TSTP Solution File: ITP118^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP118^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.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 22:23:05 EDT 2024

% Result   : Theorem 15.82s 4.57s
% Output   : Refutation 16.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  466
% Syntax   : Number of formulae    :  832 ( 485 unt; 102 typ;   0 def)
%            Number of atoms       : 1537 ( 631 equ;  20 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 5038 (  80   ~;   7   |;  50   &;4409   @)
%                                         (   0 <=>; 492  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Number of types       :   17 (  16 usr)
%            Number of type conns  :  183 ( 183   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   92 (  88 usr;  21 con; 0-3 aty)
%            Number of variables   : 1635 ( 122   ^1477   !;  36   ?;1635   :)

% Comments : 
%------------------------------------------------------------------------------
thf(finite463740460l_num1_type,type,
    finite463740460l_num1: $tType ).

thf(finite121157254l_num1_type,type,
    finite121157254l_num1: $tType ).

thf(finite337957458num1_n_type,type,
    finite337957458num1_n: $tType ).

thf(finite318270636al_n_n_type,type,
    finite318270636al_n_n: $tType ).

thf(set_Fi1257234438l_num1_type,type,
    set_Fi1257234438l_num1: $tType ).

thf(finite1183840848l_num1_type,type,
    finite1183840848l_num1: $tType ).

thf(finite2063899472l_num1_type,type,
    finite2063899472l_num1: $tType ).

thf(set_Fi1058188332real_n_type,type,
    set_Fi1058188332real_n: $tType ).

thf(finite1489363574real_n_type,type,
    finite1489363574real_n: $tType ).

thf(finite964658038_int_n_type,type,
    finite964658038_int_n: $tType ).

thf(set_real_type,type,
    set_real: $tType ).

thf(set_int_type,type,
    set_int: $tType ).

thf(numeral_num1_type,type,
    numeral_num1: $tType ).

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

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

thf(n_type,type,
    n: $tType ).

thf(archim1371465213g_real_type,type,
    archim1371465213g_real: real > int ).

thf(archim1031974863r_real_type,type,
    archim1031974863r_real: real > int ).

thf(finite627713486m1_int_type,type,
    finite627713486m1_int: numeral_num1 > int > finite2063899472l_num1 ).

thf(finite15144922381_real_type,type,
    finite15144922381_real: numeral_num1 > real > finite1183840848l_num1 ).

thf(finite1888777460_n_int_type,type,
    finite1888777460_n_int: n > int > finite964658038_int_n ).

thf(finite703491444n_real_type,type,
    finite703491444n_real: n > real > finite1489363574real_n ).

thf(finite1470207077l_num1_type,type,
    finite1470207077l_num1: int > finite2063899472l_num1 ).

thf(finite55766923_int_n_type,type,
    finite55766923_int_n: int > finite964658038_int_n ).

thf(finite1329045861l_num1_type,type,
    finite1329045861l_num1: real > finite1183840848l_num1 ).

thf(finite667548811real_n_type,type,
    finite667548811real_n: real > finite1489363574real_n ).

thf(finite1449546019l_num1_type,type,
    finite1449546019l_num1: finite463740460l_num1 > numeral_num1 > finite1183840848l_num1 ).

thf(finite1639785033num1_n_type,type,
    finite1639785033num1_n: finite337957458num1_n > n > finite1183840848l_num1 ).

thf(finite1503577981l_num1_type,type,
    finite1503577981l_num1: finite121157254l_num1 > numeral_num1 > finite1489363574real_n ).

thf(finite625646243al_n_n_type,type,
    finite625646243al_n_n: finite318270636al_n_n > n > finite1489363574real_n ).

thf(finite1800583751l_num1_type,type,
    finite1800583751l_num1: finite2063899472l_num1 > numeral_num1 > int ).

thf(finite566214509_int_n_type,type,
    finite566214509_int_n: finite964658038_int_n > n > int ).

thf(finite1106245191l_num1_type,type,
    finite1106245191l_num1: finite1183840848l_num1 > numeral_num1 > real ).

thf(finite772340589real_n_type,type,
    finite772340589real_n: finite1489363574real_n > n > real ).

thf(finite1961675766l_num1_type,type,
    finite1961675766l_num1: real > finite1183840848l_num1 > finite1183840848l_num1 ).

thf(finite2053577756real_n_type,type,
    finite2053577756real_n: real > finite1489363574real_n > finite1489363574real_n ).

thf(abs_ab948591917l_num1_type,type,
    abs_ab948591917l_num1: finite1183840848l_num1 > finite1183840848l_num1 ).

thf(abs_ab1599551059real_n_type,type,
    abs_ab1599551059real_n: finite1489363574real_n > finite1489363574real_n ).

thf(abs_abs_int_type,type,
    abs_abs_int: int > int ).

thf(abs_abs_real_type,type,
    abs_abs_real: real > real ).

thf(minus_779068585l_num1_type,type,
    minus_779068585l_num1: finite2063899472l_num1 > finite2063899472l_num1 > finite2063899472l_num1 ).

thf(minus_1196255695_int_n_type,type,
    minus_1196255695_int_n: finite964658038_int_n > finite964658038_int_n > finite964658038_int_n ).

thf(minus_249161513l_num1_type,type,
    minus_249161513l_num1: finite1183840848l_num1 > finite1183840848l_num1 > finite1183840848l_num1 ).

thf(minus_1037315151real_n_type,type,
    minus_1037315151real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).

thf(minus_minus_int_type,type,
    minus_minus_int: int > int > int ).

thf(minus_minus_real_type,type,
    minus_minus_real: real > real > real ).

thf(one_on601734293l_num1_type,type,
    one_on601734293l_num1: finite2063899472l_num1 ).

thf(one_on1516019131_int_n_type,type,
    one_on1516019131_int_n: finite964658038_int_n ).

thf(one_on1961019669l_num1_type,type,
    one_on1961019669l_num1: finite1183840848l_num1 ).

thf(one_on1253059131real_n_type,type,
    one_on1253059131real_n: finite1489363574real_n ).

thf(one_one_int_type,type,
    one_one_int: int ).

thf(one_one_Numeral_num1_type,type,
    one_one_Numeral_num1: numeral_num1 ).

thf(one_one_real_type,type,
    one_one_real: real ).

thf(if_Fin1570437642l_num1_type,type,
    if_Fin1570437642l_num1: $o > finite2063899472l_num1 > finite2063899472l_num1 > finite2063899472l_num1 ).

thf(if_Fin1767949360_int_n_type,type,
    if_Fin1767949360_int_n: $o > finite964658038_int_n > finite964658038_int_n > finite964658038_int_n ).

thf(if_Fin1668193290l_num1_type,type,
    if_Fin1668193290l_num1: $o > finite1183840848l_num1 > finite1183840848l_num1 > finite1183840848l_num1 ).

thf(if_Fin127821360real_n_type,type,
    if_Fin127821360real_n: $o > finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).

thf(ring_11529266783l_num1_type,type,
    ring_11529266783l_num1: set_Fi1257234438l_num1 ).

thf(ring_1723899781real_n_type,type,
    ring_1723899781real_n: set_Fi1058188332real_n ).

thf(ring_1_Ints_int_type,type,
    ring_1_Ints_int: set_int ).

thf(ring_1_Ints_real_type,type,
    ring_1_Ints_real: set_real ).

thf(ring_1154201247l_num1_type,type,
    ring_1154201247l_num1: int > finite1183840848l_num1 ).

thf(ring_11737179077real_n_type,type,
    ring_11737179077real_n: int > finite1489363574real_n ).

thf(ring_1_of_int_int_type,type,
    ring_1_of_int_int: int > int ).

thf(ring_1_of_int_real_type,type,
    ring_1_of_int_real: int > real ).

thf(minkow781993583real_n_type,type,
    minkow781993583real_n: finite2063899472l_num1 > finite121157254l_num1 ).

thf(minkow2063319845m1_int_type,type,
    minkow2063319845m1_int: finite2063899472l_num1 > finite2063899472l_num1 ).

thf(minkow19073400691_real_type,type,
    minkow19073400691_real: finite2063899472l_num1 > finite1183840848l_num1 ).

thf(minkow371489429real_n_type,type,
    minkow371489429real_n: finite964658038_int_n > finite318270636al_n_n ).

thf(minkow1468704075_n_int_type,type,
    minkow1468704075_n_int: finite964658038_int_n > finite964658038_int_n ).

thf(minkow1134813771n_real_type,type,
    minkow1134813771n_real: finite964658038_int_n > finite1489363574real_n ).

thf(ord_le2035778724l_num1_type,type,
    ord_le2035778724l_num1: finite1183840848l_num1 > finite1183840848l_num1 > $o ).

thf(ord_le1017090250real_n_type,type,
    ord_le1017090250real_n: finite1489363574real_n > finite1489363574real_n > $o ).

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

thf(ord_less_real_type,type,
    ord_less_real: real > real > $o ).

thf(ord_le1202326448l_num1_type,type,
    ord_le1202326448l_num1: finite2063899472l_num1 > finite2063899472l_num1 > $o ).

thf(ord_le1908593622_int_n_type,type,
    ord_le1908593622_int_n: finite964658038_int_n > finite964658038_int_n > $o ).

thf(ord_le1724070576l_num1_type,type,
    ord_le1724070576l_num1: finite1183840848l_num1 > finite1183840848l_num1 > $o ).

thf(ord_le866583254real_n_type,type,
    ord_le866583254real_n: finite1489363574real_n > finite1489363574real_n > $o ).

thf(ord_less_eq_int_type,type,
    ord_less_eq_int: int > int > $o ).

thf(ord_less_eq_real_type,type,
    ord_less_eq_real: real > real > $o ).

thf(real_V1974343547l_num1_type,type,
    real_V1974343547l_num1: finite463740460l_num1 > finite463740460l_num1 > real ).

thf(real_V845814485l_num1_type,type,
    real_V845814485l_num1: finite121157254l_num1 > finite121157254l_num1 > real ).

thf(real_V488409631l_num1_type,type,
    real_V488409631l_num1: finite1183840848l_num1 > finite1183840848l_num1 > real ).

thf(real_V783965509real_n_type,type,
    real_V783965509real_n: finite1489363574real_n > finite1489363574real_n > real ).

thf(real_V1934908667t_real_type,type,
    real_V1934908667t_real: real > real > real ).

thf(real_V316032763l_num1_type,type,
    real_V316032763l_num1: finite463740460l_num1 > real ).

thf(real_V1121707553num1_n_type,type,
    real_V1121707553num1_n: finite337957458num1_n > real ).

thf(real_V400292255l_num1_type,type,
    real_V400292255l_num1: finite1183840848l_num1 > real ).

thf(real_V739724485real_n_type,type,
    real_V739724485real_n: finite1489363574real_n > real ).

thf(real_V646646907m_real_type,type,
    real_V646646907m_real: real > real ).

thf(collec321817931real_n_type,type,
    collec321817931real_n: ( finite1489363574real_n > $o ) > set_Fi1058188332real_n ).

thf(collect_real_type,type,
    collect_real: ( real > $o ) > set_real ).

thf(member1413569767l_num1_type,type,
    member1413569767l_num1: finite1183840848l_num1 > set_Fi1257234438l_num1 > $o ).

thf(member1352538125real_n_type,type,
    member1352538125real_n: finite1489363574real_n > set_Fi1058188332real_n > $o ).

thf(member_int_type,type,
    member_int: int > set_int > $o ).

thf(member_real_type,type,
    member_real: real > set_real > $o ).

thf(a_type,type,
    a: set_Fi1058188332real_n ).

