TSTP Solution File: ITP114^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP114^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n029.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:23:03 EDT 2024

% Result   : Theorem 63.66s 25.05s
% Output   : Refutation 64.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  382
% Syntax   : Number of formulae    :  708 ( 308 unt;  58 typ;   0 def)
%            Number of atoms       : 1778 ( 768 equ;   6 cnn)
%            Maximal formula atoms :   81 (   2 avg)
%            Number of connectives : 5638 ( 198   ~;  22   |;  60   &;4492   @)
%                                         (   0 <=>; 866  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   34 (   5 avg)
%            Number of types       :    7 (   6 usr)
%            Number of type conns  :  184 ( 184   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   59 (  55 usr;   9 con; 0-4 aty)
%            Number of variables   : 1335 (  42   ^1192   !;  56   ?;1335   :)
%                                         (  45  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(extended_ereal_type,type,
    extended_ereal: $tType ).

thf(extended_enat_type,type,
    extended_enat: $tType ).

thf(real_type,type,
    real: $tType ).

thf(num_type,type,
    num: $tType ).

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

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

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

thf(zero_type,type,
    zero: 
      !>[TA: $tType] : $o ).

thf(numeral_type,type,
    numeral: 
      !>[TA: $tType] : $o ).

thf(uminus_type,type,
    uminus: 
      !>[TA: $tType] : $o ).

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

thf(ring_char_0_type,type,
    ring_char_0: 
      !>[TA: $tType] : $o ).

thf(neg_numeral_type,type,
    neg_numeral: 
      !>[TA: $tType] : $o ).

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

thf(group_add_type,type,
    group_add: 
      !>[TA: $tType] : $o ).

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

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

thf(semiring_char_0_type,type,
    semiring_char_0: 
      !>[TA: $tType] : $o ).

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

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

thf(boolean_algebra_type,type,
    boolean_algebra: 
      !>[TA: $tType] : $o ).

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

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

thf(ordere142940540dd_abs_type,type,
    ordere142940540dd_abs: 
      !>[TA: $tType] : $o ).

thf(real_V2090557954_space_type,type,
    real_V2090557954_space: 
      !>[TA: $tType] : $o ).

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

thf(topolo259154727pology_type,type,
    topolo259154727pology: 
      !>[TA: $tType] : $o ).

thf(topolo503727757_space_type,type,
    topolo503727757_space: 
      !>[TA: $tType] : $o ).

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

thf(extended_enat2_type,type,
    extended_enat2: nat > extended_enat ).

thf(extended_case_enat_type,type,
    extended_case_enat: 
      !>[TA: $tType] : ( ( nat > TA ) > TA > extended_enat > TA ) ).

thf(extended_rec_enat_type,type,
    extended_rec_enat: 
      !>[TA: $tType] : ( ( nat > TA ) > TA > extended_enat > TA ) ).

thf(extend1396239628finity_type,type,
    extend1396239628finity: 
      !>[TA: $tType] : TA ).

thf(extended_the_enat_type,type,
    extended_the_enat: extended_enat > nat ).

thf(extended_MInfty_type,type,
    extended_MInfty: extended_ereal ).

thf(extended_PInfty_type,type,
    extended_PInfty: extended_ereal ).

thf(extended_ereal2_type,type,
    extended_ereal2: real > extended_ereal ).

thf(extended_size_ereal_type,type,
    extended_size_ereal: extended_ereal > nat ).

thf(extend1771934483f_enat_type,type,
    extend1771934483f_enat: extended_enat > extended_ereal ).

thf(extend1716541707_ereal_type,type,
    extend1716541707_ereal: extended_ereal > real ).

thf(abs_abs_type,type,
    abs_abs: 
      !>[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(lower_107104146le_lsc_type,type,
    lower_107104146le_lsc: 
      !>[TA: $tType,TB: $tType] : ( ( TB > TA ) > $o ) ).

thf(lower_582600101lsc_at_type,type,
    lower_582600101lsc_at: 
      !>[TA: $tType,TB: $tType] : ( TB > ( TB > TA ) > $o ) ).

thf(lower_1879122655c_hull_type,type,
    lower_1879122655c_hull: 
      !>[TA: $tType] : ( ( TA > extended_ereal ) > TA > extended_ereal ) ).

thf(neg_numeral_dbl_type,type,
    neg_numeral_dbl: 
      !>[TA: $tType] : ( TA > TA ) ).

thf(neg_numeral_sub_type,type,
    neg_numeral_sub: 
      !>[TA: $tType] : ( num > num > TA ) ).

thf(numeral_numeral_type,type,
    numeral_numeral: 
      !>[TA: $tType] : ( num > TA ) ).

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

thf(order_Greatest_type,type,
    order_Greatest: 
      !>[TA: $tType] : ( ( TA > $o ) > TA ) ).

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

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

thf(f_type,type,
    f: a > extended_ereal ).

thf(g_type,type,
    g: a > extended_ereal ).

thf(x_type,type,
    x: a ).

thf(233,axiom,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ 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/sandbox/benchmark/theBenchmark.p',fact_98_neg__le__0__iff__le) ).

thf(1105,plain,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ 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)],[233]) ).

thf(164,axiom,
    ( ( extend1771934483f_enat @ ( zero_zero @ extended_enat ) )
    = ( zero_zero @ extended_ereal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_ereal__of__enat__zero) ).

thf(893,plain,
    ( ( extend1771934483f_enat @ ( zero_zero @ extended_enat ) )
    = ( zero_zero @ extended_ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(226,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ B @ C )
       => ( ord_less_eq @ nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_le__trans) ).

thf(1083,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ B @ C )
       => ( ord_less_eq @ nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(113,axiom,
    order @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oorder_23) ).

thf(555,plain,
    order @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(147,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ A )
           => ( ord_less_eq @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_dual__order_Otrans) ).

thf(666,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ C @ A )
           => ( ord_less_eq @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(235,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less_eq @ TA @ A @ B )
         => ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_le__cases) ).

thf(1110,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less_eq @ TA @ A @ B )
         => ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(23,axiom,
    ! [TA: $tType,A: nat > TA,B: TA,C: nat] :
      ( ( extended_rec_enat @ TA @ A @ B @ ( extended_enat2 @ C ) )
      = ( A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_enat_Osimps_I6_J) ).

thf(365,plain,
    ! [TA: $tType,A: nat > TA,B: TA,C: nat] :
      ( ( extended_rec_enat @ TA @ A @ B @ ( extended_enat2 @ C ) )
      = ( A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(262,axiom,
    ! [A: extended_ereal] : ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( abs_abs @ extended_ereal @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_abs__ereal__pos) ).

thf(1190,plain,
    ! [A: extended_ereal] : ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( abs_abs @ extended_ereal @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(5,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA] :
          ( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
          = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_add_Oinverse__inverse) ).

thf(333,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA] :
          ( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(208,axiom,
    ! [A: extended_enat] :
      ( ( ord_less_eq @ extended_enat @ A @ ( zero_zero @ extended_enat ) )
      = ( A
        = ( zero_zero @ extended_enat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_ile0__eq) ).

thf(1031,plain,
    ! [A: extended_enat] :
      ( ( ord_less_eq @ extended_enat @ A @ ( zero_zero @ extended_enat ) )
      = ( A
        = ( zero_zero @ extended_enat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(81,axiom,
    ! [TA: $tType,A: nat > TA,B: TA,C: nat] :
      ( ( extended_case_enat @ TA @ A @ B @ ( extended_enat2 @ C ) )
      = ( A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_enat_Osimps_I4_J) ).

thf(481,plain,
    ! [TA: $tType,A: nat > TA,B: TA,C: nat] :
      ( ( extended_case_enat @ TA @ A @ B @ ( extended_enat2 @ C ) )
      = ( A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(15,axiom,
    boolean_algebra @ $o,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Oboolean__algebra_11) ).

thf(352,plain,
    boolean_algebra @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(200,axiom,
    ! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_bot__nat__0_Oextremum) ).

thf(1005,plain,
    ! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(296,axiom,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ 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/sandbox/benchmark/theBenchmark.p',fact_87_neg__le__iff__le) ).

thf(1290,plain,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ 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)],[296]) ).

thf(222,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
      | ( ord_less_eq @ nat @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_nat__le__linear) ).

thf(1068,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
      | ( ord_less_eq @ nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(65,axiom,
    topolo259154727pology @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Topological__Spaces_Oorder__topology) ).

thf(449,plain,
    topolo259154727pology @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(246,axiom,
    ! [A: real] :
      ( ( ( extended_ereal2 @ A )
        = ( zero_zero @ extended_ereal ) )
      = ( A
        = ( zero_zero @ real ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_ereal__eq__0_I1_J) ).

thf(1142,plain,
    ! [A: real] :
      ( ( ( extended_ereal2 @ A )
        = ( zero_zero @ extended_ereal ) )
      = ( A
        = ( zero_zero @ real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(60,axiom,
    ord @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oord_24) ).

thf(440,plain,
    ord @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(135,axiom,
    ! [A: real] :
      ( ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ A ) @ ( zero_zero @ extended_ereal ) )
      = ( ord_less_eq @ real @ A @ ( zero_zero @ real ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_ereal__less__eq_I4_J) ).

thf(614,plain,
    ! [A: real] :
      ( ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ A ) @ ( zero_zero @ extended_ereal ) )
      = ( ord_less_eq @ real @ A @ ( zero_zero @ real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(44,axiom,
    topolo259154727pology @ extended_enat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Topological__Spaces_Oorder__topology_30) ).

thf(408,plain,
    topolo259154727pology @ extended_enat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(189,axiom,
    ! [A: extended_ereal] :
      ( ( uminus_uminus @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_ereal__uminus__uminus) ).

thf(977,plain,
    ! [A: extended_ereal] :
      ( ( uminus_uminus @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(100,axiom,
    ( ( numeral_numeral @ extended_enat )
    = ( ^ [A: num] : ( extended_enat2 @ ( numeral_numeral @ nat @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_numeral__eq__enat) ).

thf(523,plain,
    ( ( numeral_numeral @ extended_enat )
    = ( ^ [A: num] : ( extended_enat2 @ ( numeral_numeral @ nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(125,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_eq__iff) ).

thf(582,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(91,axiom,
    linorder @ $o,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_13) ).

thf(500,plain,
    linorder @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(253,axiom,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ( uminus_uminus @ extended_ereal @ A )
        = B )
      = ( A
        = ( uminus_uminus @ extended_ereal @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_ereal__uminus__eq__reorder) ).

thf(1164,plain,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ( uminus_uminus @ extended_ereal @ A )
        = B )
      = ( A
        = ( uminus_uminus @ extended_ereal @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(75,axiom,
    order @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_3) ).

thf(472,plain,
    order @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(172,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ A ) )
          = ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_less__eq__neg__nonpos) ).

thf(913,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ 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)],[172]) ).

thf(318,axiom,
    ! [A: extended_ereal] :
      ( ( ( abs_abs @ extended_ereal @ A )
        = ( extend1396239628finity @ extended_ereal ) )
     => ( ( A
         != ( extend1396239628finity @ extended_ereal ) )
       => ( A
          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_abs__eq__infinity__cases) ).

thf(1354,plain,
    ! [A: extended_ereal] :
      ( ( ( abs_abs @ extended_ereal @ A )
        = ( extend1396239628finity @ extended_ereal ) )
     => ( ( A
         != ( extend1396239628finity @ extended_ereal ) )
       => ( A
          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(149,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_zero__le) ).

thf(670,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(275,axiom,
    ! [A: real] :
      ( ( extended_ereal2 @ A )
     != ( extend1396239628finity @ extended_ereal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_PInfty__neq__ereal_I1_J) ).

thf(1222,plain,
    ! [A: real] :
      ( ( extended_ereal2 @ A )
     != ( extend1396239628finity @ extended_ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(178,axiom,
    ! [A: extended_ereal,B: real,C: real] :
      ( ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ B ) )
     => ( ( ord_less_eq @ real @ B @ C )
       => ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_le__ereal__le) ).

thf(930,plain,
    ! [A: extended_ereal,B: real,C: real] :
      ( ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ B ) )
     => ( ( ord_less_eq @ real @ B @ C )
       => ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(264,axiom,
    ! [TA: $tType] :
      ( ( real_V2090557954_space @ TA )
     => ! [A: TA > extended_ereal,B: TA > extended_ereal] :
          ( ( lower_107104146le_lsc @ TA @ extended_ereal @ A )
         => ( ! [C: TA] : ( ord_less_eq @ extended_ereal @ ( A @ C ) @ ( B @ C ) )
           => ! [C: TA] : ( ord_less_eq @ extended_ereal @ ( A @ C ) @ ( lower_1879122655c_hull @ TA @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_lsc__hull__greatest) ).

thf(1196,plain,
    ! [TA: $tType] :
      ( ( real_V2090557954_space @ TA )
     => ! [A: TA > extended_ereal,B: TA > extended_ereal] :
          ( ( lower_107104146le_lsc @ TA @ extended_ereal @ A )
         => ( ! [C: TA] : ( ord_less_eq @ extended_ereal @ ( A @ C ) @ ( B @ C ) )
           => ! [C: TA] : ( ord_less_eq @ extended_ereal @ ( A @ C ) @ ( lower_1879122655c_hull @ TA @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(166,axiom,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ B )
      = ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_ereal__uminus__le__reorder) ).

thf(898,plain,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ B )
      = ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(198,axiom,
    ! [TA: $tType] :
      ( ( boolean_algebra @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
         => ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_compl__le__swap2) ).

thf(1001,plain,
    ! [TA: $tType] :
      ( ( boolean_algebra @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
         => ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(282,axiom,
    ! [A: real] :
      ( ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A )
       => ( ( divide_divide @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ ( extended_ereal2 @ A ) )
          = ( extend1396239628finity @ extended_ereal ) ) )
      & ( ~ ( ord_less_eq @ real @ ( zero_zero @ real ) @ A )
       => ( ( divide_divide @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ ( extended_ereal2 @ A ) )
          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_ereal__divide__ereal) ).

thf(1243,plain,
    ! [A: real] :
      ( ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A )
       => ( ( divide_divide @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ ( extended_ereal2 @ A ) )
          = ( extend1396239628finity @ extended_ereal ) ) )
      & ( ~ ( ord_less_eq @ real @ ( zero_zero @ real ) @ A )
       => ( ( divide_divide @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ ( extended_ereal2 @ A ) )
          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(214,axiom,
    ! [A: extended_ereal] :
      ( ( divide_divide @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
      = ( zero_zero @ extended_ereal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_ereal__divide__zero__left) ).

thf(1046,plain,
    ! [A: extended_ereal] :
      ( ( divide_divide @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
      = ( zero_zero @ extended_ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(320,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num,B: num] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( numeral_numeral @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_neg__numeral__le__numeral) ).

thf(1359,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num,B: num] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( numeral_numeral @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(119,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = ( abs_abs @ TA @ A ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_abs__0__eq) ).

thf(565,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = ( abs_abs @ TA @ A ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(58,axiom,
    ! [A: nat,B: nat] :
      ( ( ( extended_enat2 @ A )
        = ( extended_enat2 @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_enat_Oinject) ).

thf(436,plain,
    ! [A: nat,B: nat] :
      ( ( ( extended_enat2 @ A )
        = ( extended_enat2 @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(35,axiom,
    topolo503727757_space @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Topological__Spaces_Otopological__space_1) ).

thf(389,plain,
    topolo503727757_space @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(217,axiom,
    ( ( extend1396239628finity @ extended_ereal )
   != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_MInfty__neq__PInfty_I1_J) ).

thf(1055,plain,
    ( ( extend1396239628finity @ extended_ereal )
   != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(295,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num,B: num] :
          ( ( ord_less_eq @ TA @ ( neg_numeral_sub @ TA @ A @ B ) @ ( zero_zero @ TA ) )
          = ( ord_less_eq @ num @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_sub__non__positive) ).

thf(1287,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num,B: num] :
          ( ( ord_less_eq @ TA @ ( neg_numeral_sub @ TA @ A @ B ) @ ( zero_zero @ TA ) )
          = ( ord_less_eq @ num @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(121,axiom,
    ! [A: real] :
      ( ( extended_ereal2 @ A )
     != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_MInfty__neq__ereal_I1_J) ).

thf(570,plain,
    ! [A: real] :
      ( ( extended_ereal2 @ A )
     != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(298,axiom,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TA > extended_ereal,B: TA] :
          ( ( ( A @ B )
            = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
         => ( lower_582600101lsc_at @ TA @ extended_ereal @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_lsc__at__MInfty) ).

thf(1298,plain,
    ! [TA: $tType] :
      ( ( topolo503727757_space @ TA )
     => ! [A: TA > extended_ereal,B: TA] :
          ( ( ( A @ B )
            = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
         => ( lower_582600101lsc_at @ TA @ extended_ereal @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(26,axiom,
    linorder @ num,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Olinorder_6) ).

thf(372,plain,
    linorder @ num,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(93,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] :
          ( ( ( abs_abs @ TA @ A )
            = ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_abs__eq__0) ).

