,
    canoni770627133id_add @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(8,axiom,
    ! [TA: $tType] :
      ( ( zero_neq_one @ TA @ ( type2 @ TA ) )
     => ( ( zero_neq_one_of_bool @ TA @ $true )
        = ( one_one @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_of__bool__eq_I2_J) ).

thf(294,plain,
    ! [TA: $tType] :
      ( ( zero_neq_one @ TA @ ( type2 @ TA ) )
     => ( ( zero_neq_one_of_bool @ TA @ $true )
        = ( one_one @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(26,axiom,
    ! [TA: $tType] :
      ( ( ordering @ TA )
      = ( ^ [A: TA > TA > $o,B: TA > TA > $o] :
            ( ! [C: TA,D: TA] :
                ( ( B @ C @ D )
                = ( ( A @ C @ D )
                  & ( C != D ) ) )
            & ! [C: TA] : ( A @ C @ C )
            & ! [C: TA,D: TA] :
                ( ( A @ C @ D )
               => ( ( A @ D @ C )
                 => ( C = D ) ) )
            & ! [C: TA,D: TA,E: TA] :
                ( ( A @ C @ D )
               => ( ( A @ D @ E )
                 => ( A @ C @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_ordering__def) ).

thf(341,plain,
    ! [TA: $tType] :
      ( ( ordering @ TA )
      = ( ^ [A: TA > TA > $o,B: TA > TA > $o] :
            ( ! [C: TA,D: TA] :
                ( ( B @ C @ D )
                = ( ( A @ C @ D )
                  & ( C != D ) ) )
            & ! [C: TA] : ( A @ C @ C )
            & ! [C: TA,D: TA] :
                ( ( A @ C @ D )
               => ( ( A @ D @ C )
                 => ( C = D ) ) )
            & ! [C: TA,D: TA,E: TA] :
                ( ( A @ C @ D )
               => ( ( A @ D @ E )
                 => ( A @ C @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(170,axiom,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA,E: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( A @ C @ D )
       => ( ( B @ D @ E )
         => ( B @ C @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_ordering_Ostrict__trans1) ).

thf(807,plain,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA,E: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( A @ C @ D )
       => ( ( B @ D @ E )
         => ( B @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(60,axiom,
    ! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag] :
      ( ( binDag786255756subdag @ A @ B )
     => ~ ( binDag786255756subdag @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_subdag__not__sym) ).

thf(437,plain,
    ! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag] :
      ( ( binDag786255756subdag @ A @ B )
     => ~ ( binDag786255756subdag @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(113,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_71_antisym__conv3) ).

thf(635,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[113]) ).

thf(78,axiom,
    semidom_divide @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemidom__divide) ).

thf(532,plain,
    semidom_divide @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(142,axiom,
    ! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_5) ).

thf(720,plain,
    ! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(71,axiom,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( B @ C @ D )
       => ( A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_ordering_Ostrict__implies__order) ).

thf(474,plain,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( B @ C @ D )
       => ( A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(157,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) )
            = ( ord_less @ TA @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_divide__less__eq__1__neg) ).

thf(767,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( ord_less @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) )
            = ( ord_less @ TA @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(198,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_dual__order_Orefl) ).

thf(886,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(52,axiom,
    ord @ $o @ ( type2 @ $o ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_10) ).

thf(415,plain,
    ord @ $o @ ( type2 @ $o ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(110,axiom,
    ! [TA: $tType] :
      ( ( field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( divide_divide @ TA @ A @ B )
            = ( one_one @ TA ) )
          = ( ( B
             != ( zero_zero @ TA ) )
            & ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_divide__eq__1__iff) ).

thf(624,plain,
    ! [TA: $tType] :
      ( ( field @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( ( divide_divide @ TA @ A @ B )
            = ( one_one @ TA ) )
          = ( ( B
             != ( zero_zero @ TA ) )
            & ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(150,axiom,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( B @ C @ D )
        = ( ( A @ C @ D )
          & ( C != D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_ordering_Ostrict__iff__order) ).