thf(i_type,type,
    i: n ).

thf(m_type,type,
    m: int ).

thf(x_type,type,
    x: finite1489363574real_n ).

thf(y_type,type,
    y: finite1489363574real_n ).

thf(193,axiom,
    ( real_V488409631l_num1
    = ( ^ [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( real_V1934908667t_real @ ( finite1106245191l_num1 @ A @ one_one_Numeral_num1 ) @ ( finite1106245191l_num1 @ B @ one_one_Numeral_num1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_dist__vector__1) ).

thf(1036,plain,
    ( real_V488409631l_num1
    = ( ^ [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( real_V1934908667t_real @ ( finite1106245191l_num1 @ A @ one_one_Numeral_num1 ) @ ( finite1106245191l_num1 @ B @ one_one_Numeral_num1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(301,axiom,
    ! [A: finite1489363574real_n,B: n] :
      ( ( member1352538125real_n @ A @ a )
     => ( member_real @ ( finite772340589real_n @ A @ B ) @ ring_1_Ints_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_assms) ).

thf(1337,plain,
    ! [A: finite1489363574real_n,B: n] :
      ( ( member1352538125real_n @ A @ a )
     => ( member_real @ ( finite772340589real_n @ A @ B ) @ ring_1_Ints_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(325,axiom,
    ! [A: int,B: int] :
      ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
      = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_abs__minus__commute) ).

thf(1411,plain,
    ! [A: int,B: int] :
      ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
      = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(188,axiom,
    ( ( (=) @ int )
    = ( ^ [A: int,B: int] :
          ( ( ord_less_eq_int @ A @ B )
          & ( ord_less_eq_int @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_eq__iff) ).

thf(1024,plain,
    ( ( (=) @ int )
    = ( ^ [A: int,B: int] :
          ( ( ord_less_eq_int @ A @ B )
          & ( ord_less_eq_int @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(236,axiom,
    ( ( ring_1_of_int_real @ m )
    = ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_m) ).

thf(1168,plain,
    ( ( ring_1_of_int_real @ m )
    = ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(215,axiom,
    ! [A: int,B: int] :
      ( ( ring_1_of_int_int @ ( minus_minus_int @ A @ B ) )
      = ( minus_minus_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_of__int__diff) ).

thf(1105,plain,
    ! [A: int,B: int] :
      ( ( ring_1_of_int_int @ ( minus_minus_int @ A @ B ) )
      = ( minus_minus_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(293,axiom,
    ! [A: finite964658038_int_n,B: n] :
      ( ( finite772340589real_n @ ( minkow1134813771n_real @ A ) @ B )
      = ( ring_1_of_int_real @ ( finite566214509_int_n @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_of__int__vec__nth) ).

thf(1315,plain,
    ! [A: finite964658038_int_n,B: n] :
      ( ( finite772340589real_n @ ( minkow1134813771n_real @ A ) @ B )
      = ( ring_1_of_int_real @ ( finite566214509_int_n @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(285,axiom,
    ! [A: real] :
      ( ( abs_abs_real @ ( real_V646646907m_real @ A ) )
      = ( real_V646646907m_real @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_abs__norm__cancel) ).

thf(1295,plain,
    ! [A: real] :
      ( ( abs_abs_real @ ( real_V646646907m_real @ A ) )
      = ( real_V646646907m_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(217,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_eq_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_dual__order_Ostrict__implies__order) ).

thf(1110,plain,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_eq_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(80,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( ord_less_eq_real @ A @ B )
       => ~ ( ord_less_eq_real @ B @ C ) )
     => ( ( ( ord_less_eq_real @ B @ A )
         => ~ ( ord_less_eq_real @ A @ C ) )
       => ( ( ( ord_less_eq_real @ A @ C )
           => ~ ( ord_less_eq_real @ C @ B ) )
         => ( ( ( ord_less_eq_real @ C @ B )
             => ~ ( ord_less_eq_real @ B @ A ) )
           => ( ( ( ord_less_eq_real @ B @ C )
               => ~ ( ord_less_eq_real @ C @ A ) )
             => ~ ( ( ord_less_eq_real @ C @ A )
                 => ~ ( ord_less_eq_real @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_le__cases3) ).

thf(645,plain,
    ! [A: real,B: real,C: real] :
      ( ( ( ord_less_eq_real @ A @ B )
       => ~ ( ord_less_eq_real @ B @ C ) )
     => ( ( ( ord_less_eq_real @ B @ A )
         => ~ ( ord_less_eq_real @ A @ C ) )
       => ( ( ( ord_less_eq_real @ A @ C )
           => ~ ( ord_less_eq_real @ C @ B ) )
         => ( ( ( ord_less_eq_real @ C @ B )
             => ~ ( ord_less_eq_real @ B @ A ) )
           => ( ( ( ord_less_eq_real @ B @ C )
               => ~ ( ord_less_eq_real @ C @ A ) )
             => ~ ( ( ord_less_eq_real @ C @ A )
                 => ~ ( ord_less_eq_real @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(147,axiom,
    ( ( (=) @ real )
    = ( ^ [A: real,B: real] :
          ( ( ord_less_eq_real @ B @ A )
          & ( ord_less_eq_real @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_dual__order_Oeq__iff) ).

thf(892,plain,
    ( ( (=) @ real )
    = ( ^ [A: real,B: real] :
          ( ( ord_less_eq_real @ B @ A )
          & ( ord_less_eq_real @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(360,axiom,
    ! [A: n] :
      ( ( finite772340589real_n @ one_on1253059131real_n @ A )
      = one_one_real ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_one__index) ).

thf(1501,plain,
    ! [A: n] :
      ( ( finite772340589real_n @ one_on1253059131real_n @ A )
      = one_one_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(123,axiom,
    ! [A: int,B: int] :
      ( ( ( ring_1_of_int_int @ A )
        = ( ring_1_of_int_int @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_of__int__eq__iff) ).

thf(809,plain,
    ! [A: int,B: int] :
      ( ( ( ring_1_of_int_int @ A )
        = ( ring_1_of_int_int @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(153,axiom,
    ! [A: $o,B: finite2063899472l_num1,C: finite2063899472l_num1,D: numeral_num1] :
      ( ( A
       => ( ( finite1800583751l_num1 @ ( if_Fin1570437642l_num1 @ A @ B @ C ) @ D )
          = ( finite1800583751l_num1 @ B @ D ) ) )
      & ( ~ A
       => ( ( finite1800583751l_num1 @ ( if_Fin1570437642l_num1 @ A @ B @ C ) @ D )
          = ( finite1800583751l_num1 @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_cond__component) ).

thf(909,plain,
    ! [A: $o,B: finite2063899472l_num1,C: finite2063899472l_num1,D: numeral_num1] :
      ( ( A
       => ( ( finite1800583751l_num1 @ ( if_Fin1570437642l_num1 @ A @ B @ C ) @ D )
          = ( finite1800583751l_num1 @ B @ D ) ) )
      & ( ~ A
       => ( ( finite1800583751l_num1 @ ( if_Fin1570437642l_num1 @ A @ B @ C ) @ D )
          = ( finite1800583751l_num1 @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(191,axiom,
    ( ( ring_1_of_int_int @ one_one_int )
    = one_one_int ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_of__int__1) ).

thf(1031,plain,
    ( ( ring_1_of_int_int @ one_one_int )
    = one_one_int ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(248,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
      ( ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ B ) @ C )
      = ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_diff__right__commute) ).

thf(1200,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
      ( ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ B ) @ C )
      = ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(109,axiom,
    ! [A: int,B: int,C: int] :
      ( ( A = B )
     => ( ( ord_less_eq_int @ B @ C )
       => ( ord_less_eq_int @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_ord__eq__le__trans) ).

thf(762,plain,
    ! [A: int,B: int,C: int] :
      ( ( A = B )
     => ( ( ord_less_eq_int @ B @ C )
       => ( ord_less_eq_int @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(323,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
      ( ( ord_le1017090250real_n @ A @ B )
     => ( ord_le1017090250real_n @ ( minus_1037315151real_n @ C @ B ) @ ( minus_1037315151real_n @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_diff__strict__left__mono) ).

thf(1406,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
      ( ( ord_le1017090250real_n @ A @ B )
     => ( ord_le1017090250real_n @ ( minus_1037315151real_n @ C @ B ) @ ( minus_1037315151real_n @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(90,axiom,
    ! [A: int] : ( member1352538125real_n @ ( ring_11737179077real_n @ A ) @ ring_1723899781real_n ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Ints__of__int) ).

thf(683,plain,
    ! [A: int] : ( member1352538125real_n @ ( ring_11737179077real_n @ A ) @ ring_1723899781real_n ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(283,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
      ( ( ( minus_1037315151real_n @ A @ B )
        = ( minus_1037315151real_n @ C @ D ) )
     => ( ( ord_le1017090250real_n @ A @ B )
        = ( ord_le1017090250real_n @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_diff__eq__diff__less) ).

thf(1290,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
      ( ( ( minus_1037315151real_n @ A @ B )
        = ( minus_1037315151real_n @ C @ D ) )
     => ( ( ord_le1017090250real_n @ A @ B )
        = ( ord_le1017090250real_n @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(338,axiom,
    ! [A: real,B: real] :
      ( ( member_real @ A @ ring_1_Ints_real )
     => ( ( member_real @ B @ ring_1_Ints_real )
       => ( ( A = B )
          = ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ one_one_real ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_Ints__eq__abs__less1) ).

thf(1443,plain,
    ! [A: real,B: real] :
      ( ( member_real @ A @ ring_1_Ints_real )
     => ( ( member_real @ B @ ring_1_Ints_real )
       => ( ( A = B )
          = ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ one_one_real ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(7,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1,D: finite1183840848l_num1] :
      ( ( ( minus_249161513l_num1 @ A @ B )
        = ( minus_249161513l_num1 @ C @ D ) )
     => ( ( ord_le1724070576l_num1 @ A @ B )
        = ( ord_le1724070576l_num1 @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_diff__eq__diff__less__eq) ).

thf(379,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1,D: finite1183840848l_num1] :
      ( ( ( minus_249161513l_num1 @ A @ B )
        = ( minus_249161513l_num1 @ C @ D ) )
     => ( ( ord_le1724070576l_num1 @ A @ B )
        = ( ord_le1724070576l_num1 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(289,axiom,
    ! [A: finite1489363574real_n,B: real,C: n] :
      ( ( ord_less_eq_real @ ( real_V739724485real_n @ A ) @ B )
     => ( ord_less_eq_real @ ( abs_abs_real @ ( finite772340589real_n @ A @ C ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_norm__bound__component__le__cart) ).

thf(1305,plain,
    ! [A: finite1489363574real_n,B: real,C: n] :
      ( ( ord_less_eq_real @ ( real_V739724485real_n @ A ) @ B )
     => ( ord_less_eq_real @ ( abs_abs_real @ ( finite772340589real_n @ A @ C ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(335,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V739724485real_n @ A ) @ ( real_V739724485real_n @ B ) ) @ ( real_V739724485real_n @ ( minus_1037315151real_n @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_norm__triangle__ineq2) ).

thf(1437,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V739724485real_n @ A ) @ ( real_V739724485real_n @ B ) ) @ ( real_V739724485real_n @ ( minus_1037315151real_n @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(195,axiom,
    ! [A: real] :
      ( ( ord_less_int @ ( archim1031974863r_real @ A ) @ one_one_int )
      = ( ord_less_real @ A @ one_one_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_floor__less__one) ).