thf(504,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] :
          ( ( ( abs_abs @ TA @ A )
            = ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(137,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( abs_abs @ TA @ A )
            = ( uminus_uminus @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_abs__of__nonpos) ).

thf(619,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
         => ( ( abs_abs @ TA @ A )
            = ( uminus_uminus @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(108,axiom,
    ! [TA: $tType] :
      ( ( semiring_char_0 @ TA )
     => ! [A: num,B: num] :
          ( ( ( numeral_numeral @ TA @ A )
            = ( numeral_numeral @ TA @ B ) )
          = ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_numeral__eq__iff) ).

thf(542,plain,
    ! [TA: $tType] :
      ( ( semiring_char_0 @ TA )
     => ! [A: num,B: num] :
          ( ( ( numeral_numeral @ TA @ A )
            = ( numeral_numeral @ TA @ B ) )
          = ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(168,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ B @ A )
              & ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_dual__order_Oeq__iff) ).

thf(902,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ B @ A )
              & ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(115,axiom,
    ! [TA: $tType] :
      ( ( boolean_algebra @ TA )
     => ! [A: TA] :
          ( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
          = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_double__compl) ).

thf(559,plain,
    ! [TA: $tType] :
      ( ( boolean_algebra @ TA )
     => ! [A: TA] :
          ( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(248,axiom,
    ! [A: set @ extended_ereal] :
    ? [B: extended_ereal] :
      ( ! [C: extended_ereal] :
          ( ( member @ extended_ereal @ C @ A )
         => ( ord_less_eq @ extended_ereal @ B @ C ) )
      & ! [C: extended_ereal] :
          ( ! [D: extended_ereal] :
              ( ( member @ extended_ereal @ D @ A )
             => ( ord_less_eq @ extended_ereal @ C @ D ) )
         => ( ord_less_eq @ extended_ereal @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_ereal__complete__Inf) ).

thf(1147,plain,
    ! [A: set @ extended_ereal] :
    ? [B: extended_ereal] :
      ( ! [C: extended_ereal] :
          ( ( member @ extended_ereal @ C @ A )
         => ( ord_less_eq @ extended_ereal @ B @ C ) )
      & ! [C: extended_ereal] :
          ( ! [D: extended_ereal] :
              ( ( member @ extended_ereal @ D @ A )
             => ( ord_less_eq @ extended_ereal @ C @ D ) )
         => ( ord_less_eq @ extended_ereal @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(132,axiom,
    ( ( extend1396239628finity @ extended_ereal )
    = extended_PInfty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_infinity__ereal__def) ).

thf(606,plain,
    ( ( extend1396239628finity @ extended_ereal )
    = extended_PInfty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(203,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num,B: num] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( neg_numeral_sub @ TA @ A @ B ) )
          = ( ord_less_eq @ num @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_sub__non__negative) ).

thf(1013,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num,B: num] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( neg_numeral_sub @ TA @ A @ B ) )
          = ( ord_less_eq @ num @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(49,axiom,
    ! [TA: $tType] :
      ( ( real_V2090557954_space @ TA )
     => ( type @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Real__Vector__Spaces_Ometric__space___HOL_Otype) ).

thf(416,plain,
    ! [TA: $tType] :
      ( ( real_V2090557954_space @ TA )
     => ( type @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(64,axiom,
    uminus @ $o,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ouminus_16) ).

thf(448,plain,
    uminus @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(278,axiom,
    ! [A: nat] :
      ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
      = ( A
        = ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_bot__nat__0_Oextremum__unique) ).

thf(1232,plain,
    ! [A: nat] :
      ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
      = ( A
        = ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(306,axiom,
    ! [A: a] : ( ord_less_eq @ extended_ereal @ ( g @ A ) @ ( f @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms) ).

thf(1319,plain,
    ! [A: a] : ( ord_less_eq @ extended_ereal @ ( g @ A ) @ ( f @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(52,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] :
          ( ( abs_abs @ TA @ ( uminus_uminus @ TA @ A ) )
          = ( abs_abs @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_abs__minus__cancel) ).

thf(421,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] :
          ( ( abs_abs @ TA @ ( uminus_uminus @ TA @ A ) )
          = ( abs_abs @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(78,axiom,
    real_V2090557954_space @ a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).

thf(475,plain,
    real_V2090557954_space @ a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(300,axiom,
    ( ( abs_abs @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) )
    = ( extend1396239628finity @ extended_ereal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_abs__ereal_Osimps_I3_J) ).

thf(1302,plain,
    ( ( abs_abs @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) )
    = ( extend1396239628finity @ extended_ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(311,axiom,
    ! [TA: $tType] :
      ( ( boolean_algebra @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
         => ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_compl__le__swap1) ).

thf(1334,plain,
    ! [TA: $tType] :
      ( ( boolean_algebra @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
         => ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(83,axiom,
    semiring_char_0 @ extended_enat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_32) ).

thf(485,plain,
    semiring_char_0 @ extended_enat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(16,axiom,
    topolo503727757_space @ extended_enat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Topological__Spaces_Otopological__space_29) ).

thf(353,plain,
    topolo503727757_space @ extended_enat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(294,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( A = B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_eq__refl) ).

thf(1283,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( A = B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(169,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ ( B @ C ) )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less_eq @ TA @ E @ F )
                 => ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_order__subst1) ).

thf(905,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ ( B @ C ) )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less_eq @ TA @ E @ F )
                 => ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(11,axiom,
    linordered_idom @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__idom) ).

thf(348,plain,
    linordered_idom @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(122,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TA > TB,B: TA,C: TA] :
          ( ( order_strict_mono @ TA @ TB @ A )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TB @ ( A @ B ) @ ( A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_strict__mono__leD) ).

thf(574,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TA > TB,B: TA,C: TA] :
          ( ( order_strict_mono @ TA @ TB @ A )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TB @ ( A @ B ) @ ( A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(131,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( B = C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_ord__le__eq__trans) ).

thf(602,plain,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( B = C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(255,axiom,
    ! [A: nat > $o,B: nat,C: nat] :
      ( ( A @ B )
     => ( ! [D: nat] :
            ( ( A @ D )
           => ( ord_less_eq @ nat @ D @ C ) )
       => ? [D: nat] :
            ( ( A @ D )
            & ! [E: nat] :
                ( ( A @ E )
               => ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Nat_Oex__has__greatest__nat) ).

thf(1169,plain,
    ! [A: nat > $o,B: nat,C: nat] :
      ( ( A @ B )
     => ( ! [D: nat] :
            ( ( A @ D )
           => ( ord_less_eq @ nat @ D @ C ) )
       => ? [D: nat] :
            ( ( A @ D )
            & ! [E: nat] :
                ( ( A @ E )
               => ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(272,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ 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/sandbox/benchmark/theBenchmark.p',fact_42_antimonoE) ).

thf(1215,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ 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)],[272]) ).

thf(67,axiom,
    ring_char_0 @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Oring__char__0) ).

thf(453,plain,
    ring_char_0 @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(39,axiom,
    ! [TA: $tType] :
      ( ( semiring_char_0 @ TA )
     => ! [A: num] :
          ( ( zero_zero @ TA )
         != ( numeral_numeral @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_zero__neq__numeral) ).

thf(396,plain,
    ! [TA: $tType] :
      ( ( semiring_char_0 @ TA )
     => ! [A: num] :
          ( ( zero_zero @ TA )
         != ( numeral_numeral @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(317,axiom,
    ! [A: extended_enat] :
      ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( extend1771934483f_enat @ A ) )
      = ( ord_less_eq @ extended_enat @ ( zero_zero @ extended_enat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_ereal__of__enat__ge__zero__cancel__iff) ).

thf(1351,plain,
    ! [A: extended_enat] :
      ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( extend1771934483f_enat @ A ) )
      = ( ord_less_eq @ extended_enat @ ( zero_zero @ extended_enat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(192,axiom,
    ( ( uminus_uminus @ extended_ereal @ extended_MInfty )
    = extended_PInfty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_uminus__ereal_Osimps_I3_J) ).

thf(988,plain,
    ( ( uminus_uminus @ extended_ereal @ extended_MInfty )
    = extended_PInfty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(94,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ( ( uminus_uminus @ TA @ ( zero_zero @ TA ) )
        = ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add_Oinverse__neutral) ).

thf(507,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ( ( uminus_uminus @ TA @ ( zero_zero @ TA ) )
        = ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(102,axiom,
    ordere142940540dd_abs @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add__abs) ).

thf(527,plain,
    ordere142940540dd_abs @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(55,axiom,
    ! [TA: $tType] :
      ( ( neg_numeral @ TA )
     => ! [A: num] :
          ( ( neg_numeral_dbl @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
          = ( uminus_uminus @ TA @ ( neg_numeral_dbl @ TA @ ( numeral_numeral @ TA @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_dbl__simps_I1_J) ).

thf(428,plain,
    ! [TA: $tType] :
      ( ( neg_numeral @ TA )
     => ! [A: num] :
          ( ( neg_numeral_dbl @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
          = ( uminus_uminus @ TA @ ( neg_numeral_dbl @ TA @ ( numeral_numeral @ TA @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(266,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( abs_abs @ TA @ A ) ) @ ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_abs__minus__le__zero) ).

thf(1201,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( abs_abs @ TA @ A ) ) @ ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(59,axiom,
    linord1659791738miring @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring) ).

thf(439,plain,
    linord1659791738miring @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(145,axiom,
    ! [A: num,B: extended_enat] :
      ( ( ord_less_eq @ extended_ereal @ ( numeral_numeral @ extended_ereal @ A ) @ ( extend1771934483f_enat @ B ) )
      = ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_numeral__le__ereal__of__enat__iff) ).

thf(661,plain,
    ! [A: num,B: extended_enat] :
      ( ( ord_less_eq @ extended_ereal @ ( numeral_numeral @ extended_ereal @ A ) @ ( extend1771934483f_enat @ B ) )
      = ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(176,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( abs_abs @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_abs__ge__zero) ).

thf(925,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( abs_abs @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(249,axiom,
    ! [A: extended_ereal] :
      ( ( divide_divide @ extended_ereal @ A @ ( extend1396239628finity @ extended_ereal ) )
      = ( zero_zero @ extended_ereal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_ereal__divide__Infty_I1_J) ).

thf(1153,plain,
    ! [A: extended_ereal] :
      ( ( divide_divide @ extended_ereal @ A @ ( extend1396239628finity @ extended_ereal ) )
      = ( zero_zero @ extended_ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(31,axiom,
    zero @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).

thf(381,plain,
    zero @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(171,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ A )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_neg__less__eq__nonneg) ).

thf(910,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ 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)],[171]) ).

thf(185,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( ord_less_eq @ TA @ A @ B )
           => ~ ( ord_less_eq @ TA @ B @ C ) )
         => ( ( ( ord_less_eq @ TA @ B @ A )
             => ~ ( ord_less_eq @ TA @ A @ C ) )
           => ( ( ( ord_less_eq @ TA @ A @ C )
               => ~ ( ord_less_eq @ TA @ C @ B ) )
             => ( ( ( ord_less_eq @ TA @ C @ B )
                 => ~ ( ord_less_eq @ TA @ B @ A ) )
               => ( ( ( ord_less_eq @ TA @ B @ C )
                   => ~ ( ord_less_eq @ TA @ C @ A ) )
                 => ~ ( ( ord_less_eq @ TA @ C @ A )
                     => ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_le__cases3) ).

thf(957,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( ord_less_eq @ TA @ A @ B )
           => ~ ( ord_less_eq @ TA @ B @ C ) )
         => ( ( ( ord_less_eq @ TA @ B @ A )
             => ~ ( ord_less_eq @ TA @ A @ C ) )
           => ( ( ( ord_less_eq @ TA @ A @ C )
               => ~ ( ord_less_eq @ TA @ C @ B ) )
             => ( ( ( ord_less_eq @ TA @ C @ B )
                 => ~ ( ord_less_eq @ TA @ B @ A ) )
               => ( ( ( ord_less_eq @ TA @ B @ C )
                   => ~ ( ord_less_eq @ TA @ C @ A ) )
                 => ~ ( ( ord_less_eq @ TA @ C @ A )
                     => ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(314,axiom,
    ! [TA: $tType] :
      ( ( real_V2090557954_space @ TA )
     => ! [A: TA > extended_ereal,B: TA > extended_ereal] :
          ( ( A
            = ( lower_1879122655c_hull @ TA @ B ) )
          = ( ( lower_107104146le_lsc @ TA @ extended_ereal @ A )
            & ! [C: TA] : ( ord_less_eq @ extended_ereal @ ( A @ C ) @ ( B @ C ) )
            & ! [C: TA > extended_ereal] :
                ( ( ( lower_107104146le_lsc @ TA @ extended_ereal @ C )
                  & ! [D: TA] : ( ord_less_eq @ extended_ereal @ ( C @ D ) @ ( B @ D ) ) )
               => ! [D: TA] : ( ord_less_eq @ extended_ereal @ ( C @ D ) @ ( A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_lsc__hull__iff__greatest) ).

thf(1343,plain,
    ! [TA: $tType] :
      ( ( real_V2090557954_space @ TA )
     => ! [A: TA > extended_ereal,B: TA > extended_ereal] :
          ( ( A
            = ( lower_1879122655c_hull @ TA @ B ) )
          = ( ( lower_107104146le_lsc @ TA @ extended_ereal @ A )
            & ! [C: TA] : ( ord_less_eq @ extended_ereal @ ( A @ C ) @ ( B @ C ) )
            & ! [C: TA > extended_ereal] :
                ( ( ( lower_107104146le_lsc @ TA @ extended_ereal @ C )
                  & ! [D: TA] : ( ord_less_eq @ extended_ereal @ ( C @ D ) @ ( B @ D ) ) )
               => ! [D: TA] : ( ord_less_eq @ extended_ereal @ ( C @ D ) @ ( A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(212,axiom,
    topolo259154727pology @ extended_ereal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Topological__Spaces_Oorder__topology_40) ).

thf(1042,plain,
    topolo259154727pology @ extended_ereal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(273,axiom,
    ( ( abs_abs @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
    = ( extend1396239628finity @ extended_ereal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_abs__ereal_Osimps_I2_J) ).

thf(1217,plain,
    ( ( abs_abs @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
    = ( extend1396239628finity @ extended_ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(53,axiom,
    ! [TA: $tType] :
      ( ( boolean_algebra @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( uminus_uminus @ TA @ A )
            = ( uminus_uminus @ TA @ B ) )
          = ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_compl__eq__compl__iff) ).

thf(424,plain,
    ! [TA: $tType] :
      ( ( boolean_algebra @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( uminus_uminus @ TA @ A )
            = ( uminus_uminus @ TA @ B ) )
          = ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(43,axiom,
    linord1659791738miring @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_19) ).

thf(407,plain,
    linord1659791738miring @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(323,axiom,
    preorder @ extended_ereal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Orderings_Opreorder_41) ).

thf(1370,plain,
    preorder @ extended_ereal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(280,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB,C: TA] :
          ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
         => ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_le__funD) ).

thf(1238,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB,C: TA] :
          ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
         => ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(158,axiom,
    ! [TA: $tType] :
      ( ( linordered_field @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ ( abs_abs @ TA @ B ) ) @ ( zero_zero @ TA ) )
          = ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
            | ( B
              = ( zero_zero @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_divide__le__0__abs__iff) ).

thf(862,plain,
    ! [TA: $tType] :
      ( ( linordered_field @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ ( abs_abs @ TA @ B ) ) @ ( zero_zero @ TA ) )
          = ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
            | ( B
              = ( zero_zero @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(12,axiom,
    linord1659791738miring @ extended_enat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Olinordered__nonzero__semiring_31) ).

thf(349,plain,
    linord1659791738miring @ extended_enat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(82,axiom,
    ord @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_4) ).

thf(484,plain,
    ord @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(162,axiom,
    ( ( abs_abs @ extended_ereal @ ( zero_zero @ extended_ereal ) )
    = ( zero_zero @ extended_ereal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_abs__ereal__zero) ).

thf(889,plain,
    ( ( abs_abs @ extended_ereal @ ( zero_zero @ extended_ereal ) )
    = ( zero_zero @ extended_ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(225,axiom,
    ! [A: nat > $o,B: nat,C: nat] :
      ( ( A @ B )
     => ( ! [D: nat] :
            ( ( A @ D )
           => ( ord_less_eq @ nat @ D @ C ) )
       => ( A @ ( order_Greatest @ nat @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_GreatestI__nat) ).

thf(1079,plain,
    ! [A: nat > $o,B: nat,C: nat] :
      ( ( A @ B )
     => ( ! [D: nat] :
            ( ( A @ D )
           => ( ord_less_eq @ nat @ D @ C ) )
       => ( A @ ( order_Greatest @ nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(153,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_order_Otrans) ).

thf(682,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(188,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num,B: num] :
          ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
          = ( ord_less_eq @ num @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_neg__numeral__le__iff) ).