thf(740,plain,
    ! [TA: $tType,A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] :
      ( ( ordering @ TA @ A @ B )
     => ( ( B @ C @ D )
        = ( ( A @ C @ D )
          & ( C != D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(75,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ TB ) )
     => ! [A: TA] :
        ? [B: TB] :
        ! [C: TB] :
          ( ( ord_less @ TB @ B @ C )
         => ( A = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_pinf_I11_J) ).

thf(528,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(226,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ 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_104_less__le__not__le) ).

thf(992,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ 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)],[226]) ).

thf(192,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( ordering @ TA @ ( ord_less_eq @ TA ) @ ( ord_less @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_order_Oordering__axioms) ).

thf(871,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ TA ) )
     => ( ordering @ TA @ ( ord_less_eq @ TA ) @ ( ord_less @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(270,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ 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_130_less__fun__def) ).

thf(1120,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB @ ( type2 @ 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)],[270]) ).

thf(224,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( A = B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_eq__refl) ).

thf(982,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA @ ( type2 @ TA ) )
     => ! [A: TA,B: TA] :
          ( ( A = B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(231,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( one_one @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_le__minus__one__simps_I2_J) ).

thf(1004,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA @ ( type2 @ TA ) )
     => ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( one_one @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(18,axiom,
    linord1659791738miring @ nat @ ( type2 @ nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring) ).

thf(322,plain,
    linord1659791738miring @ nat @ ( type2 @ nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(233,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_25_le__cases3) ).

thf(1009,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[233]) ).

thf(13,axiom,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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_76_order_Ostrict__trans) ).

thf(309,plain,
    ! [TA: $tType] :
      ( ( order @ TA @ ( type2 @ 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)],[13]) ).

thf(87,axiom,
    ! [TA: $tType] :
      ( ( linord1659791738miring @ TA @ ( type2 @ TA ) )
     => ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_not__one__less__zero) ).

thf(560,plain,
    ! [TA: $tType] :
      ( ( linord1659791738miring @ TA @ ( type2 @ TA ) )
     => ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(155,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_144_pinf_I1_J) ).

thf(755,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[155]) ).

thf(257,axiom,
    ( ( size_size @ binDag_Mirabelle_dag @ binDag_Mirabelle_Tip )
    = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_dag_Osize_I3_J) ).

thf(1088,plain,
    ( ( size_size @ binDag_Mirabelle_dag @ binDag_Mirabelle_Tip )
    = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(68,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_80_not__less__iff__gr__or__eq) ).

thf(454,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[68]) ).

thf(35,axiom,
    ! [TA: $tType] :
      ( ( division_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( A
           != ( zero_zero @ TA ) )
         => ( ( divide_divide @ TA @ A @ A )
            = ( one_one @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_divide__self) ).

thf(364,plain,
    ! [TA: $tType] :
      ( ( division_ring @ TA @ ( type2 @ TA ) )
     => ! [A: TA] :
          ( ( A
           != ( zero_zero @ TA ) )
         => ( ( divide_divide @ TA @ A @ A )
            = ( one_one @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(140,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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_143_pinf_I2_J) ).

thf(708,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA @ ( type2 @ 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)],[140]) ).

thf(220,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ 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_9_order__subst1) ).

thf(972,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA @ ( type2 @ TA ) )
        & ( order @ TB @ ( type2 @ 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)],[220]) ).