thf(1041,plain,
    ! [A: real] :
      ( ( ord_less_int @ ( archim1031974863r_real @ A ) @ one_one_int )
      = ( ord_less_real @ A @ one_one_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(141,axiom,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ( minus_minus_int @ A @ B )
        = ( minus_minus_int @ C @ D ) )
     => ( ( ord_less_int @ A @ B )
        = ( ord_less_int @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_diff__eq__diff__less) ).

thf(873,plain,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ( minus_minus_int @ A @ B )
        = ( minus_minus_int @ C @ D ) )
     => ( ( ord_less_int @ A @ B )
        = ( ord_less_int @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(250,axiom,
    ( ( abs_abs_int @ one_one_int )
    = one_one_int ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_abs__one) ).

thf(1205,plain,
    ( ( abs_abs_int @ one_one_int )
    = one_one_int ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(9,axiom,
    ! [A: finite2063899472l_num1,B: finite2063899472l_num1] :
      ( ( if_Fin1570437642l_num1 @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Finite____Cartesian____Product__Ovec_It__Int__Oint_Mt__Numeral____Type__Onum1_J_T) ).

thf(384,plain,
    ! [A: finite2063899472l_num1,B: finite2063899472l_num1] :
      ( ( if_Fin1570437642l_num1 @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(291,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( real_V739724485real_n @ ( minus_1037315151real_n @ A @ B ) )
      = ( real_V739724485real_n @ ( minus_1037315151real_n @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_norm__minus__commute) ).

thf(1310,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( real_V739724485real_n @ ( minus_1037315151real_n @ A @ B ) )
      = ( real_V739724485real_n @ ( minus_1037315151real_n @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(96,axiom,
    ( ord_less_real
    = ( ^ [A: real,B: real] :
          ( ( ord_less_eq_real @ A @ B )
          & ~ ( ord_less_eq_real @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_eucl__less__le__not__le) ).

thf(698,plain,
    ( ord_less_real
    = ( ^ [A: real,B: real] :
          ( ( ord_less_eq_real @ A @ B )
          & ~ ( ord_less_eq_real @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(163,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_int @ ( archim1031974863r_real @ A ) @ ( archim1031974863r_real @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_floor__mono) ).

thf(945,plain,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_int @ ( archim1031974863r_real @ A ) @ ( archim1031974863r_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(201,axiom,
    ! [A: real,B: int > real,C: int,D: int] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_int @ C @ D )
       => ( ! [E: int,F: int] :
              ( ( ord_less_eq_int @ E @ F )
             => ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_ord__eq__le__subst) ).

thf(1063,plain,
    ! [A: real,B: int > real,C: int,D: int] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_int @ C @ D )
       => ( ! [E: int,F: int] :
              ( ( ord_less_eq_int @ E @ F )
             => ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(52,axiom,
    ! [A: int] : ( ord_less_eq_int @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_order__refl) ).

thf(538,plain,
    ! [A: int] : ( ord_less_eq_int @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(303,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
      ( ( ord_le1017090250real_n @ A @ B )
     => ( ord_le1017090250real_n @ ( minus_1037315151real_n @ A @ C ) @ ( minus_1037315151real_n @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_diff__strict__right__mono) ).

thf(1342,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
      ( ( ord_le1017090250real_n @ A @ B )
     => ( ord_le1017090250real_n @ ( minus_1037315151real_n @ A @ C ) @ ( minus_1037315151real_n @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(103,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_diff__strict__right__mono) ).

thf(747,plain,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(362,axiom,
    member_real @ ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) @ ring_1_Ints_real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14__092_060open_062x_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060in_062_A_092_060int_062_092_060close_062) ).

thf(1507,plain,
    member_real @ ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) @ ring_1_Ints_real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(257,axiom,
    ! [A: real,B: int] :
      ( ( archim1031974863r_real @ ( minus_minus_real @ A @ ( ring_1_of_int_real @ B ) ) )
      = ( minus_minus_int @ ( archim1031974863r_real @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_floor__diff__of__int) ).

thf(1222,plain,
    ! [A: real,B: int] :
      ( ( archim1031974863r_real @ ( minus_minus_real @ A @ ( ring_1_of_int_real @ B ) ) )
      = ( minus_minus_int @ ( archim1031974863r_real @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(337,axiom,
    ! [A: real] : ( ord_less_real @ ( minus_minus_real @ A @ one_one_real ) @ ( ring_1_of_int_real @ ( archim1031974863r_real @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_real__of__int__floor__gt__diff__one) ).

thf(1441,plain,
    ! [A: real] : ( ord_less_real @ ( minus_minus_real @ A @ one_one_real ) @ ( ring_1_of_int_real @ ( archim1031974863r_real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(173,axiom,
    ! [A: real,B: finite1183840848l_num1,C: finite1183840848l_num1] :
      ( ( finite1961675766l_num1 @ A @ ( minus_249161513l_num1 @ B @ C ) )
      = ( minus_249161513l_num1 @ ( finite1961675766l_num1 @ A @ B ) @ ( finite1961675766l_num1 @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_vector__ssub__ldistrib) ).

thf(973,plain,
    ! [A: real,B: finite1183840848l_num1,C: finite1183840848l_num1] :
      ( ( finite1961675766l_num1 @ A @ ( minus_249161513l_num1 @ B @ C ) )
      = ( minus_249161513l_num1 @ ( finite1961675766l_num1 @ A @ B ) @ ( finite1961675766l_num1 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(309,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( ( finite772340589real_n @ A )
        = ( finite772340589real_n @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_vec__nth__inject) ).

thf(1359,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( ( finite772340589real_n @ A )
        = ( finite772340589real_n @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(316,axiom,
    ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_abs__triangle__ineq2__sym) ).

thf(1386,plain,
    ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(350,axiom,
    ! [A: int,B: int] :
      ( ( ( ring_1_of_int_real @ A )
        = ( ring_1_of_int_real @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_of__int__eq__iff) ).

thf(1475,plain,
    ! [A: int,B: int] :
      ( ( ( ring_1_of_int_real @ A )
        = ( ring_1_of_int_real @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(28,axiom,
    ! [A: real] :
      ( ( ord_less_int @ one_one_int @ ( archim1371465213g_real @ A ) )
      = ( ord_less_real @ one_one_real @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_one__less__ceiling) ).

thf(436,plain,
    ! [A: real] :
      ( ( ord_less_int @ one_one_int @ ( archim1371465213g_real @ A ) )
      = ( ord_less_real @ one_one_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(259,axiom,
    ! [A: real,B: n] :
      ( ( finite772340589real_n @ ( finite667548811real_n @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_vec__component) ).

thf(1228,plain,
    ! [A: real,B: n] :
      ( ( finite772340589real_n @ ( finite667548811real_n @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(58,axiom,
    ~ ( ord_less_int @ one_one_int @ one_one_int ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_less__numeral__extra_I4_J) ).

thf(565,plain,
    ~ ( ord_less_int @ one_one_int @ one_one_int ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(311,axiom,
    ( ( abs_abs_real @ one_one_real )
    = one_one_real ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_abs__one) ).

thf(1366,plain,
    ( ( abs_abs_real @ one_one_real )
    = one_one_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(324,axiom,
    ! [A: real,B: int] :
      ( ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ B ) )
     => ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_ceiling__le) ).

thf(1409,plain,
    ! [A: real,B: int] :
      ( ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ B ) )
     => ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(282,axiom,
    ! [A: finite1183840848l_num1,B: real,C: numeral_num1] :
      ( ( ord_less_eq_real @ ( real_V400292255l_num1 @ A ) @ B )
     => ( ord_less_eq_real @ ( abs_abs_real @ ( finite1106245191l_num1 @ A @ C ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_norm__bound__component__le__cart) ).

thf(1287,plain,
    ! [A: finite1183840848l_num1,B: real,C: numeral_num1] :
      ( ( ord_less_eq_real @ ( real_V400292255l_num1 @ A ) @ B )
     => ( ord_less_eq_real @ ( abs_abs_real @ ( finite1106245191l_num1 @ A @ C ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(60,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ord_less_eq_real @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_order_Otrans) ).

thf(570,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ord_less_eq_real @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(286,axiom,
    ! [A: real] :
    ? [B: int] : ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_ex__le__of__int) ).

thf(1298,plain,
    ! [A: real] :
    ? [B: int] : ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(292,axiom,
    ! [A: finite1489363574real_n,B: finite337957458num1_n] :
      ( ! [C: n] : ( ord_less_eq_real @ ( real_V646646907m_real @ ( finite772340589real_n @ A @ C ) ) @ ( real_V400292255l_num1 @ ( finite1639785033num1_n @ B @ C ) ) )
     => ( ord_less_eq_real @ ( real_V739724485real_n @ A ) @ ( real_V1121707553num1_n @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_norm__le__componentwise__cart) ).

thf(1313,plain,
    ! [A: finite1489363574real_n,B: finite337957458num1_n] :
      ( ! [C: n] : ( ord_less_eq_real @ ( real_V646646907m_real @ ( finite772340589real_n @ A @ C ) ) @ ( real_V400292255l_num1 @ ( finite1639785033num1_n @ B @ C ) ) )
     => ( ord_less_eq_real @ ( real_V739724485real_n @ A ) @ ( real_V1121707553num1_n @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(342,axiom,
    ! [A: real] :
    ? [B: int] : ( ord_less_real @ ( ring_1_of_int_real @ B ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_ex__of__int__less) ).

thf(1455,plain,
    ! [A: real] :
    ? [B: int] : ( ord_less_real @ ( ring_1_of_int_real @ B ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(345,axiom,
    ! [A: int] :
      ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ one_one_real )
      = ( ord_less_int @ A @ one_one_int ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_of__int__less__1__iff) ).

thf(1462,plain,
    ! [A: int] :
      ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ one_one_real )
      = ( ord_less_int @ A @ one_one_int ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(165,axiom,
    ! [A: int,B: int] :
      ( ( A != B )
     => ( ~ ( ord_less_int @ A @ B )
       => ( ord_less_int @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_linorder__neqE__linordered__idom) ).

thf(949,plain,
    ! [A: int,B: int] :
      ( ( A != B )
     => ( ~ ( ord_less_int @ A @ B )
       => ( ord_less_int @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(298,axiom,
    ( real_V1934908667t_real
    = ( ^ [A: real,B: real] : ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_dist__real__def) ).

thf(1330,plain,
    ( real_V1934908667t_real
    = ( ^ [A: real,B: real] : ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(274,axiom,
    ! [A: int] :
      ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ A ) )
      = ( ord_less_int @ one_one_int @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_of__int__1__less__iff) ).

thf(1264,plain,
    ! [A: int] :
      ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ A ) )
      = ( ord_less_int @ one_one_int @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(134,axiom,
    ! [A: numeral_num1] :
      ( ( one_one_Numeral_num1 = A )
      = ( A = one_one_Numeral_num1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_one__reorient) ).

thf(853,plain,
    ! [A: numeral_num1] :
      ( ( one_one_Numeral_num1 = A )
      = ( A = one_one_Numeral_num1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(266,axiom,
    ord_less_real @ ( real_V783965509real_n @ y @ x ) @ one_one_real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79__C1_C_I3_J) ).

thf(1247,plain,
    ord_less_real @ ( real_V783965509real_n @ y @ x ) @ one_one_real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(23,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ C @ A )
       => ( ord_less_eq_real @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_dual__order_Otrans) ).

thf(421,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ C @ A )
       => ( ord_less_eq_real @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(357,axiom,
    ( ( abs_abs_real @ one_one_real )
    = one_one_real ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_abs__1) ).