thf(974,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num,B: num] :
          ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
          = ( ord_less_eq @ num @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(173,axiom,
    ! [TA: $tType] :
      ( ( linord1659791738miring @ TA )
     => ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_le__numeral__extra_I3_J) ).

thf(916,plain,
    ! [TA: $tType] :
      ( ( linord1659791738miring @ TA )
     => ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(73,axiom,
    ! [A: extended_ereal] :
      ( ! [B: real] :
          ( A
         != ( extended_ereal2 @ B ) )
     => ( ( A != extended_PInfty )
       => ( A = extended_MInfty ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_ereal_Oexhaust) ).

thf(467,plain,
    ! [A: extended_ereal] :
      ( ! [B: real] :
          ( A
         != ( extended_ereal2 @ B ) )
     => ( ( A != extended_PInfty )
       => ( A = extended_MInfty ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(251,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ( ( ord_less_eq @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB] :
            ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_le__fun__def) ).

thf(1159,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ( ( ord_less_eq @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB] :
            ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(70,axiom,
    preorder @ $o,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_12) ).

thf(461,plain,
    preorder @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(87,axiom,
    neg_numeral @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Num_Oneg__numeral) ).

thf(493,plain,
    neg_numeral @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(270,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
      = ( ord_less_eq @ nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_enat__ord__simps_I1_J) ).

thf(1210,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
      = ( ord_less_eq @ nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(111,axiom,
    real_V2090557954_space @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space) ).

thf(551,plain,
    real_V2090557954_space @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(241,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( order_antimono @ nat @ TA )
        = ( ^ [A: nat > TA] :
            ! [B: nat,C: nat] :
              ( ( ord_less_eq @ nat @ B @ C )
             => ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_decseq__def) ).

thf(1128,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( order_antimono @ nat @ TA )
        = ( ^ [A: nat > TA] :
            ! [B: nat,C: nat] :
              ( ( ord_less_eq @ nat @ B @ C )
             => ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(99,axiom,
    ! [A: real] :
      ( ( extended_ereal2 @ A )
     != extended_PInfty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_ereal_Odistinct_I1_J) ).

thf(519,plain,
    ! [A: real] :
      ( ( extended_ereal2 @ A )
     != extended_PInfty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(142,axiom,
    ! [A: extended_ereal > extended_ereal > $o,B: extended_ereal,C: extended_ereal] :
      ( ! [D: real,E: real] : ( A @ ( extended_ereal2 @ D ) @ ( extended_ereal2 @ E ) )
     => ( ! [D: real] : ( A @ ( extended_ereal2 @ D ) @ ( extend1396239628finity @ extended_ereal ) )
       => ( ! [D: real] : ( A @ ( extend1396239628finity @ extended_ereal ) @ ( extended_ereal2 @ D ) )
         => ( ! [D: real] : ( A @ ( extended_ereal2 @ D ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
           => ( ! [D: real] : ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extended_ereal2 @ D ) )
             => ( ( A @ ( extend1396239628finity @ extended_ereal ) @ ( extend1396239628finity @ extended_ereal ) )
               => ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extend1396239628finity @ extended_ereal ) )
                 => ( ( A @ ( extend1396239628finity @ extended_ereal ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                   => ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                     => ( A @ B @ C ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_times__ereal_Oinduct) ).

thf(650,plain,
    ! [A: extended_ereal > extended_ereal > $o,B: extended_ereal,C: extended_ereal] :
      ( ! [D: real,E: real] : ( A @ ( extended_ereal2 @ D ) @ ( extended_ereal2 @ E ) )
     => ( ! [D: real] : ( A @ ( extended_ereal2 @ D ) @ ( extend1396239628finity @ extended_ereal ) )
       => ( ! [D: real] : ( A @ ( extend1396239628finity @ extended_ereal ) @ ( extended_ereal2 @ D ) )
         => ( ! [D: real] : ( A @ ( extended_ereal2 @ D ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
           => ( ! [D: real] : ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extended_ereal2 @ D ) )
             => ( ( A @ ( extend1396239628finity @ extended_ereal ) @ ( extend1396239628finity @ extended_ereal ) )
               => ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extend1396239628finity @ extended_ereal ) )
                 => ( ( A @ ( extend1396239628finity @ extended_ereal ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                   => ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                     => ( A @ B @ C ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(239,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA > $o,B: TA] :
          ( ( A @ B )
         => ( ! [C: TA] :
                ( ( A @ C )
               => ( ord_less_eq @ TA @ C @ B ) )
           => ( ( order_Greatest @ TA @ A )
              = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_Greatest__equality) ).

thf(1121,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA > $o,B: TA] :
          ( ( A @ B )
         => ( ! [C: TA] :
                ( ( A @ C )
               => ( ord_less_eq @ TA @ C @ B ) )
           => ( ( order_Greatest @ TA @ A )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(190,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA > $o,B: TA,C: TA > $o] :
          ( ( A @ B )
         => ( ! [D: TA] :
                ( ( A @ D )
               => ( ord_less_eq @ TA @ D @ B ) )
           => ( ! [D: TA] :
                  ( ( A @ D )
                 => ( ! [E: TA] :
                        ( ( A @ E )
                       => ( ord_less_eq @ TA @ E @ D ) )
                   => ( C @ D ) ) )
             => ( C @ ( order_Greatest @ TA @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_GreatestI2__order) ).

thf(980,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA > $o,B: TA,C: TA > $o] :
          ( ( A @ B )
         => ( ! [D: TA] :
                ( ( A @ D )
               => ( ord_less_eq @ TA @ D @ B ) )
           => ( ! [D: TA] :
                  ( ( A @ D )
                 => ( ! [E: TA] :
                        ( ( A @ E )
                       => ( ord_less_eq @ TA @ E @ D ) )
                   => ( C @ D ) ) )
             => ( C @ ( order_Greatest @ TA @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(230,axiom,
    ! [A: real,B: extended_ereal] :
      ( ( ord_less_eq @ real @ A @ ( extend1716541707_ereal @ B ) )
      = ( ( ( ( abs_abs @ extended_ereal @ B )
           != ( extend1396239628finity @ extended_ereal ) )
         => ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ A ) @ B ) )
        & ( ( ( abs_abs @ extended_ereal @ B )
            = ( extend1396239628finity @ extended_ereal ) )
         => ( ord_less_eq @ real @ A @ ( zero_zero @ real ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_ereal__le__real__iff) ).

thf(1096,plain,
    ! [A: real,B: extended_ereal] :
      ( ( ord_less_eq @ real @ A @ ( extend1716541707_ereal @ B ) )
      = ( ( ( ( abs_abs @ extended_ereal @ B )
           != ( extend1396239628finity @ extended_ereal ) )
         => ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ A ) @ B ) )
        & ( ( ( abs_abs @ extended_ereal @ B )
            = ( extend1396239628finity @ extended_ereal ) )
         => ( ord_less_eq @ real @ A @ ( zero_zero @ real ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(238,axiom,
    ! [A: real,B: extended_ereal,C: real] :
      ( ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ A ) @ B )
     => ( ( ord_less_eq @ real @ C @ A )
       => ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_ereal__le__le) ).

thf(1118,plain,
    ! [A: real,B: extended_ereal,C: real] :
      ( ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ A ) @ B )
     => ( ( ord_less_eq @ real @ C @ A )
       => ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(90,axiom,
    linordered_field @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Olinordered__field) ).

thf(499,plain,
    linordered_field @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(245,axiom,
    ! [A: extended_ereal] :
      ( ! [B: real] :
          ( A
         != ( extended_ereal2 @ B ) )
     => ( ( A
         != ( extend1396239628finity @ extended_ereal ) )
       => ( A
          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_real__of__ereal_Ocases) ).

thf(1138,plain,
    ! [A: extended_ereal] :
      ( ! [B: real] :
          ( A
         != ( extended_ereal2 @ B ) )
     => ( ( A
         != ( extend1396239628finity @ extended_ereal ) )
       => ( A
          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(18,axiom,
    ! [A: real] :
      ( ( extend1716541707_ereal @ ( extended_ereal2 @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_real__of__ereal_Osimps_I1_J) ).

thf(356,plain,
    ! [A: real] :
      ( ( extend1716541707_ereal @ ( extended_ereal2 @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(74,axiom,
    linorder @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Olinorder_22) ).

thf(471,plain,
    linorder @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(309,axiom,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( divide_divide @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ B )
      = ( uminus_uminus @ extended_ereal @ ( divide_divide @ extended_ereal @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_ereal__uminus__divide) ).

thf(1329,plain,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( divide_divide @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ B )
      = ( uminus_uminus @ extended_ereal @ ( divide_divide @ extended_ereal @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(207,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_order__class_Oorder_Oantisym) ).

thf(1028,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(321,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_order__refl) ).

thf(1361,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(7,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( uminus_uminus @ TA @ A )
            = ( uminus_uminus @ TA @ B ) )
          = ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_neg__equal__iff__equal) ).

thf(339,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( uminus_uminus @ TA @ A )
            = ( uminus_uminus @ TA @ B ) )
          = ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(179,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_antisym) ).

thf(933,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(259,axiom,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
          = ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_le__minus__iff) ).

thf(1182,plain,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
          = ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(85,axiom,
    zero @ extended_enat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ozero_38) ).

thf(489,plain,
    zero @ extended_enat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(110,axiom,
    ! [A: real] :
      ( ( extended_ereal2 @ A )
     != extended_MInfty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_ereal_Odistinct_I3_J) ).

thf(547,plain,
    ! [A: real] :
      ( ( extended_ereal2 @ A )
     != extended_MInfty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(167,axiom,
    ord_less_eq @ extended_ereal @ ( lower_1879122655c_hull @ a @ g @ x ) @ ( g @ x ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_calculation) ).

thf(901,plain,
    ord_less_eq @ extended_ereal @ ( lower_1879122655c_hull @ a @ g @ x ) @ ( g @ x ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(79,axiom,
    ! [TA: $tType] :
      ( ( real_V2090557954_space @ TA )
     => ( topolo503727757_space @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Real__Vector__Spaces_Ometric__space___Topological__Spaces_Otopological__space) ).

thf(476,plain,
    ! [TA: $tType] :
      ( ( real_V2090557954_space @ TA )
     => ( topolo503727757_space @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(204,axiom,
    ( ( extend1716541707_ereal @ ( zero_zero @ extended_ereal ) )
    = ( zero_zero @ real ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_real__of__ereal__0) ).

thf(1016,plain,
    ( ( extend1716541707_ereal @ ( zero_zero @ extended_ereal ) )
    = ( zero_zero @ real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(269,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( abs_abs @ TA @ A )
            = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_abs__of__nonneg) ).

thf(1207,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
         => ( ( abs_abs @ TA @ A )
            = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(152,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_le__antisym) ).

thf(679,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(211,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_order__class_Oorder_Oeq__iff) ).

thf(1039,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ( ( (=) @ TA )
        = ( ^ [A: TA,B: TA] :
              ( ( ord_less_eq @ TA @ A @ B )
              & ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(138,axiom,
    ! [A: extended_ereal,B: real] :
      ( ( ( extend1716541707_ereal @ A )
        = B )
     => ( ! [C: real] :
            ( ( A
              = ( extended_ereal2 @ C ) )
           => ( B != C ) )
       => ( ( ( A
              = ( extend1396239628finity @ extended_ereal ) )
           => ( B
             != ( zero_zero @ real ) ) )
         => ~ ( ( A
                = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
             => ( B
               != ( zero_zero @ real ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_real__of__ereal_Oelims) ).

thf(622,plain,
    ! [A: extended_ereal,B: real] :
      ( ( ( extend1716541707_ereal @ A )
        = B )
     => ( ! [C: real] :
            ( ( A
              = ( extended_ereal2 @ C ) )
           => ( B != C ) )
       => ( ( ( A
              = ( extend1396239628finity @ extended_ereal ) )
           => ( B
             != ( zero_zero @ real ) ) )
         => ~ ( ( A
                = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
             => ( B
               != ( zero_zero @ real ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(37,axiom,
    zero @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_27) ).

thf(393,plain,
    zero @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(231,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ A )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_abs__le__self__iff) ).

thf(1099,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ A )
          = ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(97,axiom,
    preorder @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Opreorder_21) ).

thf(515,plain,
    preorder @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(242,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
           => ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_abs__leI) ).

thf(1131,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
           => ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(263,axiom,
    ! [A: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
     => ( A
       != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_not__MInfty__nonneg) ).

thf(1192,plain,
    ! [A: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
     => ( A
       != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(219,axiom,
    ( ( uminus_uminus @ extended_ereal @ ( zero_zero @ extended_ereal ) )
    = ( zero_zero @ extended_ereal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_ereal__uminus__zero) ).

thf(1060,plain,
    ( ( uminus_uminus @ extended_ereal @ ( zero_zero @ extended_ereal ) )
    = ( zero_zero @ extended_ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(141,axiom,
    ( ( extend1396239628finity @ extended_ereal )
   != ( zero_zero @ extended_ereal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Infty__neq__0_I1_J) ).

thf(647,plain,
    ( ( extend1396239628finity @ extended_ereal )
   != ( zero_zero @ extended_ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(288,axiom,
    ! [A: extended_ereal] :
      ( ! [B: real] :
          ( A
         != ( extended_ereal2 @ B ) )
     => ( ( A
         != ( extend1396239628finity @ extended_ereal ) )
       => ( A
          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_ereal__cases) ).

thf(1263,plain,
    ! [A: extended_ereal] :
      ( ! [B: real] :
          ( A
         != ( extended_ereal2 @ B ) )
     => ( ( A
         != ( extend1396239628finity @ extended_ereal ) )
       => ( A
          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(227,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ ( abs_abs @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_abs__ge__self) ).

thf(1086,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ ( abs_abs @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(20,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num] :
          ( ( abs_abs @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
          = ( numeral_numeral @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_abs__neg__numeral) ).

thf(360,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num] :
          ( ( abs_abs @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
          = ( numeral_numeral @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(175,axiom,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
     => ( ( ord_less_eq @ extended_ereal @ A @ B )
       => ( ( B
           != ( extend1396239628finity @ extended_ereal ) )
         => ( ord_less_eq @ real @ ( extend1716541707_ereal @ A ) @ ( extend1716541707_ereal @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_real__of__ereal__positive__mono) ).

thf(921,plain,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
     => ( ( ord_less_eq @ extended_ereal @ A @ B )
       => ( ( B
           != ( extend1396239628finity @ extended_ereal ) )
         => ( ord_less_eq @ real @ ( extend1716541707_ereal @ A ) @ ( extend1716541707_ereal @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(254,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_dual__order_Orefl) ).

thf(1167,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(260,axiom,
    ( ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) )
   != ( zero_zero @ extended_ereal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Infty__neq__0_I3_J) ).

thf(1185,plain,
    ( ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) )
   != ( zero_zero @ extended_ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(96,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TA )
     => ( ord @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).

thf(513,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TA )
     => ( ord @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(274,axiom,
    ! [A: real] :
      ( ( A
        = ( zero_zero @ real ) )
      = ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A )
        & ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( uminus_uminus @ real @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_real__eq__0__iff__le__ge__0) ).

thf(1219,plain,
    ! [A: real] :
      ( ( A
        = ( zero_zero @ real ) )
      = ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A )
        & ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( uminus_uminus @ real @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(156,axiom,
    ! [A: extended_ereal,B: real] :
      ( ( ord_less_eq @ real @ ( extend1716541707_ereal @ A ) @ B )
      = ( ( ( ( abs_abs @ extended_ereal @ A )
           != ( extend1396239628finity @ extended_ereal ) )
         => ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ B ) ) )
        & ( ( ( abs_abs @ extended_ereal @ A )
            = ( extend1396239628finity @ extended_ereal ) )
         => ( ord_less_eq @ real @ ( zero_zero @ real ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_real__le__ereal__iff) ).

thf(856,plain,
    ! [A: extended_ereal,B: real] :
      ( ( ord_less_eq @ real @ ( extend1716541707_ereal @ A ) @ B )
      = ( ( ( ( abs_abs @ extended_ereal @ A )
           != ( extend1396239628finity @ extended_ereal ) )
         => ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ B ) ) )
        & ( ( ( abs_abs @ extended_ereal @ A )
            = ( extend1396239628finity @ extended_ereal ) )
         => ( ord_less_eq @ real @ ( zero_zero @ real ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(299,axiom,
    linorder @ extended_ereal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Orderings_Olinorder_42) ).

thf(1301,plain,
    linorder @ extended_ereal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(62,axiom,
    ordered_ab_group_add @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add) ).

thf(444,plain,
    ordered_ab_group_add @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(29,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] :
          ( ( abs_abs @ TA @ ( abs_abs @ TA @ A ) )
          = ( abs_abs @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_abs__idempotent) ).

thf(375,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] :
          ( ( abs_abs @ TA @ ( abs_abs @ TA @ A ) )
          = ( abs_abs @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(244,axiom,
    ! [A: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( uminus_uminus @ extended_ereal @ A ) )
      = ( ord_less_eq @ extended_ereal @ A @ ( zero_zero @ extended_ereal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_ereal__0__le__uminus__iff) ).