thf(1145,plain,
    $false,
    inference(e,[status(thm)],[1036,809,347,666,352,909,333,1031,1083,962,730,1068,1073,873,655,597,408,977,1078,384,533,814,698,1063,538,670,898,782,417,288,565,829,1095,724,570,460,917,702,802,344,934,357,817,638,606,448,316,1100,284,770,881,416,924,591,443,1109,376,646,574,966,821,1136,834,280,734,396,660,1104,452,920,380,439,529,546,1047,894,746,1042,297,693,429,788,1123,862,349,879,682,842,583,522,551,1128,285,1106,1143,650,615,1006,857,980,403,420,1118,884,1028,339,753,669,547,901,1075,476,679,1039,970,1114,997,1131,911,1002,371,622,837,1050,457,1086,360,805,311,541,1054,1071,1026,888,773,586,618,689,732,743,281,562,975,875,826,577,579,291,641,1139,572,313,787,335,1090,764,681,362,434,303,737,318,631,367,609,323,594,799,848,330,1112,811,387,932,1061,685,399,695,1066,780,1000,922,986,306,851,1102,722,1034,675,531,663,927,1134,355,823,1081,749,776,525,580,705,327,673,370,717,840,643,544,907,703,1141,1023,600,1052,864,727,446,612,859,1094,386,845,627,450,891,1126,688,903,588,963,652,401,786,995,568,914,383,832,536,300,447,432,1097,405,854,373,422,790,326,294,341,807,437,635,532,720,474,767,886,415,624,740,528,992,871,1120,982,1004,322,1009,309,560,755,1088,454,364,708,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : COM163^1 : TPTP v8.2.0. Released v7.0.0.
% 0.12/0.13  % Command  : run_Leo-III %s %d
% 0.12/0.34  % Computer : n003.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sun May 19 10:33:08 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 1.10/1.02  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.23/1.42  % [INFO] 	 Parsing done (395ms). 
% 2.23/1.44  % [INFO] 	 Running in sequential loop mode. 
% 3.50/1.83  % [INFO] 	 eprover registered as external prover. 
% 3.50/1.83  % [INFO] 	 cvc4 registered as external prover. 
% 3.50/1.84  % [INFO] 	 Scanning for conjecture ... 
% 3.88/2.00  % [INFO] 	 Found a conjecture (or negated_conjecture) and 282 axioms. Running axiom selection ... 
% 4.23/2.16  % [INFO] 	 Axiom selection finished. Selected 277 axioms (removed 5 axioms). 
% 5.03/2.46  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 5.37/2.49  % [INFO] 	 Type checking passed. 
% 5.37/2.50  % [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 ... 
% 33.00/16.21  % External prover 'e' found a proof!
% 33.00/16.21  % [INFO] 	 Killing All external provers ... 
% 33.00/16.21  % Time passed: 15714ms (effective reasoning time: 14771ms)
% 33.00/16.21  % 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)>
% 33.00/16.22  % Axioms used in derivation (277): fact_5_le__funD, fact_152_subdag__size, fact_185_not__less__zero, fact_51_order_Oasym, fact_186_gr__zeroI, fact_127_subdag__neq, tcon_HOL_Obool___Orderings_Opreorder_7, fact_182_zero__le, fact_33_strict__mono__less__eq, fact_171_ordering_Ostrict__trans, fact_153_dag_Osimps_I7_J, fact_108_order_Oorder__iff__strict, fact_162_dag_Osize_I3_J, fact_62_less__irrefl, fact_37_Least__equality, tcon_Nat_Onat___Orderings_Oorder_2, fact_227_neg__less__0__iff__less, fact_6_le__funE, fact_148_subdag_Osimps_I1_J, tcon_Nat_Onat___Orderings_Ono__top, fact_11_ord__eq__le__subst, fact_249_le__divide__eq__1__pos, fact_28_eq__refl, tcon_Nat_Onat___Orderings_Olinorder, fact_238_divide__eq__1__iff, fact_223_neg__0__le__iff__le, fact_20_order__trans, tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder, fact_110_dual__order_Ostrict__trans1, fact_85_leI, fact_44_gt__ex, fact_74_linorder__cases, fact_239_div__self, fact_221_divide__zero, fact_129_subdag__not__sym, fact_143_pinf_I2