thf(1494,plain,
    ( ( abs_abs_real @ one_one_real )
    = one_one_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(310,axiom,
    ! [A: int,B: int] :
      ( ( member_int @ A @ ring_1_Ints_int )
     => ( ( member_int @ B @ ring_1_Ints_int )
       => ( ( A = B )
          = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ one_one_int ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_Ints__eq__abs__less1) ).

thf(1362,plain,
    ! [A: int,B: int] :
      ( ( member_int @ A @ ring_1_Ints_int )
     => ( ( member_int @ B @ ring_1_Ints_int )
       => ( ( A = B )
          = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ one_one_int ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(213,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_real @ ( minus_minus_real @ C @ B ) @ ( minus_minus_real @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_diff__left__mono) ).

thf(1100,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_real @ ( minus_minus_real @ C @ B ) @ ( minus_minus_real @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(69,axiom,
    ! [A: int] :
      ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ A ) )
      = ( ord_less_int @ one_one_int @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_of__int__1__less__iff) ).

thf(606,plain,
    ! [A: int] :
      ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ A ) )
      = ( ord_less_int @ one_one_int @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(305,axiom,
    ! [A: int,B: int] :
      ( ( ring_11737179077real_n @ ( minus_minus_int @ A @ B ) )
      = ( minus_1037315151real_n @ ( ring_11737179077real_n @ A ) @ ( ring_11737179077real_n @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_of__int__diff) ).

thf(1347,plain,
    ! [A: int,B: int] :
      ( ( ring_11737179077real_n @ ( minus_minus_int @ A @ B ) )
      = ( minus_1037315151real_n @ ( ring_11737179077real_n @ A ) @ ( ring_11737179077real_n @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(184,axiom,
    ! [A: finite2063899472l_num1,B: finite2063899472l_num1,C: numeral_num1] :
      ( ( finite1800583751l_num1 @ ( minus_779068585l_num1 @ A @ B ) @ C )
      = ( minus_minus_int @ ( finite1800583751l_num1 @ A @ C ) @ ( finite1800583751l_num1 @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_vector__minus__component) ).

thf(1013,plain,
    ! [A: finite2063899472l_num1,B: finite2063899472l_num1,C: numeral_num1] :
      ( ( finite1800583751l_num1 @ ( minus_779068585l_num1 @ A @ B ) @ C )
      = ( minus_minus_int @ ( finite1800583751l_num1 @ A @ C ) @ ( finite1800583751l_num1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(111,axiom,
    ! [A: set_Fi1058188332real_n] :
      ( ( collec321817931real_n
        @ ^ [B: finite1489363574real_n] : ( member1352538125real_n @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Collect__mem__eq) ).

thf(770,plain,
    ! [A: set_Fi1058188332real_n] :
      ( ( collec321817931real_n
        @ ^ [B: finite1489363574real_n] : ( member1352538125real_n @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(321,axiom,
    ! [A: real] :
      ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim1371465213g_real @ A ) ) @ one_one_real ) @ A )
      & ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ ( archim1371465213g_real @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_ceiling__correct) ).

thf(1398,plain,
    ! [A: real] :
      ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim1371465213g_real @ A ) ) @ one_one_real ) @ A )
      & ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ ( archim1371465213g_real @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(144,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( minus_minus_real @ A @ B )
        = ( minus_minus_real @ C @ D ) )
     => ( ( ord_less_real @ A @ B )
        = ( ord_less_real @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_diff__eq__diff__less) ).

thf(881,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( minus_minus_real @ A @ B )
        = ( minus_minus_real @ C @ D ) )
     => ( ( ord_less_real @ A @ B )
        = ( ord_less_real @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(21,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( real_V488409631l_num1 @ ( minus_249161513l_num1 @ A @ B ) @ A )
      = ( real_V400292255l_num1 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_dist__diff_I2_J) ).

thf(416,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( real_V488409631l_num1 @ ( minus_249161513l_num1 @ A @ B ) @ A )
      = ( real_V400292255l_num1 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(355,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( real_V783965509real_n @ A @ ( minus_1037315151real_n @ A @ B ) )
      = ( real_V739724485real_n @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_dist__diff_I1_J) ).

thf(1489,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( real_V783965509real_n @ A @ ( minus_1037315151real_n @ A @ B ) )
      = ( real_V739724485real_n @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(156,axiom,
    ! [A: int,B: int] :
      ( ( ( ring_11737179077real_n @ A )
        = ( ring_11737179077real_n @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_of__int__eq__iff) ).

thf(924,plain,
    ! [A: int,B: int] :
      ( ( ( ring_11737179077real_n @ A )
        = ( ring_11737179077real_n @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(288,axiom,
    ! [A: int,B: real] :
      ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ B )
     => ( ( ord_less_eq_real @ B @ ( ring_1_of_int_real @ A ) )
       => ( ( archim1371465213g_real @ B )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_ceiling__unique) ).

thf(1302,plain,
    ! [A: int,B: real] :
      ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ B )
     => ( ( ord_less_eq_real @ B @ ( ring_1_of_int_real @ A ) )
       => ( ( archim1371465213g_real @ B )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(6,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( if_Fin1668193290l_num1 @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mt__Numeral____Type__Onum1_J_T) ).

thf(376,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( if_Fin1668193290l_num1 @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(225,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ ( archim1371465213g_real @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_ceiling__mono) ).

thf(1136,plain,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ ( archim1371465213g_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(315,axiom,
    ! [A: int,B: int] :
      ( ( ring_1_of_int_real @ ( minus_minus_int @ A @ B ) )
      = ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_of__int__diff) ).

thf(1383,plain,
    ! [A: int,B: int] :
      ( ( ring_1_of_int_real @ ( minus_minus_int @ A @ B ) )
      = ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(242,axiom,
    ! [A: real] :
      ( ( abs_abs_real @ ( abs_abs_real @ A ) )
      = ( abs_abs_real @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_abs__abs) ).

thf(1183,plain,
    ! [A: real] :
      ( ( abs_abs_real @ ( abs_abs_real @ A ) )
      = ( abs_abs_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(40,axiom,
    ! [A: numeral_num1 > real > $o] :
      ( ( ! [B: numeral_num1] :
          ? [C: real] : ( A @ B @ C ) )
      = ( ? [B: finite1183840848l_num1] :
          ! [C: numeral_num1] : ( A @ C @ ( finite1106245191l_num1 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_lambda__skolem) ).

thf(480,plain,
    ! [A: numeral_num1 > real > $o] :
      ( ( ! [B: numeral_num1] :
          ? [C: real] : ( A @ B @ C ) )
      = ( ? [B: finite1183840848l_num1] :
          ! [C: numeral_num1] : ( A @ C @ ( finite1106245191l_num1 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(44,axiom,
    ( ( '!' @ numeral_num1 )
    = ( ^ [A: numeral_num1 > $o] : ( A @ one_one_Numeral_num1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_forall__1) ).

thf(492,plain,
    ( ( '!' @ numeral_num1 )
    = ( ^ [A: numeral_num1 > $o] : ( A @ one_one_Numeral_num1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(346,axiom,
    ( ord_le866583254real_n
    = ( ^ [A: finite1489363574real_n,B: finite1489363574real_n] :
        ! [C: n] : ( ord_less_eq_real @ ( finite772340589real_n @ A @ C ) @ ( finite772340589real_n @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_less__eq__vec__def) ).

thf(1465,plain,
    ( ord_le866583254real_n
    = ( ^ [A: finite1489363574real_n,B: finite1489363574real_n] :
        ! [C: n] : ( ord_less_eq_real @ ( finite772340589real_n @ A @ C ) @ ( finite772340589real_n @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(175,axiom,
    ( ( (=) @ int )
    = ( ^ [A: int,B: int] :
          ( ( ord_less_eq_int @ B @ A )
          & ( ord_less_eq_int @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_dual__order_Oeq__iff) ).

thf(981,plain,
    ( ( (=) @ int )
    = ( ^ [A: int,B: int] :
          ( ( ord_less_eq_int @ B @ A )
          & ( ord_less_eq_int @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(92,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ord_less_eq_real @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_order__trans) ).

thf(687,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ord_less_eq_real @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(313,axiom,
    ! [A: int > $o,B: real] :
      ( ( A @ ( archim1371465213g_real @ B ) )
      = ( ! [C: int] :
            ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ C ) @ one_one_real ) @ B )
              & ( ord_less_eq_real @ B @ ( ring_1_of_int_real @ C ) ) )
           => ( A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_ceiling__split) ).

thf(1377,plain,
    ! [A: int > $o,B: real] :
      ( ( A @ ( archim1371465213g_real @ B ) )
      = ( ! [C: int] :
            ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ C ) @ one_one_real ) @ B )
              & ( ord_less_eq_real @ B @ ( ring_1_of_int_real @ C ) ) )
           => ( A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(14,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1,D: finite1183840848l_num1] :
      ( ( ord_le1724070576l_num1 @ A @ B )
     => ( ( ord_le1724070576l_num1 @ C @ D )
       => ( ord_le1724070576l_num1 @ ( minus_249161513l_num1 @ A @ D ) @ ( minus_249161513l_num1 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_diff__mono) ).

thf(396,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1,D: finite1183840848l_num1] :
      ( ( ord_le1724070576l_num1 @ A @ B )
     => ( ( ord_le1724070576l_num1 @ C @ D )
       => ( ord_le1724070576l_num1 @ ( minus_249161513l_num1 @ A @ D ) @ ( minus_249161513l_num1 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(180,axiom,
    ( real_V316032763l_num1
    = ( ^ [A: finite463740460l_num1] : ( real_V400292255l_num1 @ ( finite1449546019l_num1 @ A @ one_one_Numeral_num1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_norm__vector__1) ).

thf(998,plain,
    ( real_V316032763l_num1
    = ( ^ [A: finite463740460l_num1] : ( real_V400292255l_num1 @ ( finite1449546019l_num1 @ A @ one_one_Numeral_num1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(304,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ! [C: n] : ( ord_less_eq_real @ ( real_V646646907m_real @ ( finite772340589real_n @ A @ C ) ) @ ( real_V646646907m_real @ ( finite772340589real_n @ B @ C ) ) )
     => ( ord_less_eq_real @ ( real_V739724485real_n @ A ) @ ( real_V739724485real_n @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_norm__le__componentwise__cart) ).

thf(1345,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ! [C: n] : ( ord_less_eq_real @ ( real_V646646907m_real @ ( finite772340589real_n @ A @ C ) ) @ ( real_V646646907m_real @ ( finite772340589real_n @ B @ C ) ) )
     => ( ord_less_eq_real @ ( real_V739724485real_n @ A ) @ ( real_V739724485real_n @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(339,axiom,
    ! [A: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim1031974863r_real @ A ) ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_of__int__floor__le) ).

thf(1447,plain,
    ! [A: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim1031974863r_real @ A ) ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(167,axiom,
    ! [A: finite2063899472l_num1] :
      ( ( finite1470207077l_num1 @ ( finite1800583751l_num1 @ A @ one_one_Numeral_num1 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_vector__one__nth) ).

thf(956,plain,
    ! [A: finite2063899472l_num1] :
      ( ( finite1470207077l_num1 @ ( finite1800583751l_num1 @ A @ one_one_Numeral_num1 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(203,axiom,
    ( ( ring_11737179077real_n @ one_one_int )
    = one_on1253059131real_n ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_of__int__1) ).

thf(1074,plain,
    ( ( ring_11737179077real_n @ one_one_int )
    = one_on1253059131real_n ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(88,axiom,
    ( ( (=) @ finite2063899472l_num1 )
    = ( ^ [A: finite2063899472l_num1,B: finite2063899472l_num1] :
        ! [C: numeral_num1] :
          ( ( finite1800583751l_num1 @ A @ C )
          = ( finite1800583751l_num1 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_vec__eq__iff) ).