thf(1135,plain,
    ! [A: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( uminus_uminus @ extended_ereal @ A ) )
      = ( ord_less_eq @ extended_ereal @ A @ ( zero_zero @ extended_ereal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(47,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA )
     => ! [A: TA] :
          ( ( ( uminus_uminus @ TA @ A )
            = A )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_neg__equal__zero) ).

thf(412,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA )
     => ! [A: TA] :
          ( ( ( uminus_uminus @ TA @ A )
            = A )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(116,axiom,
    topolo503727757_space @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Otopological__space_17) ).

thf(562,plain,
    topolo503727757_space @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(201,axiom,
    ! [A: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
     => ( ( abs_abs @ extended_ereal @ A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_abs__ereal__ge0) ).

thf(1007,plain,
    ! [A: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
     => ( ( abs_abs @ extended_ereal @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(41,axiom,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( A = B )
         => ( ( uminus_uminus @ TA @ A )
            = ( uminus_uminus @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_verit__negate__coefficient_I3_J) ).

thf(402,plain,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( A = B )
         => ( ( uminus_uminus @ TA @ A )
            = ( uminus_uminus @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(124,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ B )
          = ( ( ord_less_eq @ TA @ A @ B )
            & ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_abs__le__iff) ).

thf(579,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ B )
          = ( ( ord_less_eq @ TA @ A @ B )
            & ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(285,axiom,
    ( ( extend1716541707_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
    = ( zero_zero @ real ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_real__of__ereal_Osimps_I3_J) ).

thf(1256,plain,
    ( ( extend1716541707_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
    = ( zero_zero @ real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(276,axiom,
    ! [A: extended_enat,B: extended_enat] :
      ( ( ord_less_eq @ extended_ereal @ ( extend1771934483f_enat @ A ) @ ( extend1771934483f_enat @ B ) )
      = ( ord_less_eq @ extended_enat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_ereal__of__enat__le__iff) ).

thf(1226,plain,
    ! [A: extended_enat,B: extended_enat] :
      ( ( ord_less_eq @ extended_ereal @ ( extend1771934483f_enat @ A ) @ ( extend1771934483f_enat @ B ) )
      = ( ord_less_eq @ extended_enat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(109,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( topolo503727757_space @ TA )
     => ( topolo503727757_space @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Topological__Spaces_Otopological__space) ).

thf(545,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( topolo503727757_space @ TA )
     => ( topolo503727757_space @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(139,axiom,
    ! [A: extended_ereal] :
      ( ( ( extend1716541707_ereal @ A )
        = ( zero_zero @ real ) )
      = ( ( A
          = ( extend1396239628finity @ extended_ereal ) )
        | ( A
          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
        | ( A
          = ( zero_zero @ extended_ereal ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_real__of__ereal__eq__0) ).

thf(641,plain,
    ! [A: extended_ereal] :
      ( ( ( extend1716541707_ereal @ A )
        = ( zero_zero @ real ) )
      = ( ( A
          = ( extend1396239628finity @ extended_ereal ) )
        | ( A
          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
        | ( A
          = ( zero_zero @ extended_ereal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(32,axiom,
    ord @ $o,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_15) ).

thf(382,plain,
    ord @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(304,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_neg__numeral__le__zero) ).

thf(1312,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(134,axiom,
    ! [A: real] :
      ( ( uminus_uminus @ extended_ereal @ ( extended_ereal2 @ A ) )
      = ( extended_ereal2 @ ( uminus_uminus @ real @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_uminus__ereal_Osimps_I1_J) ).

thf(611,plain,
    ! [A: real] :
      ( ( uminus_uminus @ extended_ereal @ ( extended_ereal2 @ A ) )
      = ( extended_ereal2 @ ( uminus_uminus @ real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(89,axiom,
    order @ num,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Oorder_7) ).

thf(498,plain,
    order @ num,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(218,axiom,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_le__imp__neg__le) ).

thf(1058,plain,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(310,axiom,
    ! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_less__eq__nat_Osimps_I1_J) ).

thf(1332,plain,
    ! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(229,axiom,
    ! [A: set @ extended_ereal] :
    ? [B: extended_ereal] :
      ( ! [C: extended_ereal] :
          ( ( member @ extended_ereal @ C @ A )
         => ( ord_less_eq @ extended_ereal @ C @ B ) )
      & ! [C: extended_ereal] :
          ( ! [D: extended_ereal] :
              ( ( member @ extended_ereal @ D @ A )
             => ( ord_less_eq @ extended_ereal @ D @ C ) )
         => ( ord_less_eq @ extended_ereal @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_ereal__complete__Sup) ).

thf(1090,plain,
    ! [A: set @ extended_ereal] :
    ? [B: extended_ereal] :
      ( ! [C: extended_ereal] :
          ( ( member @ extended_ereal @ C @ A )
         => ( ord_less_eq @ extended_ereal @ C @ B ) )
      & ! [C: extended_ereal] :
          ( ! [D: extended_ereal] :
              ( ( member @ extended_ereal @ D @ A )
             => ( ord_less_eq @ extended_ereal @ D @ C ) )
         => ( ord_less_eq @ extended_ereal @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(286,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_le__zero__eq) ).

thf(1258,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(183,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA )
        & ( ord @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( A
            = ( B @ C ) )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less_eq @ TA @ E @ F )
                 => ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_ord__eq__le__subst) ).

thf(947,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA )
        & ( ord @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( A
            = ( B @ C ) )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less_eq @ TA @ E @ F )
                 => ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(13,axiom,
    canoni770627133id_add @ extended_enat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_28) ).

thf(350,plain,
    canoni770627133id_add @ extended_enat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(150,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( A = B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_ord__eq__le__trans) ).

thf(672,plain,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( A = B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(63,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num] :
          ( ( abs_abs @ TA @ ( numeral_numeral @ TA @ A ) )
          = ( numeral_numeral @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_abs__numeral) ).

thf(445,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num] :
          ( ( abs_abs @ TA @ ( numeral_numeral @ TA @ A ) )
          = ( numeral_numeral @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(180,axiom,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ A @ B )
     => ( ( B
          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
       => ( A
          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_ereal__infty__less__eq2_I2_J) ).

thf(936,plain,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ A @ B )
     => ( ( B
          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
       => ( A
          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(291,axiom,
    ! [A: extended_ereal > $o,B: extended_ereal] :
      ( ! [C: real] : ( A @ ( extended_ereal2 @ C ) )
     => ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
       => ( ( A @ ( extend1396239628finity @ extended_ereal ) )
         => ( A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_abs__ereal_Oinduct) ).

thf(1271,plain,
    ! [A: extended_ereal > $o,B: extended_ereal] :
      ( ! [C: real] : ( A @ ( extended_ereal2 @ C ) )
     => ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
       => ( ( A @ ( extend1396239628finity @ extended_ereal ) )
         => ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(324,axiom,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ? [C: real] :
            ( A
            = ( extended_ereal2 @ C ) )
       => ! [C: real] :
            ( B
           != ( extended_ereal2 @ C ) ) )
     => ( ( ? [C: real] :
              ( A
              = ( extended_ereal2 @ C ) )
         => ( B
           != ( extend1396239628finity @ extended_ereal ) ) )
       => ( ( ? [C: real] :
                ( A
                = ( extended_ereal2 @ C ) )
           => ( B
             != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) )
         => ( ( ( A
                = ( extend1396239628finity @ extended_ereal ) )
             => ! [C: real] :
                  ( B
                 != ( extended_ereal2 @ C ) ) )
           => ( ( ( A
                  = ( extend1396239628finity @ extended_ereal ) )
               => ( B
                 != ( extend1396239628finity @ extended_ereal ) ) )
             => ( ( ( A
                    = ( extend1396239628finity @ extended_ereal ) )
                 => ( B
                   != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) )
               => ( ( ( A
                      = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                   => ! [C: real] :
                        ( B
                       != ( extended_ereal2 @ C ) ) )
                 => ( ( ( A
                        = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                     => ( B
                       != ( extend1396239628finity @ extended_ereal ) ) )
                   => ~ ( ( A
                          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                       => ( B
                         != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_ereal2__cases) ).

thf(1371,plain,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ? [C: real] :
            ( A
            = ( extended_ereal2 @ C ) )
       => ! [C: real] :
            ( B
           != ( extended_ereal2 @ C ) ) )
     => ( ( ? [C: real] :
              ( A
              = ( extended_ereal2 @ C ) )
         => ( B
           != ( extend1396239628finity @ extended_ereal ) ) )
       => ( ( ? [C: real] :
                ( A
                = ( extended_ereal2 @ C ) )
           => ( B
             != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) )
         => ( ( ( A
                = ( extend1396239628finity @ extended_ereal ) )
             => ! [C: real] :
                  ( B
                 != ( extended_ereal2 @ C ) ) )
           => ( ( ( A
                  = ( extend1396239628finity @ extended_ereal ) )
               => ( B
                 != ( extend1396239628finity @ extended_ereal ) ) )
             => ( ( ( A
                    = ( extend1396239628finity @ extended_ereal ) )
                 => ( B
                   != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) )
               => ( ( ( A
                      = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                   => ! [C: real] :
                        ( B
                       != ( extended_ereal2 @ C ) ) )
                 => ( ( ( A
                        = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                     => ( B
                       != ( extend1396239628finity @ extended_ereal ) ) )
                   => ~ ( ( A
                          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                       => ( B
                         != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(42,axiom,
    ord @ num,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Oord_8) ).

thf(406,plain,
    ord @ num,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(51,axiom,
    ( ( zero_zero @ extended_enat )
    = ( extended_enat2 @ ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_zero__enat__def) ).

thf(419,plain,
    ( ( zero_zero @ extended_enat )
    = ( extended_enat2 @ ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(316,axiom,
    ! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_le__refl) ).

thf(1349,plain,
    ! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(213,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ B )
         => ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less_eq @ TB @ E @ F )
                 => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_order__subst2) ).

thf(1043,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ B )
         => ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less_eq @ TB @ E @ F )
                 => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(256,axiom,
    ! [TA: $tType] :
      ( ( real_V2090557954_space @ TA )
     => ! [A: TA > extended_ereal,B: TA] : ( ord_less_eq @ extended_ereal @ ( lower_1879122655c_hull @ TA @ A @ B ) @ ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_lsc__hull__le) ).

thf(1175,plain,
    ! [TA: $tType] :
      ( ( real_V2090557954_space @ TA )
     => ! [A: TA > extended_ereal,B: TA] : ( ord_less_eq @ extended_ereal @ ( lower_1879122655c_hull @ TA @ A @ B ) @ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(193,axiom,
    order @ extended_ereal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Orderings_Oorder_43) ).

thf(990,plain,
    order @ extended_ereal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(196,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( linorder @ TA )
        & ( order @ 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/sandbox/benchmark/theBenchmark.p',fact_52_strict__mono__less__eq) ).

thf(996,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( linorder @ TA )
        & ( order @ 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)],[196]) ).

thf(88,axiom,
    ! [A: extended_ereal] :
      ( ! [B: real] :
          ( A
         != ( extended_ereal2 @ B ) )
     => ( ( A != extended_PInfty )
       => ( A = extended_MInfty ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_uminus__ereal_Ocases) ).

thf(494,plain,
    ! [A: extended_ereal] :
      ( ! [B: real] :
          ( A
         != ( extended_ereal2 @ B ) )
     => ( ( A != extended_PInfty )
       => ( A = extended_MInfty ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(313,axiom,
    ! [A: extended_ereal] :
      ( ! [B: real] :
          ( A
         != ( extended_ereal2 @ B ) )
     => ( ( A
         != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
       => ( A
          = ( extend1396239628finity @ extended_ereal ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_abs__ereal_Ocases) ).

thf(1339,plain,
    ! [A: extended_ereal] :
      ( ! [B: real] :
          ( A
         != ( extended_ereal2 @ B ) )
     => ( ( A
         != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
       => ( A
          = ( extend1396239628finity @ extended_ereal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(106,axiom,
    numeral @ extended_enat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Num_Onumeral_37) ).

thf(535,plain,
    numeral @ extended_enat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(129,axiom,
    ! [A: extended_ereal > extended_ereal > $o,B: extended_ereal,C: extended_ereal] :
      ( ! [D: real,E: real] : ( A @ ( extended_ereal2 @ D ) @ ( extended_ereal2 @ E ) )
     => ( ! [D: extended_ereal] : ( A @ ( extend1396239628finity @ extended_ereal ) @ D )
       => ( ! [D: extended_ereal] : ( A @ D @ ( extend1396239628finity @ extended_ereal ) )
         => ( ! [D: real] : ( A @ ( extended_ereal2 @ D ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
           => ( ! [D: real] : ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extended_ereal2 @ D ) )
             => ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
               => ( A @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_plus__ereal_Oinduct) ).

thf(594,plain,
    ! [A: extended_ereal > extended_ereal > $o,B: extended_ereal,C: extended_ereal] :
      ( ! [D: real,E: real] : ( A @ ( extended_ereal2 @ D ) @ ( extended_ereal2 @ E ) )
     => ( ! [D: extended_ereal] : ( A @ ( extend1396239628finity @ extended_ereal ) @ D )
       => ( ! [D: extended_ereal] : ( A @ D @ ( extend1396239628finity @ extended_ereal ) )
         => ( ! [D: real] : ( A @ ( extended_ereal2 @ D ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
           => ( ! [D: real] : ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extended_ereal2 @ D ) )
             => ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
               => ( A @ B @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(252,axiom,
    ! [TA: $tType] :
      ( ( linord1659791738miring @ TA )
     => ! [A: num] :
          ~ ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_not__numeral__le__zero) ).

thf(1162,plain,
    ! [TA: $tType] :
      ( ( linord1659791738miring @ TA )
     => ! [A: num] :
          ~ ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(308,axiom,
    ! [A: nat > $o,B: nat] :
      ( ? [C: nat] : ( A @ C )
     => ( ! [C: nat] :
            ( ( A @ C )
           => ( ord_less_eq @ nat @ C @ B ) )
       => ( A @ ( order_Greatest @ nat @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_GreatestI__ex__nat) ).

thf(1325,plain,
    ! [A: nat > $o,B: nat] :
      ( ? [C: nat] : ( A @ C )
     => ( ! [C: nat] :
            ( ( A @ C )
           => ( ord_less_eq @ nat @ C @ B ) )
       => ( A @ ( order_Greatest @ nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(165,axiom,
    ! [A: extended_ereal] :
      ( ( extend1716541707_ereal @ ( uminus_uminus @ extended_ereal @ A ) )
      = ( uminus_uminus @ real @ ( extend1716541707_ereal @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_real__of__ereal) ).

thf(895,plain,
    ! [A: extended_ereal] :
      ( ( extend1716541707_ereal @ ( uminus_uminus @ extended_ereal @ A ) )
      = ( uminus_uminus @ real @ ( extend1716541707_ereal @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(182,axiom,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ A @ B )
     => ( ( A
          = ( extend1396239628finity @ extended_ereal ) )
       => ( B
          = ( extend1396239628finity @ extended_ereal ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_ereal__infty__less__eq2_I1_J) ).

thf(943,plain,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ A @ B )
     => ( ( A
          = ( extend1396239628finity @ extended_ereal ) )
       => ( B
          = ( extend1396239628finity @ extended_ereal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(257,axiom,
    ! [A: nat > nat,B: nat] :
      ( ( order_strict_mono @ nat @ nat @ A )
     => ( ord_less_eq @ nat @ B @ ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_strict__mono__imp__increasing) ).

thf(1177,plain,
    ! [A: nat > nat,B: nat] :
      ( ( order_strict_mono @ nat @ nat @ A )
     => ( ord_less_eq @ nat @ B @ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(4,axiom,
    ! [TA: $tType] :
      ( ( neg_numeral @ TA )
     => ( ( neg_numeral_dbl @ TA @ ( zero_zero @ TA ) )
        = ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_dbl__simps_I2_J) ).

thf(330,plain,
    ! [TA: $tType] :
      ( ( neg_numeral @ TA )
     => ( ( neg_numeral_dbl @ TA @ ( zero_zero @ TA ) )
        = ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(71,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ( ( abs_abs @ TA @ ( zero_zero @ TA ) )
        = ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_abs__zero) ).

thf(462,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ( ( abs_abs @ TA @ ( zero_zero @ TA ) )
        = ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(236,axiom,
    ! [A: nat > $o,B: nat,C: nat] :
      ( ( A @ B )
     => ( ! [D: nat] :
            ( ( A @ D )
           => ( ord_less_eq @ nat @ D @ C ) )
       => ( ord_less_eq @ nat @ B @ ( order_Greatest @ nat @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Greatest__le__nat) ).

thf(1112,plain,
    ! [A: nat > $o,B: nat,C: nat] :
      ( ( A @ B )
     => ( ! [D: nat] :
            ( ( A @ D )
           => ( ord_less_eq @ nat @ D @ C ) )
       => ( ord_less_eq @ nat @ B @ ( order_Greatest @ nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(9,axiom,
    group_add @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ogroup__add) ).