_J, fact_193_sgn__pos, fact_3_le__dag__refl, fact_40_ord__less__eq__subst, fact_96_antisym__conv1, fact_91_order__less__le__subst2, fact_198_le__numeral__extra_I1_J, tcon_Nat_Onat___Rings_Ozero__neq__one, fact_18_linorder__wlog, fact_176_ordering_Orefl, fact_215_neg__less__iff__less, fact_14_antisym, tcon_fun___Orderings_Oord, fact_38_LeastI2__order, fact_214_neg__le__iff__le, fact_16_dual__order_Oantisym, fact_30_antimonoI, fact_2_x__y, fact_255_le__minus__one__simps_I4_J, tcon_Nat_Onat___Rings_Ozero__less__one, fact_123_complete__interval, fact_160_dag_Odistinct_I1_J, fact_219_divide__eq__0__iff, fact_169_ordering_Ostrict__trans2, fact_201_le__numeral__extra_I4_J, fact_8_le__fun__def, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, fact_119_minf_I8_J, fact_112_dense__ge__bounded, tcon_HOL_Obool___Orderings_Oorder_9, fact_31_antimonoE, fact_222_divide__1, fact_7_le__funI, fact_120_minf_I6_J, fact_229_neg__less__pos, fact_23_ord__eq__le__trans, fact_253_less__minus__one__simps_I2_J, fact_92_not__le, fact_241_divide__le__0__1__iff, fact_90_order__less__le__subst1, fact_246_less__divide__eq__1__neg, tcon_Nat_Onat___Rings_Olinordered__semidom, fact_41_order__less__subst1, fact_53_LeastI2, fact_180_le__zero__eq, fact_170_ordering_Ostrict__trans1, fact_242_zero__le__divide__1__iff, fact_206_not__one__le__zero, fact_245_divide__less__eq__1__pos, fact_26_order_Otrans, fact_25_le__cases3, fact_159_dag_Oinduct, fact_164_ordering_Onot__eq__order__implies__strict, fact_27_le__cases, fact_111_dual__order_Ostrict__trans2, fact_226_neg__less__eq__nonneg, fact_243_divide__less__0__1__iff, fact_76_order_Ostrict__trans, fact_61_less__linear, fact_72_less__imp__not__eq2, fact_67_less__imp__not__eq, help_If_1_1_T, fact_54_less__imp__neq, fact_218_divide__cancel__left, fact_183_zero__less__iff__neq__zero, fact_244_divide__less__eq__1__neg, fact_49_neqE, fact_17_dual__order_Otrans, fact_137_minf_I1_J, fact_64_ord__eq__less__trans, fact_126_linorder__neqE__linordered__idom, fact_98_le__less__trans, fact_117_dual__order_Ostrict__implies__order, tcon_Set_Oset___Orderings_Oord_6, fact_43_lt__ex, fact_9_order__subst1, fact_217_divide__cancel__right, fact_230_less__neg__neg, fact_139_pinf_I7_J, fact_187_less__numeral__extra_I3_J, fact_89_order__le__less__subst2, tcon_Nat_Onat___Orderings_Owellorder, fact_115_dual__order_Oorder__iff__strict, fact_190_sgn__sgn, fact_99_less__le__trans, fact_248_zero__less__divide__1__iff, fact_132_minf_I7_J, fact_224_neg__le__0__iff__le, fact_84_leD, fact_251_divide__le__eq__1__pos, fact_88_order__le__less__subst1, fact_156_subdag__NodeD, fact_158_dag_Oexhaust, fact_235_divide__self__if, fact_205_zero__le__one, tcon_HOL_Obool___Orderings_Oord_10, fact_52_dense, fact_122_pinf_I6_J, fact_236_divide__self, fact_80_not__less__iff__gr__or__eq, fact_50_neq__iff, fact_21_order__class_Oorder_Oantisym, fact_202_of__bool__eq__iff, fact_138_pinf_I11_J, fact_184_gr__implies__not__zero, fact_102_le__less__linear, fact_56_strict__monoI, fact_254_le__minus__one__simps_I2_J, fact_29_antimono__def, fact_86_le__less, fact_240_divide__minus1, fact_247_less__divide__eq__1__pos, fact_250_le__divide__eq__1__neg, fact_173_ordering_Oirrefl, tcon_Nat_Onat___Orderings_Oord_3, fact_144_pinf_I1_J, fact_118_order_Onot__eq__order__implies__strict, fact_131_minf_I11_J, fact_124_less__dag__def, fact_97_antisym__conv2, fact_70_less__induct, fact_207_of__bool__def, fact_66_dual__order_Oasym, fact_109_order_Ostrict__iff__order, fact_75_dual__order_Oirrefl, fact_134_minf_I4_J, fact_210_split__