thf(678,plain,
    ( ( (=) @ finite2063899472l_num1 )
    = ( ^ [A: finite2063899472l_num1,B: finite2063899472l_num1] :
        ! [C: numeral_num1] :
          ( ( finite1800583751l_num1 @ A @ C )
          = ( finite1800583751l_num1 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(82,axiom,
    ! [A: int,B: int] :
      ( ( A != B )
     => ( ( ord_less_eq_int @ A @ B )
       => ( ord_less_int @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_order_Onot__eq__order__implies__strict) ).

thf(661,plain,
    ! [A: int,B: int] :
      ( ( A != B )
     => ( ( ord_less_eq_int @ A @ B )
       => ( ord_less_int @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(348,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
      ( ( ord_le866583254real_n @ A @ B )
     => ( ord_le866583254real_n @ ( minus_1037315151real_n @ A @ C ) @ ( minus_1037315151real_n @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_diff__right__mono) ).

thf(1470,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
      ( ( ord_le866583254real_n @ A @ B )
     => ( ord_le866583254real_n @ ( minus_1037315151real_n @ A @ C ) @ ( minus_1037315151real_n @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(1,conjecture,
    ( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
    = ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
   != ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(366,plain,
    ( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
   != ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(234,axiom,
    ! [A: int] :
      ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ one_one_real )
      = ( ord_less_eq_int @ A @ one_one_int ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_of__int__le__1__iff) ).

thf(1163,plain,
    ! [A: int] :
      ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ one_one_real )
      = ( ord_less_eq_int @ A @ one_one_int ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(162,axiom,
    ! [A: real,B: real,C: finite1183840848l_num1] :
      ( ( finite1961675766l_num1 @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_249161513l_num1 @ ( finite1961675766l_num1 @ A @ C ) @ ( finite1961675766l_num1 @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_vec_Oscale__left__diff__distrib) ).

thf(942,plain,
    ! [A: real,B: real,C: finite1183840848l_num1] :
      ( ( finite1961675766l_num1 @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_249161513l_num1 @ ( finite1961675766l_num1 @ A @ C ) @ ( finite1961675766l_num1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(29,axiom,
    ! [A: real,B: real > real,C: real,D: real] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_real @ C @ D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_ord__eq__le__subst) ).

thf(439,plain,
    ! [A: real,B: real > real,C: real,D: real] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_real @ C @ D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(55,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ! [C: numeral_num1] : ( ord_less_eq_real @ ( real_V646646907m_real @ ( finite1106245191l_num1 @ A @ C ) ) @ ( real_V646646907m_real @ ( finite1106245191l_num1 @ B @ C ) ) )
     => ( ord_less_eq_real @ ( real_V400292255l_num1 @ A ) @ ( real_V400292255l_num1 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_norm__le__componentwise__cart) ).

thf(546,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ! [C: numeral_num1] : ( ord_less_eq_real @ ( real_V646646907m_real @ ( finite1106245191l_num1 @ A @ C ) ) @ ( real_V646646907m_real @ ( finite1106245191l_num1 @ B @ C ) ) )
     => ( ord_less_eq_real @ ( real_V400292255l_num1 @ A ) @ ( real_V400292255l_num1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(118,axiom,
    ord_less_eq_int @ one_one_int @ one_one_int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_le__numeral__extra_I4_J) ).

thf(793,plain,
    ord_less_eq_int @ one_one_int @ one_one_int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(148,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1] :
      ( ( minus_249161513l_num1 @ ( minus_249161513l_num1 @ A @ B ) @ C )
      = ( minus_249161513l_num1 @ ( minus_249161513l_num1 @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_diff__right__commute) ).

thf(894,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1] :
      ( ( minus_249161513l_num1 @ ( minus_249161513l_num1 @ A @ B ) @ C )
      = ( minus_249161513l_num1 @ ( minus_249161513l_num1 @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(209,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1] :
      ( ( ord_le2035778724l_num1 @ A @ B )
     => ( ord_le2035778724l_num1 @ ( minus_249161513l_num1 @ C @ B ) @ ( minus_249161513l_num1 @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_diff__strict__left__mono) ).

thf(1091,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1] :
      ( ( ord_le2035778724l_num1 @ A @ B )
     => ( ord_le2035778724l_num1 @ ( minus_249161513l_num1 @ C @ B ) @ ( minus_249161513l_num1 @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(166,axiom,
    ! [A: finite1489363574real_n] :
      ( ( member1352538125real_n @ A @ ring_1723899781real_n )
     => ~ ! [B: int] :
            ( A
           != ( ring_11737179077real_n @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Ints__cases) ).

thf(952,plain,
    ! [A: finite1489363574real_n] :
      ( ( member1352538125real_n @ A @ ring_1723899781real_n )
     => ~ ! [B: int] :
            ( A
           != ( ring_11737179077real_n @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(137,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1,D: finite1183840848l_num1] :
      ( ( ord_le2035778724l_num1 @ A @ B )
     => ( ( ord_le2035778724l_num1 @ C @ D )
       => ( ord_le2035778724l_num1 @ ( minus_249161513l_num1 @ A @ D ) @ ( minus_249161513l_num1 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_diff__strict__mono) ).

thf(862,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1,D: finite1183840848l_num1] :
      ( ( ord_le2035778724l_num1 @ A @ B )
     => ( ( ord_le2035778724l_num1 @ C @ D )
       => ( ord_le2035778724l_num1 @ ( minus_249161513l_num1 @ A @ D ) @ ( minus_249161513l_num1 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(239,axiom,
    ! [A: int] :
      ( ( real_V646646907m_real @ ( ring_1_of_int_real @ A ) )
      = ( abs_abs_real @ ( ring_1_of_int_real @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_norm__of__int) ).

thf(1174,plain,
    ! [A: int] :
      ( ( real_V646646907m_real @ ( ring_1_of_int_real @ A ) )
      = ( abs_abs_real @ ( ring_1_of_int_real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(66,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_int @ ( archim1371465213g_real @ A ) @ ( archim1371465213g_real @ B ) )
     => ( ord_less_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_ceiling__less__cancel) ).

thf(598,plain,
    ! [A: real,B: real] :
      ( ( ord_less_int @ ( archim1371465213g_real @ A ) @ ( archim1371465213g_real @ B ) )
     => ( ord_less_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(354,axiom,
    ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_abs__triangle__ineq2) ).

thf(1487,plain,
    ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(24,axiom,
    ! [A: int] : ( ord_less_eq_int @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_dual__order_Orefl) ).

thf(424,plain,
    ! [A: int] : ( ord_less_eq_int @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(26,axiom,
    ! [A: real,B: real,C: finite1183840848l_num1] :
      ( ( finite1961675766l_num1 @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_249161513l_num1 @ ( finite1961675766l_num1 @ A @ C ) @ ( finite1961675766l_num1 @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_vector__sub__rdistrib) ).

thf(429,plain,
    ! [A: real,B: real,C: finite1183840848l_num1] :
      ( ( finite1961675766l_num1 @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_249161513l_num1 @ ( finite1961675766l_num1 @ A @ C ) @ ( finite1961675766l_num1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(125,axiom,
    ! [A: int,B: int,C: int > int,D: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: int,F: int] :
              ( ( ord_less_eq_int @ E @ F )
             => ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_int @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_ord__le__eq__subst) ).

thf(815,plain,
    ! [A: int,B: int,C: int > int,D: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: int,F: int] :
              ( ( ord_less_eq_int @ E @ F )
             => ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_int @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(18,axiom,
    ! [A: finite964658038_int_n,B: finite964658038_int_n] :
      ( ( ( finite566214509_int_n @ A )
        = ( finite566214509_int_n @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_vec__nth__inject) ).

thf(407,plain,
    ! [A: finite964658038_int_n,B: finite964658038_int_n] :
      ( ( ( finite566214509_int_n @ A )
        = ( finite566214509_int_n @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(94,axiom,
    ! [A: int] : ( member_int @ ( ring_1_of_int_int @ A ) @ ring_1_Ints_int ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Ints__of__int) ).

thf(693,plain,
    ! [A: int] : ( member_int @ ( ring_1_of_int_int @ A ) @ ring_1_Ints_int ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(329,axiom,
    ( real_V488409631l_num1
    = ( ^ [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( abs_abs_real @ ( minus_minus_real @ ( finite1106245191l_num1 @ A @ one_one_Numeral_num1 ) @ ( finite1106245191l_num1 @ B @ one_one_Numeral_num1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_dist__real) ).

thf(1423,plain,
    ( real_V488409631l_num1
    = ( ^ [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( abs_abs_real @ ( minus_minus_real @ ( finite1106245191l_num1 @ A @ one_one_Numeral_num1 ) @ ( finite1106245191l_num1 @ B @ one_one_Numeral_num1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(143,axiom,
    ( real_V1974343547l_num1
    = ( ^ [A: finite463740460l_num1,B: finite463740460l_num1] : ( real_V488409631l_num1 @ ( finite1449546019l_num1 @ A @ one_one_Numeral_num1 ) @ ( finite1449546019l_num1 @ B @ one_one_Numeral_num1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_dist__vector__1) ).

thf(879,plain,
    ( real_V1974343547l_num1
    = ( ^ [A: finite463740460l_num1,B: finite463740460l_num1] : ( real_V488409631l_num1 @ ( finite1449546019l_num1 @ A @ one_one_Numeral_num1 ) @ ( finite1449546019l_num1 @ B @ one_one_Numeral_num1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(343,axiom,
    ! [A: int] :
      ( ( ring_1_of_int_real @ ( abs_abs_int @ A ) )
      = ( abs_abs_real @ ( ring_1_of_int_real @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_of__int__abs) ).

thf(1457,plain,
    ! [A: int] :
      ( ( ring_1_of_int_real @ ( abs_abs_int @ A ) )
      = ( abs_abs_real @ ( ring_1_of_int_real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(232,axiom,
    ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_abs__triangle__ineq3) ).

thf(1159,plain,
    ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(252,axiom,
    ! [A: real,B: int] :
      ( ( ord_less_int @ ( archim1371465213g_real @ A ) @ B )
      = ( ord_less_eq_real @ A @ ( minus_minus_real @ ( ring_1_of_int_real @ B ) @ one_one_real ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_ceiling__less__iff) ).

thf(1210,plain,
    ! [A: real,B: int] :
      ( ( ord_less_int @ ( archim1371465213g_real @ A ) @ B )
      = ( ord_less_eq_real @ A @ ( minus_minus_real @ ( ring_1_of_int_real @ B ) @ one_one_real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(205,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ C @ D )
       => ( ord_less_eq_real @ ( minus_minus_real @ A @ D ) @ ( minus_minus_real @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_diff__mono) ).

thf(1079,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ C @ D )
       => ( ord_less_eq_real @ ( minus_minus_real @ A @ D ) @ ( minus_minus_real @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(107,axiom,
    ( real_V845814485l_num1
    = ( ^ [A: finite121157254l_num1,B: finite121157254l_num1] : ( real_V783965509real_n @ ( finite1503577981l_num1 @ A @ one_one_Numeral_num1 ) @ ( finite1503577981l_num1 @ B @ one_one_Numeral_num1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_dist__vector__1) ).