thf(345,plain,
    group_add @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(112,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA] :
          ( ( ( uminus_uminus @ TA @ A )
            = ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_neg__equal__0__iff__equal) ).

thf(552,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA] :
          ( ( ( uminus_uminus @ TA @ A )
            = ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(297,axiom,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( A
       != ( extend1396239628finity @ extended_ereal ) )
     => ( ( ord_less_eq @ extended_ereal @ B @ A )
       => ( B
         != ( extend1396239628finity @ extended_ereal ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_neq__PInf__trans) ).

thf(1293,plain,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( A
       != ( extend1396239628finity @ extended_ereal ) )
     => ( ( ord_less_eq @ extended_ereal @ B @ A )
       => ( B
         != ( extend1396239628finity @ extended_ereal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(148,axiom,
    ! [A: extended_ereal] : ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_ereal__less__eq_I2_J) ).

thf(668,plain,
    ! [A: extended_ereal] : ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(265,axiom,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ ( uminus_uminus @ extended_ereal @ B ) )
      = ( ord_less_eq @ extended_ereal @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_ereal__minus__le__minus) ).

thf(1198,plain,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ ( uminus_uminus @ extended_ereal @ B ) )
      = ( ord_less_eq @ extended_ereal @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(40,axiom,
    ! [A: nat] :
      ( ( ( extended_enat2 @ A )
        = ( zero_zero @ extended_enat ) )
      = ( A
        = ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_enat__0__iff_I1_J) ).

thf(399,plain,
    ! [A: nat] :
      ( ( ( extended_enat2 @ A )
        = ( zero_zero @ extended_enat ) )
      = ( A
        = ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(271,axiom,
    ! [TA: $tType] :
      ( ( linord1659791738miring @ TA )
     => ! [A: num] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( numeral_numeral @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_zero__le__numeral) ).

thf(1213,plain,
    ! [TA: $tType] :
      ( ( linord1659791738miring @ TA )
     => ! [A: num] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( numeral_numeral @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(160,axiom,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ( uminus_uminus @ extended_ereal @ A )
        = B )
     => ( ! [C: real] :
            ( ( A
              = ( extended_ereal2 @ C ) )
           => ( B
             != ( extended_ereal2 @ ( uminus_uminus @ real @ C ) ) ) )
       => ( ( ( A = extended_PInfty )
           => ( B != extended_MInfty ) )
         => ~ ( ( A = extended_MInfty )
             => ( B != extended_PInfty ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_uminus__ereal_Oelims) ).

thf(868,plain,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ( uminus_uminus @ extended_ereal @ A )
        = B )
     => ( ! [C: real] :
            ( ( A
              = ( extended_ereal2 @ C ) )
           => ( B
             != ( extended_ereal2 @ ( uminus_uminus @ real @ C ) ) ) )
       => ( ( ( A = extended_PInfty )
           => ( B != extended_MInfty ) )
         => ~ ( ( A = extended_MInfty )
             => ( B != extended_PInfty ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(69,axiom,
    ! [A: extended_ereal > $o,B: extended_ereal] :
      ( ! [C: real] : ( A @ ( extended_ereal2 @ C ) )
     => ( ( A @ extended_PInfty )
       => ( ( A @ extended_MInfty )
         => ( A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_ereal_Oinduct) ).

thf(455,plain,
    ! [A: extended_ereal > $o,B: extended_ereal] :
      ( ! [C: real] : ( A @ ( extended_ereal2 @ C ) )
     => ( ( A @ extended_PInfty )
       => ( ( A @ extended_MInfty )
         => ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(133,axiom,
    ! [A: extended_ereal] :
      ( ( divide_divide @ extended_ereal @ A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
      = ( zero_zero @ extended_ereal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_ereal__divide__Infty_I2_J) ).

thf(608,plain,
    ! [A: extended_ereal] :
      ( ( divide_divide @ extended_ereal @ A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
      = ( zero_zero @ extended_ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(117,axiom,
    numeral @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Num_Onumeral_26) ).

thf(563,plain,
    numeral @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(283,axiom,
    ! [A: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ ( zero_zero @ extended_ereal ) )
      = ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_ereal__uminus__le__0__iff) ).

thf(1250,plain,
    ! [A: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ ( zero_zero @ extended_ereal ) )
      = ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(232,axiom,
    ! [A: extended_ereal] :
      ( ( ( abs_abs @ extended_ereal @ A )
       != ( extend1396239628finity @ extended_ereal ) )
     => ( ( extended_ereal2 @ ( extend1716541707_ereal @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_ereal__real_H) ).

thf(1102,plain,
    ! [A: extended_ereal] :
      ( ( ( abs_abs @ extended_ereal @ A )
       != ( extend1396239628finity @ extended_ereal ) )
     => ( ( extended_ereal2 @ ( extend1716541707_ereal @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(56,axiom,
    preorder @ num,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Opreorder_5) ).

thf(431,plain,
    preorder @ num,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(144,axiom,
    ! [A: nat] :
      ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
      = ( A
        = ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_le__0__eq) ).

thf(658,plain,
    ! [A: nat] :
      ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
      = ( A
        = ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(38,axiom,
    ( ( extended_size_ereal @ extended_MInfty )
    = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_ereal_Osize__gen_I3_J) ).

thf(394,plain,
    ( ( extended_size_ereal @ extended_MInfty )
    = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(191,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB] :
          ( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
         => ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_le__funI) ).

thf(986,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB] :
          ( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
         => ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(209,axiom,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
     => ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ B )
       => ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( divide_divide @ extended_ereal @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_zero__le__divide__ereal) ).

thf(1034,plain,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
     => ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ B )
       => ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( divide_divide @ extended_ereal @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(86,axiom,
    ! [A: real] :
      ( ( extended_size_ereal @ ( extended_ereal2 @ A ) )
      = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_ereal_Osize__gen_I1_J) ).

thf(490,plain,
    ! [A: real] :
      ( ( extended_size_ereal @ ( extended_ereal2 @ A ) )
      = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(301,axiom,
    ! [A: extended_ereal] :
      ( ( ( abs_abs @ extended_ereal @ A )
       != ( extend1396239628finity @ extended_ereal ) )
     => ~ ! [B: real] :
            ( A
           != ( extended_ereal2 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_abs__neq__infinity__cases) ).

thf(1304,plain,
    ! [A: extended_ereal] :
      ( ( ( abs_abs @ extended_ereal @ A )
       != ( extend1396239628finity @ extended_ereal ) )
     => ~ ! [B: real] :
            ( A
           != ( extended_ereal2 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(104,axiom,
    linorder @ extended_enat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Olinorder_34) ).

thf(531,plain,
    linorder @ extended_enat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(292,axiom,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ( uminus_uminus @ extended_ereal @ A )
        = ( uminus_uminus @ extended_ereal @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_ereal__uminus__eq__iff) ).

thf(1277,plain,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ( uminus_uminus @ extended_ereal @ A )
        = ( uminus_uminus @ extended_ereal @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(8,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( A
            = ( uminus_uminus @ TA @ B ) )
          = ( B
            = ( uminus_uminus @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_equation__minus__iff) ).

thf(342,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( A
            = ( uminus_uminus @ TA @ B ) )
          = ( B
            = ( uminus_uminus @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(215,axiom,
    ! [A: extended_ereal] :
      ( ( A
       != ( extend1396239628finity @ extended_ereal ) )
     => ( ( A
         != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
       => ( ( abs_abs @ extended_ereal @ A )
         != ( extend1396239628finity @ extended_ereal ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_ereal__infinity__cases) ).

thf(1049,plain,
    ! [A: extended_ereal] :
      ( ( A
       != ( extend1396239628finity @ extended_ereal ) )
     => ( ( A
         != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
       => ( ( abs_abs @ extended_ereal @ A )
         != ( extend1396239628finity @ extended_ereal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(76,axiom,
    preorder @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_2) ).

thf(473,plain,
    preorder @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(224,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_dual__order_Oantisym) ).

thf(1076,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
           => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(267,axiom,
    uminus @ extended_ereal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Groups_Ouminus_45) ).

thf(1203,plain,
    uminus @ extended_ereal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(127,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ( ( ord_less_eq @ ( $o > TA ) )
        = ( ^ [A: $o > TA,B: $o > TA] :
              ( ( ord_less_eq @ TA @ ( A @ $false ) @ ( B @ $false ) )
              & ( ord_less_eq @ TA @ ( A @ $true ) @ ( B @ $true ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_le__rel__bool__arg__iff) ).

thf(589,plain,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ( ( ord_less_eq @ ( $o > TA ) )
        = ( ^ [A: $o > TA,B: $o > TA] :
              ( ( ord_less_eq @ TA @ ( A @ $false ) @ ( B @ $false ) )
              & ( ord_less_eq @ TA @ ( A @ $true ) @ ( B @ $true ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(177,axiom,
    ! [A: nat] :
      ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
     => ( A
        = ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_bot__nat__0_Oextremum__uniqueI) ).

thf(927,plain,
    ! [A: nat] :
      ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
     => ( A
        = ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(28,axiom,
    topolo503727757_space @ $o,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Otopological__space_9) ).

thf(374,plain,
    topolo503727757_space @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(136,axiom,
    ! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_le0) ).

thf(617,plain,
    ! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(98,axiom,
    extended_PInfty != extended_MInfty,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_ereal_Odistinct_I5_J) ).

thf(516,plain,
    extended_PInfty != extended_MInfty,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(247,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: nat > TA,B: nat,C: nat] :
          ( ( order_antimono @ nat @ TA @ A )
         => ( ( ord_less_eq @ nat @ B @ C )
           => ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_decseqD) ).

thf(1145,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: nat > TA,B: nat,C: nat] :
          ( ( order_antimono @ nat @ TA @ A )
         => ( ( ord_less_eq @ nat @ B @ C )
           => ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(205,axiom,
    ! [A: extended_ereal] :
      ( ( ( ( abs_abs @ extended_ereal @ A )
          = ( extend1396239628finity @ extended_ereal ) )
       => ( ( extended_ereal2 @ ( extend1716541707_ereal @ A ) )
          = ( zero_zero @ extended_ereal ) ) )
      & ( ( ( abs_abs @ extended_ereal @ A )
         != ( extend1396239628finity @ extended_ereal ) )
       => ( ( extended_ereal2 @ ( extend1716541707_ereal @ A ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_ereal__real) ).

thf(1018,plain,
    ! [A: extended_ereal] :
      ( ( ( ( abs_abs @ extended_ereal @ A )
          = ( extend1396239628finity @ extended_ereal ) )
       => ( ( extended_ereal2 @ ( extend1716541707_ereal @ A ) )
          = ( zero_zero @ extended_ereal ) ) )
      & ( ( ( abs_abs @ extended_ereal @ A )
         != ( extend1396239628finity @ extended_ereal ) )
       => ( ( extended_ereal2 @ ( extend1716541707_ereal @ A ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(101,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( uminus @ TA )
     => ( uminus @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Groups_Ouminus) ).

thf(525,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( uminus @ TA )
     => ( uminus @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(199,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
          | ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_linear) ).

thf(1003,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
          | ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(206,axiom,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ! [C: real] :
          ( ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ C ) )
         => ( ord_less_eq @ extended_ereal @ B @ ( extended_ereal2 @ C ) ) )
     => ( ord_less_eq @ extended_ereal @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_ereal__le__real) ).

thf(1025,plain,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ! [C: real] :
          ( ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ C ) )
         => ( ord_less_eq @ extended_ereal @ B @ ( extended_ereal2 @ C ) ) )
     => ( ord_less_eq @ extended_ereal @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(223,axiom,
    ! [A: extended_ereal > $o,B: extended_ereal] :
      ( ! [C: real] : ( A @ ( extended_ereal2 @ C ) )
     => ( ( A @ ( extend1396239628finity @ extended_ereal ) )
       => ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
         => ( A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_real__of__ereal_Oinduct) ).

thf(1070,plain,
    ! [A: extended_ereal > $o,B: extended_ereal] :
      ( ! [C: real] : ( A @ ( extended_ereal2 @ C ) )
     => ( ( A @ ( extend1396239628finity @ extended_ereal ) )
       => ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
         => ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(250,axiom,
    ! [A: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ A )
      = ( A
        = ( extend1396239628finity @ extended_ereal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_ereal__infty__less__eq_I1_J) ).

thf(1156,plain,
    ! [A: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ A )
      = ( A
        = ( extend1396239628finity @ extended_ereal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(161,axiom,
    ( extended_MInfty
    = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_MInfty__eq__minfinity) ).

thf(887,plain,
    ( extended_MInfty
    = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(186,axiom,
    numeral @ extended_ereal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Num_Onumeral_46) ).

thf(971,plain,
    numeral @ extended_ereal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(3,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( uminus_uminus @ TA @ A )
            = B )
          = ( ( uminus_uminus @ TA @ B )
            = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_minus__equation__iff) ).

thf(327,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( uminus_uminus @ TA @ A )
            = B )
          = ( ( uminus_uminus @ TA @ B )
            = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(184,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ A ) @ ( extended_ereal2 @ B ) )
      = ( ord_less_eq @ real @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_ereal__less__eq_I3_J) ).

thf(954,plain,
    ! [A: real,B: real] :
      ( ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ A ) @ ( extended_ereal2 @ B ) )
      = ( ord_less_eq @ real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(289,axiom,
    ord @ extended_ereal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Orderings_Oord_44) ).

thf(1267,plain,
    ord @ extended_ereal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(45,axiom,
    topolo259154727pology @ $o,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Oorder__topology_10) ).

thf(409,plain,
    topolo259154727pology @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(195,axiom,
    ! [A: num,B: nat] :
      ( ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ ( extended_enat2 @ B ) )
      = ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_numeral__le__enat__iff) ).

thf(993,plain,
    ! [A: num,B: nat] :
      ( ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ ( extended_enat2 @ B ) )
      = ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(261,axiom,
    ! [TA: $tType] :
      ( ( real_V2090557954_space @ TA )
     => ! [A: TA > extended_ereal] : ( lower_107104146le_lsc @ TA @ extended_ereal @ ( lower_1879122655c_hull @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_lsc__lsc__hull) ).

thf(1188,plain,
    ! [TA: $tType] :
      ( ( real_V2090557954_space @ TA )
     => ! [A: TA > extended_ereal] : ( lower_107104146le_lsc @ TA @ extended_ereal @ ( lower_1879122655c_hull @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(61,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( uminus @ TB )
     => ( ( uminus_uminus @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_uminus__apply) ).

thf(441,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( uminus @ TB )
     => ( ( uminus_uminus @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(126,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( ord_less_eq @ nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_eq__imp__le) ).

thf(585,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( ord_less_eq @ nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(279,axiom,
    ! [A: num,B: num] :
      ( ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ ( numeral_numeral @ extended_enat @ B ) )
      = ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ A ) @ ( numeral_numeral @ nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_enat__ord__number_I1_J) ).

thf(1235,plain,
    ! [A: num,B: num] :
      ( ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ ( numeral_numeral @ extended_enat @ B ) )
      = ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ A ) @ ( numeral_numeral @ nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(123,axiom,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ( divide_divide @ extended_ereal @ A @ B )
        = ( zero_zero @ extended_ereal ) )
      = ( ( A
          = ( zero_zero @ extended_ereal ) )
        | ( ( abs_abs @ extended_ereal @ B )
          = ( extend1396239628finity @ extended_ereal ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_ereal__divide__eq__0__iff) ).

thf(576,plain,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ( divide_divide @ extended_ereal @ A @ B )
        = ( zero_zero @ extended_ereal ) )
      = ( ( A
          = ( zero_zero @ extended_ereal ) )
        | ( ( abs_abs @ extended_ereal @ B )
          = ( extend1396239628finity @ extended_ereal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(19,axiom,
    topolo259154727pology @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Oorder__topology_18) ).

thf(359,plain,
    topolo259154727pology @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(312,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_abs__le__zero__iff) ).

thf(1336,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(6,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA] :
          ( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
          = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_verit__minus__simplify_I4_J) ).

thf(336,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA] :
          ( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(143,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num] :
          ~ ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_not__zero__le__neg__numeral) ).

thf(656,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num] :
          ~ ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(130,axiom,
    ! [A: extended_enat] : ( ord_less_eq @ extended_enat @ ( zero_zero @ extended_enat ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_i0__lb) ).

thf(600,plain,
    ! [A: extended_enat] : ( ord_less_eq @ extended_enat @ ( zero_zero @ extended_enat ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(216,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( A = B )
          | ~ ( ord_less_eq @ TA @ A @ B )
          | ~ ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_verit__la__disequality) ).

thf(1052,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( A = B )
          | ~ ( ord_less_eq @ TA @ A @ B )
          | ~ ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(34,axiom,
    ! [TA: $tType] :
      ( ( ring_char_0 @ TA )
     => ! [A: num,B: num] :
          ( ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
            = ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
          = ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_neg__numeral__eq__iff) ).