of__bool__asm, fact_203_zero__less__one, fact_77_strict__mono__less, fact_179_not__gr__zero, fact_208_zero__neq__one, fact_73_less__imp__triv, fact_35_LeastI2__wellorder__ex, help_If_2_1_T, tcon_Set_Oset___Orderings_Opreorder_4, fact_177_ordering_Oasym, fact_93_not__less, fact_125_ex__gt__or__lt, help_If_3_1_T, fact_15_linear, fact_34_le__dag__def, fact_135_minf_I3_J, fact_209_split__of__bool, fact_58_less__asym_H, fact_174_ordering_Otrans, fact_104_less__le__not__le, fact_165_ordering_Ostrict__implies__not__eq, fact_234_divide__eq__eq__1, fact_103_le__imp__less__or__eq, fact_194_of__bool__eq_I1_J, fact_213_divide__le__eq__1__neg, fact_68_strict__mono__def, fact_178_ordering__def, fact_147_linordered__field__no__ub, fact_181_dag_Osize__gen_I1_J, fact_231_zero__eq__1__divide__iff, fact_167_ordering_Ostrict__iff__order, fact_157_subdag_Osimps_I2_J, fact_107_order_Ostrict__trans2, fact_252_less__minus__one__simps_I4_J, fact_151_dag_Osimps_I6_J, fact_211_sgn__1__pos, fact_216_division__ring__divide__zero, fact_82_dual__order_Ostrict__implies__not__eq, fact_79_dual__order_Ostrict__trans, fact_172_ordering_Oantisym, tcon_fun___Orderings_Opreorder, fact_71_antisym__conv3, fact_105_not__le__imp__less, tcon_Set_Oset___Orderings_Oorder_5, fact_130_less__fun__def, fact_24_antisym__conv, fact_114_order_Ostrict__implies__order, fact_225_less__eq__neg__nonpos, fact_81_order_Ostrict__implies__not__eq, fact_212_sgn__neg, fact_32_antimonoD, fact_60_LeastI__ex, tcon_Nat_Onat___Orderings_Opreorder_1, fact_113_dense__le__bounded, fact_55_strict__monoD, fact_59_less__trans, fact_12_ord__le__eq__subst, fact_196_less__numeral__extra_I2_J, fact_106_order_Ostrict__trans1, tcon_HOL_Obool___Orderings_Olinorder_8, fact_155_dag_Oinject, fact_220_divide__zero__left, fact_146_linordered__field__no__lb, fact_188_le__numeral__extra_I3_J, fact_57_less__asym, fact_149_DAG_Osimps_I1_J, fact_78_less__imp__not__less, fact_189_sgn__greater, fact_200_less__numeral__extra_I4_J, fact_195_of__bool__eq_I2_J, fact_22_ord__le__eq__trans, fact_39_ord__eq__less__subst, fact_94_le__neq__trans, fact_13_eq__iff, fact_100_dense__ge, tcon_fun___Orderings_Oorder, fact_36_LeastI2__wellorder, fact_140_pinf_I5_J, fact_197_less__numeral__extra_I1_J, fact_128_subdag__trans, fact_142_pinf_I3_J, fact_192_sgn__0__0, fact_233_eq__divide__eq__1, tcon_Nat_Onat___Rings_Osemidom__divide, fact_121_pinf_I8_J, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_133_minf_I5_J, fact_69_less__not__sym, fact_87_less__le, fact_116_dual__order_Ostrict__iff__order, fact_63_LeastI2__ex, fact_0_True, fact_4_order__refl, fact_204_not__one__less__zero, fact_199_le__numeral__extra_I2_J, fact_175_ordering_Ointro, fact_42_order__less__subst2, fact_141_pinf_I4_J, fact_228_neg__0__less__iff__less, fact_232_one__divide__eq__0__iff, fact_136_minf_I2_J, fact_95_less__imp__le, fact_191_sgn__less, fact_237_one__eq__divide__iff, fact_83_strict__mono__eq, fact_163_order_Oordering__axioms, fact_1_y__z, fact_19_dual__order_Orefl, fact_10_order__subst2, fact_168_ordering_Oorder__iff__strict, fact_65_ord__less__eq__trans, fact_150_dag_Osimps_I4_J, fact_101_dense__le, fact_166_ordering_Ostrict__implies__order, fact_154_dag_Osimps_I5_J, fact_145_dependent__wellorder__choice
% 33.00/16.22  % No. of inferences in proof: 558
% 33.00/16.22  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 15714 ms resp. 14771 ms w/o parsing
% 33.92/16.37  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 33.92/16.37  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------