thf(757,plain,
    ( real_V845814485l_num1
    = ( ^ [A: finite121157254l_num1,B: finite121157254l_num1] : ( real_V783965509real_n @ ( finite1503577981l_num1 @ A @ one_one_Numeral_num1 ) @ ( finite1503577981l_num1 @ B @ one_one_Numeral_num1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(246,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( abs_abs_real @ ( real_V783965509real_n @ A @ B ) )
      = ( real_V783965509real_n @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_real__abs__dist) ).

thf(1195,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( abs_abs_real @ ( real_V783965509real_n @ A @ B ) )
      = ( real_V783965509real_n @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(57,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ( ord_less_eq_int @ A @ B )
       => ~ ( ord_less_eq_int @ B @ C ) )
     => ( ( ( ord_less_eq_int @ B @ A )
         => ~ ( ord_less_eq_int @ A @ C ) )
       => ( ( ( ord_less_eq_int @ A @ C )
           => ~ ( ord_less_eq_int @ C @ B ) )
         => ( ( ( ord_less_eq_int @ C @ B )
             => ~ ( ord_less_eq_int @ B @ A ) )
           => ( ( ( ord_less_eq_int @ B @ C )
               => ~ ( ord_less_eq_int @ C @ A ) )
             => ~ ( ( ord_less_eq_int @ C @ A )
                 => ~ ( ord_less_eq_int @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_le__cases3) ).

thf(551,plain,
    ! [A: int,B: int,C: int] :
      ( ( ( ord_less_eq_int @ A @ B )
       => ~ ( ord_less_eq_int @ B @ C ) )
     => ( ( ( ord_less_eq_int @ B @ A )
         => ~ ( ord_less_eq_int @ A @ C ) )
       => ( ( ( ord_less_eq_int @ A @ C )
           => ~ ( ord_less_eq_int @ C @ B ) )
         => ( ( ( ord_less_eq_int @ C @ B )
             => ~ ( ord_less_eq_int @ B @ A ) )
           => ( ( ( ord_less_eq_int @ B @ C )
               => ~ ( ord_less_eq_int @ C @ A ) )
             => ~ ( ( ord_less_eq_int @ C @ A )
                 => ~ ( ord_less_eq_int @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(132,axiom,
    ! [A: int,B: int,C: int > real,D: real] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: int,F: int] :
              ( ( ord_less_eq_int @ E @ F )
             => ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_ord__le__eq__subst) ).

thf(842,plain,
    ! [A: int,B: int,C: int > real,D: real] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: int,F: int] :
              ( ( ord_less_eq_int @ E @ F )
             => ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(306,axiom,
    ! [A: finite1183840848l_num1,B: real,C: numeral_num1] :
      ( ( ord_less_real @ ( real_V400292255l_num1 @ A ) @ B )
     => ( ord_less_real @ ( abs_abs_real @ ( finite1106245191l_num1 @ A @ C ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_norm__bound__component__lt__cart) ).

thf(1350,plain,
    ! [A: finite1183840848l_num1,B: real,C: numeral_num1] :
      ( ( ord_less_real @ ( real_V400292255l_num1 @ A ) @ B )
     => ( ord_less_real @ ( abs_abs_real @ ( finite1106245191l_num1 @ A @ C ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(261,axiom,
    ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_abs__ge__self) ).

thf(1234,plain,
    ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(72,axiom,
    ! [A: real] :
      ( ( archim1371465213g_real @ ( minus_minus_real @ A @ one_one_real ) )
      = ( minus_minus_int @ ( archim1371465213g_real @ A ) @ one_one_int ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_ceiling__diff__one) ).

thf(615,plain,
    ! [A: real] :
      ( ( archim1371465213g_real @ ( minus_minus_real @ A @ one_one_real ) )
      = ( minus_minus_int @ ( archim1371465213g_real @ A ) @ one_one_int ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(219,axiom,
    ! [A: finite2063899472l_num1,B: finite2063899472l_num1] :
      ( ( ( minkow19073400691_real @ A )
        = ( minkow19073400691_real @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_of__int__vec__eq__iff) ).

thf(1121,plain,
    ! [A: finite2063899472l_num1,B: finite2063899472l_num1] :
      ( ( ( minkow19073400691_real @ A )
        = ( minkow19073400691_real @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(359,axiom,
    ! [A: real,B: int] :
      ( ( ( archim1371465213g_real @ A )
        = B )
      = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ B ) @ one_one_real ) @ A )
        & ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_ceiling__eq__iff) ).

thf(1498,plain,
    ! [A: real,B: int] :
      ( ( ( archim1371465213g_real @ A )
        = B )
      = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ B ) @ one_one_real ) @ A )
        & ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(330,axiom,
    ! [A: real,B: real,C: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V1934908667t_real @ A @ B ) @ ( real_V1934908667t_real @ B @ C ) ) ) @ ( real_V1934908667t_real @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_abs__dist__diff__le) ).

thf(1425,plain,
    ! [A: real,B: real,C: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V1934908667t_real @ A @ B ) @ ( real_V1934908667t_real @ B @ C ) ) ) @ ( real_V1934908667t_real @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(211,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: numeral_num1] :
      ( ( finite1106245191l_num1 @ ( minus_249161513l_num1 @ A @ B ) @ C )
      = ( minus_minus_real @ ( finite1106245191l_num1 @ A @ C ) @ ( finite1106245191l_num1 @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_vector__minus__component) ).

thf(1096,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: numeral_num1] :
      ( ( finite1106245191l_num1 @ ( minus_249161513l_num1 @ A @ B ) @ C )
      = ( minus_minus_real @ ( finite1106245191l_num1 @ A @ C ) @ ( finite1106245191l_num1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(11,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1] :
      ( ( ord_le1724070576l_num1 @ A @ B )
     => ( ord_le1724070576l_num1 @ ( minus_249161513l_num1 @ C @ B ) @ ( minus_249161513l_num1 @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_diff__left__mono) ).

thf(388,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1] :
      ( ( ord_le1724070576l_num1 @ A @ B )
     => ( ord_le1724070576l_num1 @ ( minus_249161513l_num1 @ C @ B ) @ ( minus_249161513l_num1 @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(226,axiom,
    ! [A: int,B: int > int,C: int,D: int] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_int @ C @ D )
       => ( ! [E: int,F: int] :
              ( ( ord_less_eq_int @ E @ F )
             => ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_int @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_ord__eq__le__subst) ).

thf(1138,plain,
    ! [A: int,B: int > int,C: int,D: int] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_int @ C @ D )
       => ( ! [E: int,F: int] :
              ( ( ord_less_eq_int @ E @ F )
             => ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_int @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(115,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ A )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_dual__order_Oantisym) ).

thf(783,plain,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ A )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(47,axiom,
    ( ( archim1371465213g_real @ one_one_real )
    = one_one_int ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_ceiling__one) ).

thf(499,plain,
    ( ( archim1371465213g_real @ one_one_real )
    = one_one_int ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(276,axiom,
    ! [A: n > real > $o] :
      ( ( ! [B: n] :
          ? [C: real] : ( A @ B @ C ) )
      = ( ? [B: finite1489363574real_n] :
          ! [C: n] : ( A @ C @ ( finite772340589real_n @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_lambda__skolem) ).

thf(1270,plain,
    ! [A: n > real > $o] :
      ( ( ! [B: n] :
          ? [C: real] : ( A @ B @ C ) )
      = ( ? [B: finite1489363574real_n] :
          ! [C: n] : ( A @ C @ ( finite772340589real_n @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(272,axiom,
    ! [A: int] :
      ( ( abs_abs_int @ ( abs_abs_int @ A ) )
      = ( abs_abs_int @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_abs__idempotent) ).

thf(1259,plain,
    ! [A: int] :
      ( ( abs_abs_int @ ( abs_abs_int @ A ) )
      = ( abs_abs_int @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(145,axiom,
    ! [A: real > real > $o,B: real,C: real] :
      ( ! [D: real,E: real] :
          ( ( ord_less_eq_real @ D @ E )
         => ( A @ D @ E ) )
     => ( ! [D: real,E: real] :
            ( ( A @ E @ D )
           => ( A @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_linorder__wlog) ).

thf(884,plain,
    ! [A: real > real > $o,B: real,C: real] :
      ( ! [D: real,E: real] :
          ( ( ord_less_eq_real @ D @ E )
         => ( A @ D @ E ) )
     => ( ! [D: real,E: real] :
            ( ( A @ E @ D )
           => ( A @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(105,axiom,
    ( ( '?' @ numeral_num1 )
    = ( ^ [A: numeral_num1 > $o] : ( A @ one_one_Numeral_num1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_ex__1) ).

thf(753,plain,
    ( ( '?' @ numeral_num1 )
    = ( ^ [A: numeral_num1 > $o] : ( A @ one_one_Numeral_num1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(85,axiom,
    ! [A: real] :
      ( ( ord_less_eq_int @ one_one_int @ ( archim1031974863r_real @ A ) )
      = ( ord_less_eq_real @ one_one_real @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_one__le__floor) ).

thf(669,plain,
    ! [A: real] :
      ( ( ord_less_eq_int @ one_one_int @ ( archim1031974863r_real @ A ) )
      = ( ord_less_eq_real @ one_one_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(39,axiom,
    ! [A: int] :
      ( ( member_int @ A @ ring_1_Ints_int )
     => ~ ! [B: int] :
            ( A
           != ( ring_1_of_int_int @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Ints__cases) ).

thf(476,plain,
    ! [A: int] :
      ( ( member_int @ A @ ring_1_Ints_int )
     => ~ ! [B: int] :
            ( A
           != ( ring_1_of_int_int @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(79,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ B @ A )
        = ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_antisym__conv) ).

thf(642,plain,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ B @ A )
        = ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(326,axiom,
    ! [A: int] :
      ( ( abs_abs_int @ ( abs_abs_int @ A ) )
      = ( abs_abs_int @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_abs__abs) ).

thf(1414,plain,
    ! [A: int] :
      ( ( abs_abs_int @ ( abs_abs_int @ A ) )
      = ( abs_abs_int @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(43,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ord_less_real @ A @ B )
     => ( ( ord_less_real @ C @ D )
       => ( ord_less_real @ ( minus_minus_real @ A @ D ) @ ( minus_minus_real @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_diff__strict__mono) ).

thf(489,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ord_less_real @ A @ B )
     => ( ( ord_less_real @ C @ D )
       => ( ord_less_real @ ( minus_minus_real @ A @ D ) @ ( minus_minus_real @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(172,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_real @ ( minus_minus_real @ C @ B ) @ ( minus_minus_real @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_diff__strict__left__mono) ).

thf(970,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_real @ ( minus_minus_real @ C @ B ) @ ( minus_minus_real @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(190,axiom,
    ! [A: int,B: int,C: int] :
      ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
      = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_diff__right__commute) ).

thf(1028,plain,
    ! [A: int,B: int,C: int] :
      ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
      = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(206,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( if_Fin127821360real_n @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_T) ).

thf(1082,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( if_Fin127821360real_n @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(185,axiom,
    ! [A: numeral_num1,B: int] :
      ( ( finite1800583751l_num1 @ ( finite627713486m1_int @ A @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_axis__nth) ).

thf(1016,plain,
    ! [A: numeral_num1,B: int] :
      ( ( finite1800583751l_num1 @ ( finite627713486m1_int @ A @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(251,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ A @ B ) )
      = ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_abs__minus__commute) ).

thf(1207,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ A @ B ) )
      = ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(212,axiom,
    ord_less_eq_real @ one_one_real @ one_one_real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_le__numeral__extra_I4_J) ).

thf(1099,plain,
    ord_less_eq_real @ one_one_real @ one_one_real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(351,axiom,
    ! [A: real,B: real] :
      ( ( finite667548811real_n @ ( minus_minus_real @ A @ B ) )
      = ( minus_1037315151real_n @ ( finite667548811real_n @ A ) @ ( finite667548811real_n @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_vec__sub) ).