thf(386,plain,
    ! [TA: $tType] :
      ( ( ring_char_0 @ TA )
     => ! [A: num,B: num] :
          ( ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
            = ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
          = ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(157,axiom,
    ! [A: extended_ereal > extended_ereal > $o,B: extended_ereal,C: extended_ereal] :
      ( ! [D: real,E: real] : ( A @ ( extended_ereal2 @ D ) @ ( extended_ereal2 @ E ) )
     => ( ! [D: extended_ereal] : ( A @ ( extend1396239628finity @ extended_ereal ) @ D )
       => ( ! [D: extended_ereal] : ( A @ D @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
         => ( ! [D: real] : ( A @ ( extended_ereal2 @ D ) @ ( extend1396239628finity @ extended_ereal ) )
           => ( ! [D: real] : ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extended_ereal2 @ D ) )
             => ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extend1396239628finity @ extended_ereal ) )
               => ( A @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_less__ereal_Oinduct) ).

thf(859,plain,
    ! [A: extended_ereal > extended_ereal > $o,B: extended_ereal,C: extended_ereal] :
      ( ! [D: real,E: real] : ( A @ ( extended_ereal2 @ D ) @ ( extended_ereal2 @ E ) )
     => ( ! [D: extended_ereal] : ( A @ ( extend1396239628finity @ extended_ereal ) @ D )
       => ( ! [D: extended_ereal] : ( A @ D @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
         => ( ! [D: real] : ( A @ ( extended_ereal2 @ D ) @ ( extend1396239628finity @ extended_ereal ) )
           => ( ! [D: real] : ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extended_ereal2 @ D ) )
             => ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extend1396239628finity @ extended_ereal ) )
               => ( A @ B @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(281,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ 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/sandbox/benchmark/theBenchmark.p',fact_41_antimonoI) ).

thf(1240,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ 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)],[281]) ).

thf(194,axiom,
    ( ( uminus_uminus @ extended_ereal @ extended_PInfty )
    = extended_MInfty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_uminus__ereal_Osimps_I2_J) ).

thf(991,plain,
    ( ( uminus_uminus @ extended_ereal @ extended_PInfty )
    = extended_MInfty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(72,axiom,
    ( ( extended_size_ereal @ extended_PInfty )
    = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_ereal_Osize__gen_I2_J) ).

thf(465,plain,
    ( ( extended_size_ereal @ extended_PInfty )
    = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(66,axiom,
    ! [A: real,B: real] :
      ( ( ( extended_ereal2 @ A )
        = ( extended_ereal2 @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_ereal_Oinject) ).

thf(450,plain,
    ! [A: real,B: real] :
      ( ( ( extended_ereal2 @ A )
        = ( extended_ereal2 @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(258,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB,C: TA] :
          ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
         => ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_le__funE) ).

thf(1180,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB,C: TA] :
          ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
         => ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(307,axiom,
    ! [A: extended_enat,B: nat] :
      ( ( ord_less_eq @ extended_enat @ A @ ( extended_enat2 @ B ) )
     => ? [C: nat] :
          ( A
          = ( extended_enat2 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_enat__ile) ).

thf(1321,plain,
    ! [A: extended_enat,B: nat] :
      ( ( ord_less_eq @ extended_enat @ A @ ( extended_enat2 @ B ) )
     => ? [C: nat] :
          ( A
          = ( extended_enat2 @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(163,axiom,
    ( ( zero_zero @ extended_ereal )
    = ( extended_ereal2 @ ( zero_zero @ real ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_zero__ereal__def) ).

thf(891,plain,
    ( ( zero_zero @ extended_ereal )
    = ( extended_ereal2 @ ( zero_zero @ real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(240,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_order__trans) ).

thf(1126,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(202,axiom,
    ! [A: extended_ereal] :
      ( ( ord_less_eq @ real @ ( extend1716541707_ereal @ A ) @ ( zero_zero @ real ) )
      = ( ( ord_less_eq @ extended_ereal @ A @ ( zero_zero @ extended_ereal ) )
        | ( A
          = ( extend1396239628finity @ extended_ereal ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_real__of__ereal__le__0) ).

thf(1010,plain,
    ! [A: extended_ereal] :
      ( ( ord_less_eq @ real @ ( extend1716541707_ereal @ A ) @ ( zero_zero @ real ) )
      = ( ( ord_less_eq @ extended_ereal @ A @ ( zero_zero @ extended_ereal ) )
        | ( A
          = ( extend1396239628finity @ extended_ereal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(24,axiom,
    canoni770627133id_add @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).

thf(368,plain,
    canoni770627133id_add @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(234,axiom,
    ! [A: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
     => ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( extend1716541707_ereal @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_real__of__ereal__pos) ).

thf(1108,plain,
    ! [A: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
     => ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( extend1716541707_ereal @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(21,axiom,
    semiring_char_0 @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osemiring__char__0) ).

thf(363,plain,
    semiring_char_0 @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(114,axiom,
    ! [A: nat] :
      ( ( ( zero_zero @ extended_enat )
        = ( extended_enat2 @ A ) )
      = ( A
        = ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_enat__0__iff_I2_J) ).

thf(556,plain,
    ! [A: nat] :
      ( ( ( zero_zero @ extended_enat )
        = ( extended_enat2 @ A ) )
      = ( A
        = ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(284,axiom,
    ! [TA: $tType] :
      ( ( boolean_algebra @ 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/sandbox/benchmark/theBenchmark.p',fact_147_compl__le__compl__iff) ).

thf(1253,plain,
    ! [TA: $tType] :
      ( ( boolean_algebra @ 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)],[284]) ).

thf(220,axiom,
    ! [TA: $tType] :
      ( ( linord1659791738miring @ TA )
     => ! [A: num,B: num] :
          ( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
          = ( ord_less_eq @ num @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_numeral__le__iff) ).

thf(1062,plain,
    ! [TA: $tType] :
      ( ( linord1659791738miring @ TA )
     => ! [A: num,B: num] :
          ( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
          = ( ord_less_eq @ num @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(14,axiom,
    uminus @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ouminus_25) ).

thf(351,plain,
    uminus @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(36,axiom,
    ! [TA: $tType] :
      ( ( ring_char_0 @ TA )
     => ! [A: num] :
          ( ( zero_zero @ TA )
         != ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_zero__neq__neg__numeral) ).

thf(390,plain,
    ! [TA: $tType] :
      ( ( ring_char_0 @ TA )
     => ! [A: num] :
          ( ( zero_zero @ TA )
         != ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(50,axiom,
    ord @ extended_enat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oord_36) ).

thf(418,plain,
    ord @ extended_enat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(120,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num,B: num] :
          ~ ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_not__numeral__le__neg__numeral) ).

thf(568,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: num,B: num] :
          ~ ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(30,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( uminus @ TB )
     => ( ( uminus_uminus @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_fun__Compl__def) ).

thf(378,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( uminus @ TB )
     => ( ( uminus_uminus @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(95,axiom,
    ! [TA: $tType] :
      ( ( ring_char_0 @ TA )
     => ! [A: num,B: num] :
          ( ( numeral_numeral @ TA @ A )
         != ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_numeral__neq__neg__numeral) ).

thf(510,plain,
    ! [TA: $tType] :
      ( ( ring_char_0 @ TA )
     => ! [A: num,B: num] :
          ( ( numeral_numeral @ TA @ A )
         != ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(302,axiom,
    topolo503727757_space @ extended_ereal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Topological__Spaces_Otopological__space_39) ).

thf(1308,plain,
    topolo503727757_space @ extended_ereal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(80,axiom,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = ( uminus_uminus @ TA @ A ) )
          = ( ( zero_zero @ TA )
            = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_neg__0__equal__iff__equal) ).

thf(478,plain,
    ! [TA: $tType] :
      ( ( group_add @ TA )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = ( uminus_uminus @ TA @ A ) )
          = ( ( zero_zero @ TA )
            = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(33,axiom,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA )
     => ! [A: TA] :
          ( ( A
            = ( uminus_uminus @ TA @ A ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_equal__neg__zero) ).

thf(383,plain,
    ! [TA: $tType] :
      ( ( linord219039673up_add @ TA )
     => ! [A: TA] :
          ( ( A
            = ( uminus_uminus @ TA @ A ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(154,axiom,
    ! [A: extended_ereal,B: extended_ereal,C: extended_ereal] :
      ( ( ? [D: real] :
            ( A
            = ( extended_ereal2 @ D ) )
       => ( ? [D: real] :
              ( B
              = ( extended_ereal2 @ D ) )
         => ! [D: real] :
              ( C
             != ( extended_ereal2 @ D ) ) ) )
     => ( ( ? [D: real] :
              ( A
              = ( extended_ereal2 @ D ) )
         => ( ? [D: real] :
                ( B
                = ( extended_ereal2 @ D ) )
           => ( C
             != ( extend1396239628finity @ extended_ereal ) ) ) )
       => ( ( ? [D: real] :
                ( A
                = ( extended_ereal2 @ D ) )
           => ( ? [D: real] :
                  ( B
                  = ( extended_ereal2 @ D ) )
             => ( C
               != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
         => ( ( ? [D: real] :
                  ( A
                  = ( extended_ereal2 @ D ) )
             => ( ( B
                  = ( extend1396239628finity @ extended_ereal ) )
               => ! [D: real] :
                    ( C
                   != ( extended_ereal2 @ D ) ) ) )
           => ( ( ? [D: real] :
                    ( A
                    = ( extended_ereal2 @ D ) )
               => ( ( B
                    = ( extend1396239628finity @ extended_ereal ) )
                 => ( C
                   != ( extend1396239628finity @ extended_ereal ) ) ) )
             => ( ( ? [D: real] :
                      ( A
                      = ( extended_ereal2 @ D ) )
                 => ( ( B
                      = ( extend1396239628finity @ extended_ereal ) )
                   => ( C
                     != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
               => ( ( ? [D: real] :
                        ( A
                        = ( extended_ereal2 @ D ) )
                   => ( ( B
                        = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                     => ! [D: real] :
                          ( C
                         != ( extended_ereal2 @ D ) ) ) )
                 => ( ( ? [D: real] :
                          ( A
                          = ( extended_ereal2 @ D ) )
                     => ( ( B
                          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                       => ( C
                         != ( extend1396239628finity @ extended_ereal ) ) ) )
                   => ( ( ? [D: real] :
                            ( A
                            = ( extended_ereal2 @ D ) )
                       => ( ( B
                            = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                         => ( C
                           != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
                     => ( ( ( A
                            = ( extend1396239628finity @ extended_ereal ) )
                         => ( ? [D: real] :
                                ( B
                                = ( extended_ereal2 @ D ) )
                           => ! [D: real] :
                                ( C
                               != ( extended_ereal2 @ D ) ) ) )
                       => ( ( ( A
                              = ( extend1396239628finity @ extended_ereal ) )
                           => ( ? [D: real] :
                                  ( B
                                  = ( extended_ereal2 @ D ) )
                             => ( C
                               != ( extend1396239628finity @ extended_ereal ) ) ) )
                         => ( ( ( A
                                = ( extend1396239628finity @ extended_ereal ) )
                             => ( ? [D: real] :
                                    ( B
                                    = ( extended_ereal2 @ D ) )
                               => ( C
                                 != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
                           => ( ( ( A
                                  = ( extend1396239628finity @ extended_ereal ) )
                               => ( ( B
                                    = ( extend1396239628finity @ extended_ereal ) )
                                 => ! [D: real] :
                                      ( C
                                     != ( extended_ereal2 @ D ) ) ) )
                             => ( ( ( A
                                    = ( extend1396239628finity @ extended_ereal ) )
                                 => ( ( B
                                      = ( extend1396239628finity @ extended_ereal ) )
                                   => ( C
                                     != ( extend1396239628finity @ extended_ereal ) ) ) )
                               => ( ( ( A
                                      = ( extend1396239628finity @ extended_ereal ) )
                                   => ( ( B
                                        = ( extend1396239628finity @ extended_ereal ) )
                                     => ( C
                                       != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
                                 => ( ( ( A
                                        = ( extend1396239628finity @ extended_ereal ) )
                                     => ( ( B
                                          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                       => ! [D: real] :
                                            ( C
                                           != ( extended_ereal2 @ D ) ) ) )
                                   => ( ( ( A
                                          = ( extend1396239628finity @ extended_ereal ) )
                                       => ( ( B
                                            = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                         => ( C
                                           != ( extend1396239628finity @ extended_ereal ) ) ) )
                                     => ( ( ( A
                                            = ( extend1396239628finity @ extended_ereal ) )
                                         => ( ( B
                                              = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                           => ( C
                                             != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
                                       => ( ( ( A
                                              = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                           => ( ? [D: real] :
                                                  ( B
                                                  = ( extended_ereal2 @ D ) )
                                             => ! [D: real] :
                                                  ( C
                                                 != ( extended_ereal2 @ D ) ) ) )
                                         => ( ( ( A
                                                = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                             => ( ? [D: real] :
                                                    ( B
                                                    = ( extended_ereal2 @ D ) )
                                               => ( C
                                                 != ( extend1396239628finity @ extended_ereal ) ) ) )
                                           => ( ( ( A
                                                  = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                               => ( ? [D: real] :
                                                      ( B
                                                      = ( extended_ereal2 @ D ) )
                                                 => ( C
                                                   != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
                                             => ( ( ( A
                                                    = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                 => ( ( B
                                                      = ( extend1396239628finity @ extended_ereal ) )
                                                   => ! [D: real] :
                                                        ( C
                                                       != ( extended_ereal2 @ D ) ) ) )
                                               => ( ( ( A
                                                      = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                   => ( ( B
                                                        = ( extend1396239628finity @ extended_ereal ) )
                                                     => ( C
                                                       != ( extend1396239628finity @ extended_ereal ) ) ) )
                                                 => ( ( ( A
                                                        = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                     => ( ( B
                                                          = ( extend1396239628finity @ extended_ereal ) )
                                                       => ( C
                                                         != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
                                                   => ( ( ( A
                                                          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                       => ( ( B
                                                            = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                         => ! [D: real] :
                                                              ( C
                                                             != ( extended_ereal2 @ D ) ) ) )
                                                     => ( ( ( A
                                                            = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                         => ( ( B
                                                              = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                           => ( C
                                                             != ( extend1396239628finity @ extended_ereal ) ) ) )
                                                       => ~ ( ( A
                                                              = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                           => ( ( B
                                                                = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                             => ( C
                                                               != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_ereal3__cases) ).

thf(684,plain,
    ! [A: extended_ereal,B: extended_ereal,C: extended_ereal] :
      ( ( ? [D: real] :
            ( A
            = ( extended_ereal2 @ D ) )
       => ( ? [D: real] :
              ( B
              = ( extended_ereal2 @ D ) )
         => ! [D: real] :
              ( C
             != ( extended_ereal2 @ D ) ) ) )
     => ( ( ? [D: real] :
              ( A
              = ( extended_ereal2 @ D ) )
         => ( ? [D: real] :
                ( B
                = ( extended_ereal2 @ D ) )
           => ( C
             != ( extend1396239628finity @ extended_ereal ) ) ) )
       => ( ( ? [D: real] :
                ( A
                = ( extended_ereal2 @ D ) )
           => ( ? [D: real] :
                  ( B
                  = ( extended_ereal2 @ D ) )
             => ( C
               != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
         => ( ( ? [D: real] :
                  ( A
                  = ( extended_ereal2 @ D ) )
             => ( ( B
                  = ( extend1396239628finity @ extended_ereal ) )
               => ! [D: real] :
                    ( C
                   != ( extended_ereal2 @ D ) ) ) )
           => ( ( ? [D: real] :
                    ( A
                    = ( extended_ereal2 @ D ) )
               => ( ( B
                    = ( extend1396239628finity @ extended_ereal ) )
                 => ( C
                   != ( extend1396239628finity @ extended_ereal ) ) ) )
             => ( ( ? [D: real] :
                      ( A
                      = ( extended_ereal2 @ D ) )
                 => ( ( B
                      = ( extend1396239628finity @ extended_ereal ) )
                   => ( C
                     != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
               => ( ( ? [D: real] :
                        ( A
                        = ( extended_ereal2 @ D ) )
                   => ( ( B
                        = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                     => ! [D: real] :
                          ( C
                         != ( extended_ereal2 @ D ) ) ) )
                 => ( ( ? [D: real] :
                          ( A
                          = ( extended_ereal2 @ D ) )
                     => ( ( B
                          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                       => ( C
                         != ( extend1396239628finity @ extended_ereal ) ) ) )
                   => ( ( ? [D: real] :
                            ( A
                            = ( extended_ereal2 @ D ) )
                       => ( ( B
                            = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                         => ( C
                           != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
                     => ( ( ( A
                            = ( extend1396239628finity @ extended_ereal ) )
                         => ( ? [D: real] :
                                ( B
                                = ( extended_ereal2 @ D ) )
                           => ! [D: real] :
                                ( C
                               != ( extended_ereal2 @ D ) ) ) )
                       => ( ( ( A
                              = ( extend1396239628finity @ extended_ereal ) )
                           => ( ? [D: real] :
                                  ( B
                                  = ( extended_ereal2 @ D ) )
                             => ( C
                               != ( extend1396239628finity @ extended_ereal ) ) ) )
                         => ( ( ( A
                                = ( extend1396239628finity @ extended_ereal ) )
                             => ( ? [D: real] :
                                    ( B
                                    = ( extended_ereal2 @ D ) )
                               => ( C
                                 != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
                           => ( ( ( A
                                  = ( extend1396239628finity @ extended_ereal ) )
                               => ( ( B
                                    = ( extend1396239628finity @ extended_ereal ) )
                                 => ! [D: real] :
                                      ( C
                                     != ( extended_ereal2 @ D ) ) ) )
                             => ( ( ( A
                                    = ( extend1396239628finity @ extended_ereal ) )
                                 => ( ( B
                                      = ( extend1396239628finity @ extended_ereal ) )
                                   => ( C
                                     != ( extend1396239628finity @ extended_ereal ) ) ) )
                               => ( ( ( A
                                      = ( extend1396239628finity @ extended_ereal ) )
                                   => ( ( B
                                        = ( extend1396239628finity @ extended_ereal ) )
                                     => ( C
                                       != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
                                 => ( ( ( A
                                        = ( extend1396239628finity @ extended_ereal ) )
                                     => ( ( B
                                          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                       => ! [D: real] :
                                            ( C
                                           != ( extended_ereal2 @ D ) ) ) )
                                   => ( ( ( A
                                          = ( extend1396239628finity @ extended_ereal ) )
                                       => ( ( B
                                            = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                         => ( C
                                           != ( extend1396239628finity @ extended_ereal ) ) ) )
                                     => ( ( ( A
                                            = ( extend1396239628finity @ extended_ereal ) )
                                         => ( ( B
                                              = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                           => ( C
                                             != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
                                       => ( ( ( A
                                              = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                           => ( ? [D: real] :
                                                  ( B
                                                  = ( extended_ereal2 @ D ) )
                                             => ! [D: real] :
                                                  ( C
                                                 != ( extended_ereal2 @ D ) ) ) )
                                         => ( ( ( A
                                                = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                             => ( ? [D: real] :
                                                    ( B
                                                    = ( extended_ereal2 @ D ) )
                                               => ( C
                                                 != ( extend1396239628finity @ extended_ereal ) ) ) )
                                           => ( ( ( A
                                                  = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                               => ( ? [D: real] :
                                                      ( B
                                                      = ( extended_ereal2 @ D ) )
                                                 => ( C
                                                   != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
                                             => ( ( ( A
                                                    = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                 => ( ( B
                                                      = ( extend1396239628finity @ extended_ereal ) )
                                                   => ! [D: real] :
                                                        ( C
                                                       != ( extended_ereal2 @ D ) ) ) )
                                               => ( ( ( A
                                                      = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                   => ( ( B
                                                        = ( extend1396239628finity @ extended_ereal ) )
                                                     => ( C
                                                       != ( extend1396239628finity @ extended_ereal ) ) ) )
                                                 => ( ( ( A
                                                        = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                     => ( ( B
                                                          = ( extend1396239628finity @ extended_ereal ) )
                                                       => ( C
                                                         != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
                                                   => ( ( ( A
                                                          = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                       => ( ( B
                                                            = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                         => ! [D: real] :
                                                              ( C
                                                             != ( extended_ereal2 @ D ) ) ) )
                                                     => ( ( ( A
                                                            = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                         => ( ( B
                                                              = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                           => ( C
                                                             != ( extend1396239628finity @ extended_ereal ) ) ) )
                                                       => ~ ( ( A
                                                              = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                           => ( ( B
                                                                = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
                                                             => ( C
                                                               != ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(107,axiom,
    ! [A: extended_ereal > $o,B: extended_ereal] :
      ( ! [C: real] : ( A @ ( extended_ereal2 @ C ) )
     => ( ( A @ extended_PInfty )
       => ( ( A @ extended_MInfty )
         => ( A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_uminus__ereal_Oinduct) ).

thf(536,plain,
    ! [A: extended_ereal > $o,B: extended_ereal] :
      ( ! [C: real] : ( A @ ( extended_ereal2 @ C ) )
     => ( ( A @ extended_PInfty )
       => ( ( A @ extended_MInfty )
         => ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(10,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( boolean_algebra @ TA )
     => ( boolean_algebra @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Oboolean__algebra) ).

thf(346,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( boolean_algebra @ TA )
     => ( boolean_algebra @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(303,axiom,
    ! [A: extended_ereal] :
      ( ( ( uminus_uminus @ extended_ereal @ A )
        = ( zero_zero @ extended_ereal ) )
      = ( A
        = ( zero_zero @ extended_ereal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_ereal__uminus__zero__iff) ).

thf(1309,plain,
    ! [A: extended_ereal] :
      ( ( ( uminus_uminus @ extended_ereal @ A )
        = ( zero_zero @ extended_ereal ) )
      = ( A
        = ( zero_zero @ extended_ereal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(237,axiom,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ A @ B )
     => ( ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ B )
       => ( ord_less_eq @ extended_ereal @ ( abs_abs @ extended_ereal @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_ereal__abs__leI) ).

thf(1116,plain,
    ! [A: extended_ereal,B: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ A @ B )
     => ( ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ B )
       => ( ord_less_eq @ extended_ereal @ ( abs_abs @ extended_ereal @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(243,axiom,
    ! [TA: $tType] :
      ( ( boolean_algebra @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_compl__mono) ).

thf(1133,plain,
    ! [TA: $tType] :
      ( ( boolean_algebra @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(197,axiom,
    ( ( '!' @ extended_ereal )
    = ( ^ [A: extended_ereal > $o] :
          ( ( A @ ( extend1396239628finity @ extended_ereal ) )
          & ! [B: real] : ( A @ ( extended_ereal2 @ B ) )
          & ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_ereal__all__split) ).

thf(999,plain,
    ( ( '!' @ extended_ereal )
    = ( ^ [A: extended_ereal > $o] :
          ( ( A @ ( extend1396239628finity @ extended_ereal ) )
          & ! [B: real] : ( A @ ( extended_ereal2 @ B ) )
          & ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(293,axiom,
    ! [A: real] :
      ( ( ( zero_zero @ extended_ereal )
        = ( extended_ereal2 @ A ) )
      = ( A
        = ( zero_zero @ real ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_ereal__eq__0_I2_J) ).

thf(1280,plain,
    ! [A: real] :
      ( ( ( zero_zero @ extended_ereal )
        = ( extended_ereal2 @ A ) )
      = ( A
        = ( zero_zero @ real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(57,axiom,
    ! [A: real,B: real] :
      ( ( A = B )
     => ( ( extended_ereal2 @ A )
        = ( extended_ereal2 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_ereal__cong) ).

thf(432,plain,
    ! [A: real,B: real] :
      ( ( A = B )
     => ( ( extended_ereal2 @ A )
        = ( extended_ereal2 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(46,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( preorder @ TA )
     => ( preorder @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).

thf(410,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( preorder @ TA )
     => ( preorder @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(277,axiom,
    ! [A: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
      = ( A
        = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_ereal__infty__less__eq_I2_J) ).

thf(1229,plain,
    ! [A: extended_ereal] :
      ( ( ord_less_eq @ extended_ereal @ A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
      = ( A
        = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(155,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_abs__le__D1) ).

thf(854,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(159,axiom,
    ! [A: extended_ereal] :
      ( ! [B: real] : ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ B ) )
     => ( A
        = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_ereal__bot) ).

thf(865,plain,
    ! [A: extended_ereal] :
      ( ! [B: real] : ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ B ) )
     => ( A
        = ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(27,axiom,
    preorder @ extended_enat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Opreorder_33) ).

thf(373,plain,
    preorder @ extended_enat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(118,axiom,
    numeral @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Num_Onumeral) ).

thf(564,plain,
    numeral @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(1,conjecture,
    ord_less_eq @ extended_ereal @ ( g @ x ) @ ( f @ x ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( ord_less_eq @ extended_ereal @ ( g @ x ) @ ( f @ x ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(326,plain,
    ~ ( ord_less_eq @ extended_ereal @ ( g @ x ) @ ( f @ x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(174,axiom,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
          = ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_minus__le__iff) ).

thf(918,plain,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
          = ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(146,axiom,
    ! [A: extended_enat] : ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( extend1771934483f_enat @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_ereal__of__enat__nonneg) ).

thf(664,plain,
    ! [A: extended_enat] : ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( extend1771934483f_enat @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(315,axiom,
    ! [A: real] :
      ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( extended_ereal2 @ A ) )
      = ( ord_less_eq @ real @ ( zero_zero @ real ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_ereal__less__eq_I5_J) ).

thf(1346,plain,
    ! [A: real] :
      ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( extended_ereal2 @ A ) )
      = ( ord_less_eq @ real @ ( zero_zero @ real ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(48,axiom,
    linorder @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).

thf(415,plain,
    linorder @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(322,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA )
        & ( ord @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ B )
         => ( ( ( C @ B )
              = D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less_eq @ TB @ E @ F )
                 => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_ord__le__eq__subst) ).

thf(1363,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA )
        & ( ord @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ B )
         => ( ( ( C @ B )
              = D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less_eq @ TB @ E @ F )
                 => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(305,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA > TA > $o,B: TA,C: TA] :
          ( ! [D: TA,E: TA] :
              ( ( ord_less_eq @ TA @ D @ E )
             => ( A @ D @ E ) )
         => ( ! [D: TA,E: TA] :
                ( ( A @ E @ D )
               => ( A @ D @ E ) )
           => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_linorder__wlog) ).

thf(1314,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA > TA > $o,B: TA,C: TA] :
          ( ! [D: TA,E: TA] :
              ( ( ord_less_eq @ TA @ D @ E )
             => ( A @ D @ E ) )
         => ( ! [D: TA,E: TA] :
                ( ( A @ E @ D )
               => ( A @ D @ E ) )
           => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(77,axiom,
    semiring_char_0 @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Osemiring__char__0_20) ).

thf(474,plain,
    semiring_char_0 @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(325,axiom,
    zero @ extended_ereal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Groups_Ozero_47) ).

thf(1410,plain,
    zero @ extended_ereal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(105,axiom,
    ! [TA: $tType] :
      ( ( ring_char_0 @ TA )
     => ! [A: num,B: num] :
          ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
         != ( numeral_numeral @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_neg__numeral__neq__numeral) ).

thf(532,plain,
    ! [TA: $tType] :
      ( ( ring_char_0 @ TA )
     => ! [A: num,B: num] :
          ( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
         != ( numeral_numeral @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(221,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ 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/sandbox/benchmark/theBenchmark.p',fact_40_antimono__def) ).

thf(1065,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ 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)],[221]) ).

thf(287,axiom,
    ( ( extend1716541707_ereal @ ( extend1396239628finity @ extended_ereal ) )
    = ( zero_zero @ real ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_real__of__ereal_Osimps_I2_J) ).

thf(1261,plain,
    ( ( extend1716541707_ereal @ ( extend1396239628finity @ extended_ereal ) )
    = ( zero_zero @ real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(290,axiom,
    ! [A: extended_ereal] :
      ( ( abs_abs @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) )
      = ( abs_abs @ extended_ereal @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_abs__ereal__uminus) ).

thf(1268,plain,
    ! [A: extended_ereal] :
      ( ( abs_abs @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) )
      = ( abs_abs @ extended_ereal @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(54,axiom,
    order @ extended_enat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oorder_35) ).

thf(427,plain,
    order @ extended_enat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(103,axiom,
    ! [TA: $tType] :
      ( ( zero @ TA )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = A )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_zero__reorient) ).

thf(528,plain,
    ! [TA: $tType] :
      ( ( zero @ TA )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = A )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(140,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
            = ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_antisym__conv) ).

thf(644,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ A )
            = ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(319,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( abs_abs @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_abs__ge__minus__self) ).

thf(1357,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( abs_abs @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(170,axiom,
    ! [A: extended_ereal] : ( ord_less_eq @ extended_ereal @ A @ ( extend1396239628finity @ extended_ereal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_ereal__less__eq_I1_J) ).

thf(908,plain,
    ! [A: extended_ereal] : ( ord_less_eq @ extended_ereal @ A @ ( extend1396239628finity @ extended_ereal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(92,axiom,
    ! [A: nat] :
      ( ( extended_the_enat @ ( extended_enat2 @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_the__enat_Osimps) ).

thf(501,plain,
    ! [A: nat] :
      ( ( extended_the_enat @ ( extended_enat2 @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(25,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( topolo503727757_space @ TA )
        & ( topolo259154727pology @ TB ) )
     => ( ( lower_107104146le_lsc @ TA @ TB )
        = ( ^ [A: TA > TB] :
            ! [B: TA] : ( lower_582600101lsc_at @ TA @ TB @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_lsc__def) ).

thf(369,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( topolo503727757_space @ TA )
        & ( topolo259154727pology @ TB ) )
     => ( ( lower_107104146le_lsc @ TA @ TB )
        = ( ^ [A: TA > TB] :
            ! [B: TA] : ( lower_582600101lsc_at @ TA @ TB @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(84,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( linorder @ TA )
        & ( order @ TB ) )
     => ! [A: TA > TB,B: TA,C: TA] :
          ( ( order_strict_mono @ TA @ TB @ A )
         => ( ( ( A @ B )
              = ( A @ C ) )
            = ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_strict__mono__eq) ).

thf(486,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( linorder @ TA )
        & ( order @ 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)],[84]) ).

thf(181,axiom,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ 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/sandbox/benchmark/theBenchmark.p',fact_97_neg__0__le__iff__le) ).

thf(940,plain,
    ! [TA: $tType] :
      ( ( ordered_ab_group_add @ 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)],[181]) ).

thf(17,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( order @ TA )
     => ( order @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).

thf(354,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( order @ TA )
     => ( order @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(210,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ 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/sandbox/benchmark/theBenchmark.p',fact_43_antimonoD) ).

thf(1037,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( order @ TA )
        & ( order @ 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)],[210]) ).

thf(151,axiom,
    ! [A: extended_ereal] :
      ( ( ( abs_abs @ extended_ereal @ A )
       != ( extend1396239628finity @ extended_ereal ) )
      = ( ? [B: real] :
            ( A
            = ( extended_ereal2 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_not__infty__ereal) ).

thf(676,plain,
    ! [A: extended_ereal] :
      ( ( ( abs_abs @ extended_ereal @ A )
       != ( extend1396239628finity @ extended_ereal ) )
      = ( ? [B: real] :
            ( A
            = ( extended_ereal2 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(228,axiom,
    ( ( numeral_numeral @ extended_ereal )
    = ( ^ [A: num] : ( extended_ereal2 @ ( numeral_numeral @ real @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_numeral__eq__ereal) ).

thf(1088,plain,
    ( ( numeral_numeral @ extended_ereal )
    = ( ^ [A: num] : ( extended_ereal2 @ ( numeral_numeral @ real @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(268,axiom,
    ! [A: extended_ereal] :
      ( ! [B: real] : ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ B ) @ A )
     => ( A
        = ( extend1396239628finity @ extended_ereal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_ereal__top) ).

thf(1204,plain,
    ! [A: extended_ereal] :
      ( ! [B: real] : ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ B ) @ A )
     => ( A
        = ( extend1396239628finity @ extended_ereal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(128,axiom,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ B )
         => ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_abs__le__D2) ).

thf(592,plain,
    ! [TA: $tType] :
      ( ( ordere142940540dd_abs @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ B )
         => ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(68,axiom,
    linord219039673up_add @ real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Olinordered__ab__group__add) ).

thf(454,plain,
    linord219039673up_add @ real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(22,axiom,
    order @ $o,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_14) ).

thf(364,plain,
    order @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(187,axiom,
    ( ( '?' @ extended_ereal )
    = ( ^ [A: extended_ereal > $o] :
          ( ( A @ ( extend1396239628finity @ extended_ereal ) )
          | ? [B: real] : ( A @ ( extended_ereal2 @ B ) )
          | ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_ereal__ex__split) ).