thf(1478,plain,
    ! [A: real,B: real] :
      ( ( finite667548811real_n @ ( minus_minus_real @ A @ B ) )
      = ( minus_1037315151real_n @ ( finite667548811real_n @ A ) @ ( finite667548811real_n @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(260,axiom,
    ! [A: real,B: real > $o] :
      ( ( member_real @ A @ ring_1_Ints_real )
     => ( ! [C: int] : ( B @ ( ring_1_of_int_real @ C ) )
       => ( B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_Ints__induct) ).

thf(1231,plain,
    ! [A: real,B: real > $o] :
      ( ( member_real @ A @ ring_1_Ints_real )
     => ( ! [C: int] : ( B @ ( ring_1_of_int_real @ C ) )
       => ( B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(223,axiom,
    ! [A: real] :
      ( ( archim1031974863r_real @ ( minus_minus_real @ A @ one_one_real ) )
      = ( minus_minus_int @ ( archim1031974863r_real @ A ) @ one_one_int ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_floor__diff__one) ).

thf(1131,plain,
    ! [A: real] :
      ( ( archim1031974863r_real @ ( minus_minus_real @ A @ one_one_real ) )
      = ( minus_minus_int @ ( archim1031974863r_real @ A ) @ one_one_int ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(245,axiom,
    ! [A: real,B: real,C: finite1489363574real_n] :
      ( ( finite2053577756real_n @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_1037315151real_n @ ( finite2053577756real_n @ A @ C ) @ ( finite2053577756real_n @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_vector__sub__rdistrib) ).

thf(1192,plain,
    ! [A: real,B: real,C: finite1489363574real_n] :
      ( ( finite2053577756real_n @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_1037315151real_n @ ( finite2053577756real_n @ A @ C ) @ ( finite2053577756real_n @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(200,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_antisym) ).

thf(1060,plain,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(332,axiom,
    ! [A: int,B: real] :
      ( ( ord_less_eq_int @ A @ ( archim1031974863r_real @ B ) )
      = ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_le__floor__iff) ).

thf(1429,plain,
    ! [A: int,B: real] :
      ( ( ord_less_eq_int @ A @ ( archim1031974863r_real @ B ) )
      = ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(75,axiom,
    ! [A: real] : ( ord_less_eq_real @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_dual__order_Orefl) ).

thf(622,plain,
    ! [A: real] : ( ord_less_eq_real @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(130,axiom,
    ( ( (=) @ real )
    = ( ^ [A: real,B: real] :
          ( ( ord_less_eq_real @ A @ B )
          & ( ord_less_eq_real @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_order__class_Oorder_Oeq__iff) ).

thf(837,plain,
    ( ( (=) @ real )
    = ( ^ [A: real,B: real] :
          ( ( ord_less_eq_real @ A @ B )
          & ( ord_less_eq_real @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(296,axiom,
    member1352538125real_n @ x @ a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__C1_C_I1_J) ).

thf(1324,plain,
    member1352538125real_n @ x @ a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(13,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1] :
      ( ( ord_le1724070576l_num1 @ A @ B )
     => ( ord_le1724070576l_num1 @ ( minus_249161513l_num1 @ A @ C ) @ ( minus_249161513l_num1 @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_diff__right__mono) ).

thf(393,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1] :
      ( ( ord_le1724070576l_num1 @ A @ B )
     => ( ord_le1724070576l_num1 @ ( minus_249161513l_num1 @ A @ C ) @ ( minus_249161513l_num1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(49,axiom,
    ! [A: finite1183840848l_num1] :
      ( ( finite1329045861l_num1 @ ( finite1106245191l_num1 @ A @ one_one_Numeral_num1 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_vector__one__nth) ).

thf(503,plain,
    ! [A: finite1183840848l_num1] :
      ( ( finite1329045861l_num1 @ ( finite1106245191l_num1 @ A @ one_one_Numeral_num1 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(319,axiom,
    ! [A: real] :
    ? [B: int] : ( ord_less_real @ A @ ( ring_1_of_int_real @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_ex__less__of__int) ).

thf(1393,plain,
    ! [A: real] :
    ? [B: int] : ( ord_less_real @ A @ ( ring_1_of_int_real @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(294,axiom,
    ! [A: int] :
      ( ( ( ring_1_of_int_real @ A )
        = one_one_real )
      = ( A = one_one_int ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_of__int__eq__1__iff) ).

thf(1318,plain,
    ! [A: int] :
      ( ( ( ring_1_of_int_real @ A )
        = one_one_real )
      = ( A = one_one_int ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(161,axiom,
    ! [A: finite1183840848l_num1,B: set_Fi1257234438l_num1,C: finite1183840848l_num1] :
      ( ( member1413569767l_num1 @ A @ B )
     => ( ( member1413569767l_num1 @ C @ B )
       => ( ( A = C )
          = ( ! [D: finite1183840848l_num1] :
                ( ( member1413569767l_num1 @ D @ B )
               => ( ( real_V488409631l_num1 @ A @ D )
                  = ( real_V488409631l_num1 @ C @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_metric__eq__thm) ).

thf(938,plain,
    ! [A: finite1183840848l_num1,B: set_Fi1257234438l_num1,C: finite1183840848l_num1] :
      ( ( member1413569767l_num1 @ A @ B )
     => ( ( member1413569767l_num1 @ C @ B )
       => ( ( A = C )
          = ( ! [D: finite1183840848l_num1] :
                ( ( member1413569767l_num1 @ D @ B )
               => ( ( real_V488409631l_num1 @ A @ D )
                  = ( real_V488409631l_num1 @ C @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(264,axiom,
    ! [A: int] :
      ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ A ) )
      = ( ord_less_eq_int @ one_one_int @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_of__int__1__le__iff) ).

thf(1241,plain,
    ! [A: int] :
      ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ A ) )
      = ( ord_less_eq_int @ one_one_int @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(155,axiom,
    ! [A: finite964658038_int_n,B: finite964658038_int_n,C: n] :
      ( ( finite566214509_int_n @ ( minus_1196255695_int_n @ A @ B ) @ C )
      = ( minus_minus_int @ ( finite566214509_int_n @ A @ C ) @ ( finite566214509_int_n @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_vector__minus__component) ).

thf(921,plain,
    ! [A: finite964658038_int_n,B: finite964658038_int_n,C: n] :
      ( ( finite566214509_int_n @ ( minus_1196255695_int_n @ A @ B ) @ C )
      = ( minus_minus_int @ ( finite566214509_int_n @ A @ C ) @ ( finite566214509_int_n @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(237,axiom,
    ! [A: real] : ( ord_less_eq_real @ ( minus_minus_real @ A @ one_one_real ) @ ( ring_1_of_int_real @ ( archim1031974863r_real @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_real__of__int__floor__ge__diff__one) ).

thf(1170,plain,
    ! [A: real] : ( ord_less_eq_real @ ( minus_minus_real @ A @ one_one_real ) @ ( ring_1_of_int_real @ ( archim1031974863r_real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(202,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( abs_ab948591917l_num1 @ ( minus_249161513l_num1 @ A @ B ) )
      = ( abs_ab948591917l_num1 @ ( minus_249161513l_num1 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_abs__minus__commute) ).

thf(1071,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( abs_ab948591917l_num1 @ ( minus_249161513l_num1 @ A @ B ) )
      = ( abs_ab948591917l_num1 @ ( minus_249161513l_num1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(189,axiom,
    ! [A: int,B: int] :
      ( ~ ( ord_less_eq_int @ A @ B )
     => ( ord_less_eq_int @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_le__cases) ).

thf(1026,plain,
    ! [A: int,B: int] :
      ( ~ ( ord_less_eq_int @ A @ B )
     => ( ord_less_eq_int @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(102,axiom,
    ! [A: real,B: real,C: real > $o] :
      ( ( ord_less_real @ A @ B )
     => ( ( C @ A )
       => ( ~ ( C @ B )
         => ? [D: real] :
              ( ( ord_less_eq_real @ A @ D )
              & ( ord_less_eq_real @ D @ B )
              & ! [E: real] :
                  ( ( ( ord_less_eq_real @ A @ E )
                    & ( ord_less_real @ E @ D ) )
                 => ( C @ E ) )
              & ! [E: real] :
                  ( ! [F: real] :
                      ( ( ( ord_less_eq_real @ A @ F )
                        & ( ord_less_real @ F @ E ) )
                     => ( C @ F ) )
                 => ( ord_less_eq_real @ E @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_complete__interval) ).

thf(718,plain,
    ! [A: real,B: real,C: real > $o] :
      ( ( ord_less_real @ A @ B )
     => ( ( C @ A )
       => ( ~ ( C @ B )
         => ? [D: real] :
              ( ( ord_less_eq_real @ A @ D )
              & ( ord_less_eq_real @ D @ B )
              & ! [E: real] :
                  ( ( ( ord_less_eq_real @ A @ E )
                    & ( ord_less_real @ E @ D ) )
                 => ( C @ E ) )
              & ! [E: real] :
                  ( ! [F: real] :
                      ( ( ( ord_less_eq_real @ A @ F )
                        & ( ord_less_real @ F @ E ) )
                     => ( C @ F ) )
                 => ( ord_less_eq_real @ E @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(112,axiom,
    ! [A: finite1183840848l_num1,B: numeral_num1] : ( ord_less_eq_real @ ( real_V646646907m_real @ ( finite1106245191l_num1 @ A @ B ) ) @ ( real_V400292255l_num1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_Finite__Cartesian__Product_Onorm__nth__le) ).

thf(773,plain,
    ! [A: finite1183840848l_num1,B: numeral_num1] : ( ord_less_eq_real @ ( real_V646646907m_real @ ( finite1106245191l_num1 @ A @ B ) ) @ ( real_V400292255l_num1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(119,axiom,
    ( ( (=) @ finite964658038_int_n )
    = ( ^ [A: finite964658038_int_n,B: finite964658038_int_n] :
        ! [C: n] :
          ( ( finite566214509_int_n @ A @ C )
          = ( finite566214509_int_n @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_vec__eq__iff) ).

thf(794,plain,
    ( ( (=) @ finite964658038_int_n )
    = ( ^ [A: finite964658038_int_n,B: finite964658038_int_n] :
        ! [C: n] :
          ( ( finite566214509_int_n @ A @ C )
          = ( finite566214509_int_n @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(152,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1,D: finite1183840848l_num1] :
      ( ( ( minus_249161513l_num1 @ A @ B )
        = ( minus_249161513l_num1 @ C @ D ) )
     => ( ( A = B )
        = ( C = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_diff__eq__diff__eq) ).

thf(906,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1,D: finite1183840848l_num1] :
      ( ( ( minus_249161513l_num1 @ A @ B )
        = ( minus_249161513l_num1 @ C @ D ) )
     => ( ( A = B )
        = ( C = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(279,axiom,
    ! [A: real] :
      ( ( member_real @ A @ ring_1_Ints_real )
     => ~ ! [B: int] :
            ( A
           != ( ring_1_of_int_real @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Ints__cases) ).

thf(1278,plain,
    ! [A: real] :
      ( ( member_real @ A @ ring_1_Ints_real )
     => ~ ! [B: int] :
            ( A
           != ( ring_1_of_int_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(227,axiom,
    ! [A: real,B: numeral_num1] :
      ( ( finite1106245191l_num1 @ ( finite1329045861l_num1 @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_vec__component) ).