thf(972,plain,
    ( ( '?' @ extended_ereal )
    = ( ^ [A: extended_ereal > $o] :
          ( ( A @ ( extend1396239628finity @ extended_ereal ) )
          | ? [B: real] : ( A @ ( extended_ereal2 @ B ) )
          | ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(1411,plain,
    $false,
    inference(cvc4,[status(thm)],[1105,893,1083,555,666,1110,365,1190,333,1031,481,352,1005,1290,1068,449,1142,440,614,408,977,523,582,500,1164,472,913,1354,670,1222,930,1196,898,1001,1243,1046,1359,565,436,389,1055,1287,570,1298,372,504,619,542,902,559,1147,606,1013,416,448,1232,1319,421,475,1302,1334,485,353,1283,905,348,574,602,1169,1215,453,396,1351,988,507,527,428,1201,439,661,925,1153,381,910,957,1343,1042,1217,424,407,1370,1238,862,349,484,889,1079,682,974,916,467,1159,461,493,1210,551,1128,519,650,1121,980,1096,1118,499,1138,356,471,1329,1028,1361,339,933,1182,489,547,901,476,1016,1207,679,1039,622,393,1099,515,1131,1192,1060,647,1263,1086,360,921,1167,1185,513,1219,856,1301,444,375,1135,412,562,1007,402,579,1256,1226,545,641,382,1312,611,498,1058,1332,1090,1258,947,350,672,445,936,1271,1371,406,419,1349,1043,1175,990,996,494,1339,535,594,1162,1325,895,943,1177,330,462,1112,345,552,1293,668,1198,399,1213,868,455,608,563,1250,1102,431,658,394,986,1034,490,1304,531,1277,342,1049,473,1076,1203,589,927,374,617,516,1145,1018,525,1003,1025,1070,1156,887,971,327,954,1267,409,993,1188,441,585,1235,576,359,1336,336,656,600,1052,386,859,1240,991,465,450,1180,1321,891,1126,1010,368,1108,363,556,1253,1062,351,390,418,568,378,510,1308,478,383,684,536,346,1309,1116,1133,999,1280,432,410,1229,854,865,373,564,326,918,664,1346,415,1363,1314,474,1410,532,1065,1261,1268,427,528,644,1357,908,501,369,486,940,354,1037,676,1088,1204,592,454,364,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ITP114^2 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n029.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Sat May 18 17:28:54 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.99/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.75/1.10  % [INFO] 	 Parsing done (229ms). 
% 1.75/1.11  % [INFO] 	 Running in sequential loop mode. 
% 2.43/1.32  % [INFO] 	 eprover registered as external prover. 
% 2.43/1.32  % [INFO] 	 cvc4 registered as external prover. 
% 2.43/1.32  % [INFO] 	 Scanning for conjecture ... 
% 2.78/1.41  % [INFO] 	 Found a conjecture (or negated_conjecture) and 324 axioms. Running axiom selection ... 
% 3.02/1.50  % [INFO] 	 Axiom selection finished. Selected 323 axioms (removed 1 axioms). 
% 3.71/1.65  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.71/1.67  % [INFO] 	 Type checking passed. 
% 3.71/1.67  % [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 ... 
% 63.66/25.04  % External prover 'cvc4' found a proof!
% 63.66/25.05  % [INFO] 	 Killing All external provers ... 
% 63.66/25.05  % Time passed: 24516ms (effective reasoning time: 23937ms)
% 63.66/25.05  % 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)>
% 63.66/25.05  % Axioms used in derivation (323): fact_5_le__funD, fact_169_numeral__eq__ereal, fact_83_ereal__uminus__zero, tcon_Nat_Onat___Topological__Spaces_Otopological__space_1, fact_43_antimonoD, tcon_Extended__Real_Oereal___Topological__Spaces_Otopological__space_39, fact_177_zero__ereal__def, tcon_Extended__Nat_Oenat___Topological__Spaces_Otopological__space_29, fact_247_abs__minus__le__zero, fact_6_le__funE, tcon_HOL_Obool___Orderings_Oorder_14, tfree_0, fact_171_ereal__eq__0_I2_J, fact_105_equation__minus__iff, fact_153_ereal__uminus__uminus, fact_35_Greatest__equality, fact_81_verit__minus__simplify_I4_J, tcon_Nat_Onat___Orderings_Olinorder, tcon_HOL_Obool___Lattices_Oboolean__algebra_11, fact_29_eq__refl, fact_217_abs__minus__cancel, fact_158_compl__le__swap1, fact_129_real__of__ereal__positive__mono, fact_234_abs__eq__infinity__cases, tcon_Real_Oreal___Groups_Oordered__ab__group__add__abs, fact_151_compl__eq__compl__iff, fact_63_not__numeral__le__zero, fact_137_GreatestI__nat, fact_20_order__trans, fact_47_decseq__def, tcon_HOL_Obool___Orderings_Opreorder_12, fact_100_neg__less__eq__nonneg, tcon_Extended__Nat_Oenat___Orderings_Oorder_35, tcon_HOL_Obool___Topological__Spaces_Otopological__space_9, fact_238_abs__ge__zero, fact_134_le__trans, fact_42_antimonoE, fact_65_ile0__eq, fact_53_ereal__of__enat__zero, tcon_Extended__Nat_Oenat___Orderings_Opreorder_33, fact_204_uminus__ereal_Oinduct, fact_150_double__compl, fact_225_abs__neg__numeral, fact_123_neg__numeral__le__numeral, fact_31_antisym, fact_132_not__MInfty__nonneg, fact_212_abs__idempotent, fact_131_not__zero__le__neg__numeral, fact_172_ereal__less__eq_I3_J, fact_186_ereal__all__split, tcon_fun___Orderings_Oord, tcon_Extended__Real_Oereal___Groups_Ozero_47, fact_18_linorder__wlog, fact_251_divide__le__0__abs__iff, fact_148_the__enat_Osimps, tcon_Real_Oreal___Topological__Spaces_Oorder__topology_18, fact_89_equal__neg__zero, tcon_Real_Oreal___Topological__Spaces_Otopological__space_17, fact_146_less__eq__nat_Osimps_I1_J, fact_85_enat_Oinject, fact_138_nat__le__linear, tcon_fun___Topological__Spaces_Otopological__space, fact_162_dbl__simps_I1_J, fact_62_zero__le__numeral, tcon_HOL_Obool___Orderings_Oord_15, tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_28, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, fact_214_abs__eq__0, fact_221_ereal__divide__zero__left, fact_194_uminus__ereal_Osimps_I1_J, fact_229_ereal__divide__Infty_I2_J, fact_168_ereal_Oinject, tcon_Real_Oreal___Nat_Oring__char__0, fact_115_enat__0__iff_I1_J, fact_152_enat_Osimps_I4_J, tcon_Extended__Real_Oereal___Orderings_Oord_44, fact_199_uminus__ereal_Oelims, fact_87_neg__le__iff__le, fact_8_le__fun__def, fact_104_minus__equation__iff, fact_51_ereal__infty__less__eq_I1_J, fact_68_zero__reorient, fact_37_le__rel__bool__arg__iff, fact_118_MInfty__neq__PInfty_I1_J, subcl_Real__Vector__Spaces_Ometric__space___Topological__Spaces_Otopological__space, fact_160_real__eq__0__iff__le__ge__0, fact_116_enat__0__iff_I2_J, fact_210_ereal__divide__ereal, fact_174_real__of__ereal_Osimps_I1_J, fact_7_le__funI, fact_60_numeral__le__iff, fact_197_ereal_Osize__gen_I3_J, fact_41_antimonoI, fact_23_ord__eq__le__trans, fact_188_ereal__ex__split, tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_32, fact_170_ereal__eq__0_I1_J, fact_92_add_Oinverse__neutral, fact_59_ereal__less__eq_I1_J, fact_149_uminus__apply, fact_93_neg__numeral__eq__iff, fact_15_dual__order_Oantisym, fact_201_ereal_Osize__gen_I2_J, fact_139_Greatest__le__nat, fact_196_real__of__ereal_Oelims, tcon_Real_Oreal___Num_Onumeral_26, fact_109_le__imp__neg__le, fact_112_numeral__neq__neg__numeral, subcl_Real__Vector__Spaces_Ometric__space___HOL_Otype, fact_113_neg__numeral__neq__numeral, fact_195_ereal__bot, fact_154_ereal__uminus__eq__iff, fact_233_ereal__infinity__cases, fact_215_abs__0__eq, fact_44_lsc__def, tcon_Num_Onum___Orderings_Oorder_7, fact_88_neg__equal__zero, fact_4_ereal__complete__Sup, fact_50_numeral__le__ereal__of__enat__iff, fact_16_dual__order_Oeq__iff, tcon_Real_Oreal___Groups_Oordered__ab__group__add, tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space, fact_79_neg__equal__iff__equal, fact_144_bot__nat__0_Oextremum__unique, fact_230_not__infty__ereal, fact_73_le0, fact_126_Infty__neq__0_I3_J, fact_157_compl__le__swap2, tcon_HOL_Obool___Groups_Ouminus_16, tcon_Real_Oreal___Orderings_Oord_24, fact_17_dual__order_Otrans, fact_57_neq__PInf__trans, fact_36_GreatestI2__order, fact_111_le__minus__iff, fact_110_minus__le__iff, fact_216_abs__numeral, fact_103_real__of__ereal_Osimps_I3_J, fact_13_ord__le__eq__subst, fact_236_abs__ereal__pos, fact_97_neg__0__le__iff__le, fact_9_order__subst1, fact_80_add_Oinverse__inverse, fact_231_abs__neq__infinity__cases, fact_142_strict__mono__imp__increasing, fact_226_abs__ereal__ge0, fact_26_le__cases3, fact_155_ereal__uminus__eq__reorder, fact_190_ereal2__cases, fact_107_real__of__ereal__eq__0, fact_70_le__numeral__extra_I3_J, fact_90_neg__equal__0__iff__equal, fact_240_abs__le__D2, fact_40_antimono__def, fact_237_zero__le__divide__ereal, tcon_Nat_Onat___Groups_Ozero, tcon_Extended__Real_Oereal___Orderings_Olinorder_42, fact_175_ereal__le__real, fact_213_abs__zero, fact_211_ereal__le__real__iff, fact_39_ereal__of__enat__le__iff, fact_193_ereal__top, fact_64_numeral__eq__iff, fact_98_neg__le__0__iff__le, fact_192_MInfty__neq__ereal_I1_J, fact_71_zero__neq__numeral, fact_128_ereal__less__eq_I2_J, fact_38_lsc__lsc__hull, fact_28_le__cases, fact_140_GreatestI__ex__nat, fact_120_enat__ile, fact_66_i0__lb, fact_232_abs__ereal_Osimps_I2_J, fact_33_lsc__hull__iff__greatest, fact_125_zero__neq__neg__numeral, fact_14_lsc__hull__le, fact_21_order__class_Oorder_Oantisym, fact_76_sub__non__positive, fact_145_le__0__eq, fact_235_ereal__abs__leI, fact_82_ereal__uminus__zero__iff, fact_191_ereal__cases, fact_69_zero__le, tcon_Extended__Real_Oereal___Topological__Spaces_Oorder__topology_40, fact_176_PInfty__neq__ereal_I1_J, fact_121_numeral__eq__enat, tcon_Extended__Real_Oereal___Orderings_Opreorder_41, fact_198_ereal_Osize__gen_I1_J, fact_136_le__antisym, fact_34_lsc__hull__greatest, tcon_Nat_Onat___Orderings_Opreorder_2, fact_78_real__of__ereal__le__0, fact_141_Nat_Oex__has__greatest__nat, fact_182_times__ereal_Oinduct, fact_1_calculation, fact_209_uminus__ereal_Osimps_I3_J, fact_135_eq__imp__le, fact_179_ereal__le__le, fact_12_ord__eq__le__subst, fact_227_ereal__divide__Infty_I1_J, fact_202_infinity__ereal__def, fact_77_sub__non__negative, tcon_Extended__Nat_Oenat___Topological__Spaces_Oorder__topology_30, fact_91_neg__0__equal__iff__equal, tcon_Extended__Real_Oereal___Orderings_Oorder_43, tcon_Real_Oreal___Orderings_Opreorder_21, tcon_Extended__Real_Oereal___Groups_Ouminus_45, fact_52_strict__mono__less__eq, tcon_Real_Oreal___Nat_Osemiring__char__0_20, fact_95_ereal__uminus__le__0__iff, tcon_HOL_Obool___Orderings_Olinorder_13, fact_241_abs__le__iff, fact_117_lsc__at__MInfty, tcon_fun___Lattices_Oboolean__algebra, fact_181_real__of__ereal_Ocases, fact_246_abs__le__D1, fact_178_le__ereal__le, fact_48_ereal__of__enat__nonneg, fact_3_ereal__complete__Inf, tcon_Real_Oreal___Groups_Ogroup__add, fact_30_linear, fact_24_order__class_Oorder_Oeq__iff, fact_203_ereal_Odistinct_I5_J, fact_206_ereal_Oexhaust, fact_224_abs__le__zero__iff, tcon_Nat_Onat___Num_Onumeral, fact_161_enat_Osimps_I6_J, tcon_Extended__Nat_Oenat___Orderings_Olinorder_34, fact_25_antisym__conv, fact_75_numeral__le__enat__iff, tcon_Nat_Onat___Orderings_Oorder_3, tcon_Real_Oreal___Groups_Ozero_27, fact_2_order__refl, fact_167_ereal__cong, tcon_Extended__Nat_Oenat___Groups_Ozero_38, tcon_fun___Orderings_Opreorder, tcon_Extended__Real_Oereal___Num_Onumeral_46, tcon_Num_Onum___Orderings_Opreorder_5, fact_11_verit__la__disequality, fact_101_real__of__ereal__0, tcon_Real_Oreal___Fields_Olinordered__field, tcon_Real_Oreal___Rings_Olinordered__idom, fact_250_real__le__ereal__iff, fact_165_ereal__less__eq_I4_J, fact_108_real__of__ereal_Osimps_I2_J, fact_156_fun__Compl__def, fact_46_decseqD, fact_243_ereal__divide__eq__0__iff, fact_114_zero__enat__def, fact_249_ereal__real, tcon_Extended__Nat_Oenat___Rings_Olinordered__nonzero__semiring_31, fact_58_ereal__infty__less__eq2_I1_J, fact_102_enat__ord__simps_I1_J, fact_220_ereal__uminus__divide, fact_61_le__zero__eq, fact_67_enat__ord__number_I1_J, fact_99_less__eq__neg__nonpos, fact_72_bot__nat__0_Oextremum, fact_133_le__refl, tcon_Extended__Nat_Oenat___Orderings_Oord_36, fact_218_abs__ereal__uminus, tcon_Nat_Onat___Topological__Spaces_Oorder__topology, fact_96_ereal__0__le__uminus__iff, tcon_HOL_Obool___Topological__Spaces_Oorder__topology_10, tcon_Num_Onum___Orderings_Olinorder_6, tcon_Real_Oreal___Num_Oneg__numeral, fact_74_neg__numeral__le__iff, tcon_Real_Oreal___Orderings_Olinorder_22, tcon_fun___Orderings_Oorder, fact_147_compl__le__compl__iff, fact_22_ord__le__eq__trans, fact_180_real__of__ereal_Oinduct, fact_84_ereal__minus__le__minus, fact_222_abs__of__nonneg, fact_208_uminus__ereal_Osimps_I2_J, tcon_Real_Oreal___Groups_Olinordered__ab__group__add, tcon_Real_Oreal___Orderings_Oorder_23, fact_119_ereal__uminus__le__reorder, fact_106_verit__negate__coefficient_I3_J, fact_228_abs__of__nonpos, fact_207_ereal_Oinduct, fact_223_abs__le__self__iff, fact_242_abs__ge__minus__self, fact_205_uminus__ereal_Ocases, tcon_Nat_Onat___Orderings_Oord_4, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, tcon_fun___Groups_Ouminus, fact_163_dbl__simps_I2_J, tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_19, fact_184_less__ereal_Oinduct, fact_55_Infty__neq__0_I1_J, fact_86_real__of__ereal, fact_245_abs__ge__self, tcon_Real_Oreal___Groups_Ouminus_25, fact_189_ereal3__cases, fact_248_ereal__real_H, fact_0_assms, fact_94_ereal__infty__less__eq_I2_J, fact_164_ereal__less__eq_I5_J, fact_166_MInfty__eq__minfinity, fact_187_abs__ereal_Ocases, fact_54_strict__mono__eq, fact_219_abs__ereal__zero, fact_49_ereal__of__enat__ge__zero__cancel__iff, tcon_Nat_Onat___Nat_Osemiring__char__0, fact_239_abs__leI, fact_10_order__subst2, fact_122_real__of__ereal__pos, fact_56_strict__mono__leD, fact_124_not__numeral__le__neg__numeral, tcon_Num_Onum___Orderings_Oord_8, fact_183_plus__ereal_Oinduct, fact_27_order_Otrans, fact_244_abs__ereal_Osimps_I3_J, fact_19_dual__order_Orefl, fact_130_neg__numeral__le__zero, fact_159_compl__mono, fact_143_bot__nat__0_Oextremum__uniqueI, fact_185_abs__ereal_Oinduct, fact_200_ereal_Odistinct_I1_J, fact_127_ereal__infty__less__eq2_I2_J, fact_173_ereal_Odistinct_I3_J, tcon_Extended__Nat_Oenat___Num_Onumeral_37, fact_32_eq__iff
% 63.66/25.05  % No. of inferences in proof: 650
% 63.66/25.05  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 24516 ms resp. 23937 ms w/o parsing
% 64.10/25.25  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 64.10/25.25  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------