thf(1146,plain,
    ! [A: real,B: numeral_num1] :
      ( ( finite1106245191l_num1 @ ( finite1329045861l_num1 @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(214,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ ( real_V1934908667t_real @ A @ B ) @ C )
     => ( ord_less_real @ ( real_V1934908667t_real @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_dist__commute__lessI) ).

thf(1103,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ ( real_V1934908667t_real @ A @ B ) @ C )
     => ( ord_less_real @ ( real_V1934908667t_real @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(277,axiom,
    ! [A: n,B: real] :
      ( ( finite772340589real_n @ ( finite703491444n_real @ A @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_axis__nth) ).

thf(1273,plain,
    ! [A: n,B: real] :
      ( ( finite772340589real_n @ ( finite703491444n_real @ A @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(135,axiom,
    ! [A: finite2063899472l_num1,B: numeral_num1] :
      ( ( finite1800583751l_num1 @ ( minkow2063319845m1_int @ A ) @ B )
      = ( ring_1_of_int_int @ ( finite1800583751l_num1 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_of__int__vec__nth) ).

thf(856,plain,
    ! [A: finite2063899472l_num1,B: numeral_num1] :
      ( ( finite1800583751l_num1 @ ( minkow2063319845m1_int @ A ) @ B )
      = ( ring_1_of_int_int @ ( finite1800583751l_num1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(61,axiom,
    ! [A: finite2063899472l_num1,B: numeral_num1] :
      ( ( finite1503577981l_num1 @ ( minkow781993583real_n @ A ) @ B )
      = ( ring_11737179077real_n @ ( finite1800583751l_num1 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_of__int__vec__nth) ).

thf(573,plain,
    ! [A: finite2063899472l_num1,B: numeral_num1] :
      ( ( finite1503577981l_num1 @ ( minkow781993583real_n @ A ) @ B )
      = ( ring_11737179077real_n @ ( finite1800583751l_num1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(104,axiom,
    ! [A: finite2063899472l_num1,B: finite2063899472l_num1] :
      ( ( ( finite1800583751l_num1 @ A )
        = ( finite1800583751l_num1 @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_vec__nth__inject) ).

thf(750,plain,
    ! [A: finite2063899472l_num1,B: finite2063899472l_num1] :
      ( ( ( finite1800583751l_num1 @ A )
        = ( finite1800583751l_num1 @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(364,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) )
      = ( ord_less_int @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_of__int__less__iff) ).

thf(1510,plain,
    ! [A: int,B: int] :
      ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) )
      = ( ord_less_int @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(269,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] : ( ord_le866583254real_n @ ( minus_1037315151real_n @ ( abs_ab1599551059real_n @ A ) @ ( abs_ab1599551059real_n @ B ) ) @ ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_abs__triangle__ineq2__sym) ).

thf(1251,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] : ( ord_le866583254real_n @ ( minus_1037315151real_n @ ( abs_ab1599551059real_n @ A ) @ ( abs_ab1599551059real_n @ B ) ) @ ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(73,axiom,
    ( ord_le1908593622_int_n
    = ( ^ [A: finite964658038_int_n,B: finite964658038_int_n] :
        ! [C: n] : ( ord_less_eq_int @ ( finite566214509_int_n @ A @ C ) @ ( finite566214509_int_n @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_less__eq__vec__def) ).

thf(618,plain,
    ( ord_le1908593622_int_n
    = ( ^ [A: finite964658038_int_n,B: finite964658038_int_n] :
        ! [C: n] : ( ord_less_eq_int @ ( finite566214509_int_n @ A @ C ) @ ( finite566214509_int_n @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(16,axiom,
    ! [A: finite2063899472l_num1,B: finite2063899472l_num1] :
      ( ( if_Fin1570437642l_num1 @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Finite____Cartesian____Product__Ovec_It__Int__Oint_Mt__Numeral____Type__Onum1_J_T) ).

thf(402,plain,
    ! [A: finite2063899472l_num1,B: finite2063899472l_num1] :
      ( ( if_Fin1570437642l_num1 @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(317,axiom,
    ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_abs__ge__self) ).

thf(1388,plain,
    ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(63,axiom,
    ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V646646907m_real @ A ) @ ( real_V646646907m_real @ B ) ) @ ( real_V646646907m_real @ ( minus_minus_real @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_norm__triangle__ineq2) ).

thf(579,plain,
    ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V646646907m_real @ A ) @ ( real_V646646907m_real @ B ) ) @ ( real_V646646907m_real @ ( minus_minus_real @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(322,axiom,
    ! [A: real,B: int] :
      ( ( ord_less_int @ ( archim1031974863r_real @ A ) @ B )
      = ( ord_less_real @ A @ ( ring_1_of_int_real @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_floor__less__iff) ).

thf(1403,plain,
    ! [A: real,B: int] :
      ( ( ord_less_int @ ( archim1031974863r_real @ A ) @ B )
      = ( ord_less_real @ A @ ( ring_1_of_int_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(220,axiom,
    ( real_V488409631l_num1
    = ( ^ [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( real_V488409631l_num1 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_dist__commute) ).

thf(1124,plain,
    ( real_V488409631l_num1
    = ( ^ [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( real_V488409631l_num1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(271,axiom,
    ! [A: real,B: finite1489363574real_n,C: finite1489363574real_n] :
      ( ( finite2053577756real_n @ A @ ( minus_1037315151real_n @ B @ C ) )
      = ( minus_1037315151real_n @ ( finite2053577756real_n @ A @ B ) @ ( finite2053577756real_n @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_vec_Oscale__right__diff__distrib) ).

thf(1256,plain,
    ! [A: real,B: finite1489363574real_n,C: finite1489363574real_n] :
      ( ( finite2053577756real_n @ A @ ( minus_1037315151real_n @ B @ C ) )
      = ( minus_1037315151real_n @ ( finite2053577756real_n @ A @ B ) @ ( finite2053577756real_n @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(20,axiom,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ( minus_minus_int @ A @ B )
        = ( minus_minus_int @ C @ D ) )
     => ( ( A = B )
        = ( C = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_diff__eq__diff__eq) ).

thf(413,plain,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ( minus_minus_int @ A @ B )
        = ( minus_minus_int @ C @ D ) )
     => ( ( A = B )
        = ( C = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(65,axiom,
    ! [A: int,B: int,C: int > $o] :
      ( ( ord_less_int @ A @ B )
     => ( ( C @ ( minus_minus_int @ B @ one_one_int ) )
       => ( ! [D: int] :
              ( ( ord_less_int @ D @ B )
             => ( ( C @ D )
               => ( C @ ( minus_minus_int @ D @ one_one_int ) ) ) )
         => ( C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_int__less__induct) ).

thf(584,plain,
    ! [A: int,B: int,C: int > $o] :
      ( ( ord_less_int @ A @ B )
     => ( ( C @ ( minus_minus_int @ B @ one_one_int ) )
       => ( ! [D: int] :
              ( ( ord_less_int @ D @ B )
             => ( ( C @ D )
               => ( C @ ( minus_minus_int @ D @ one_one_int ) ) ) )
         => ( C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(230,axiom,
    real_V646646907m_real = abs_abs_real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_real__norm__def) ).

thf(1154,plain,
    real_V646646907m_real = abs_abs_real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(127,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ B )
      | ( ord_less_eq_int @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_linear) ).

thf(826,plain,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ B )
      | ( ord_less_eq_int @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(99,axiom,
    ( ord_less_eq_real
    = ( ^ [A: real,B: real] :
          ( ( ord_less_real @ A @ B )
          | ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_less__eq__real__def) ).

thf(711,plain,
    ( ord_less_eq_real
    = ( ^ [A: real,B: real] :
          ( ( ord_less_real @ A @ B )
          | ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(78,axiom,
    member1352538125real_n @ one_on1253059131real_n @ ring_1723899781real_n,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_Ints__1) ).

thf(641,plain,
    member1352538125real_n @ one_on1253059131real_n @ ring_1723899781real_n,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(12,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( ord_le1724070576l_num1 @ ( minus_249161513l_num1 @ ( abs_ab948591917l_num1 @ A ) @ ( abs_ab948591917l_num1 @ B ) ) @ ( abs_ab948591917l_num1 @ ( minus_249161513l_num1 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_abs__triangle__ineq2__sym) ).

thf(391,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( ord_le1724070576l_num1 @ ( minus_249161513l_num1 @ ( abs_ab948591917l_num1 @ A ) @ ( abs_ab948591917l_num1 @ B ) ) @ ( abs_ab948591917l_num1 @ ( minus_249161513l_num1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(8,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( ord_le1724070576l_num1 @ ( minus_249161513l_num1 @ ( abs_ab948591917l_num1 @ A ) @ ( abs_ab948591917l_num1 @ B ) ) @ ( abs_ab948591917l_num1 @ ( minus_249161513l_num1 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_abs__triangle__ineq2) ).

thf(382,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( ord_le1724070576l_num1 @ ( minus_249161513l_num1 @ ( abs_ab948591917l_num1 @ A ) @ ( abs_ab948591917l_num1 @ B ) ) @ ( abs_ab948591917l_num1 @ ( minus_249161513l_num1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(100,axiom,
    ! [A: finite964658038_int_n,B: n] :
      ( ( finite625646243al_n_n @ ( minkow371489429real_n @ A ) @ B )
      = ( ring_11737179077real_n @ ( finite566214509_int_n @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_of__int__vec__nth) ).

thf(713,plain,
    ! [A: finite964658038_int_n,B: n] :
      ( ( finite625646243al_n_n @ ( minkow371489429real_n @ A ) @ B )
      = ( ring_11737179077real_n @ ( finite566214509_int_n @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(199,axiom,
    ( real_V1934908667t_real
    = ( ^ [A: real,B: real] : ( real_V1934908667t_real @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_dist__commute) ).

thf(1058,plain,
    ( real_V1934908667t_real
    = ( ^ [A: real,B: real] : ( real_V1934908667t_real @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(263,axiom,
    ( ( abs_abs_int @ one_one_int )
    = one_one_int ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_abs__1) ).

thf(1239,plain,
    ( ( abs_abs_int @ one_one_int )
    = one_one_int ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(299,axiom,
    ! [A: finite1183840848l_num1] :
      ( ( abs_abs_real @ ( real_V400292255l_num1 @ A ) )
      = ( real_V400292255l_num1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_abs__norm__cancel) ).

thf(1332,plain,
    ! [A: finite1183840848l_num1] :
      ( ( abs_abs_real @ ( real_V400292255l_num1 @ A ) )
      = ( real_V400292255l_num1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(36,axiom,
    ! [A: int,B: int] :
      ( ( ring_1154201247l_num1 @ ( minus_minus_int @ A @ B ) )
      = ( minus_249161513l_num1 @ ( ring_1154201247l_num1 @ A ) @ ( ring_1154201247l_num1 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_of__int__diff) ).

thf(466,plain,
    ! [A: int,B: int] :
      ( ( ring_1154201247l_num1 @ ( minus_minus_int @ A @ B ) )
      = ( minus_249161513l_num1 @ ( ring_1154201247l_num1 @ A ) @ ( ring_1154201247l_num1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(164,axiom,
    ( ( (=) @ int )
    = ( ^ [A: int,B: int] :
          ( ( ord_less_eq_int @ A @ B )
          & ( ord_less_eq_int @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_order__class_Oorder_Oeq__iff) ).

thf(947,plain,
    ( ( (=) @ int )
    = ( ^ [A: int,B: int] :
          ( ( ord_less_eq_int @ A @ B )
          & ( ord_less_eq_int @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(308,axiom,
    ! [A: int] :
      ( ( archim1031974863r_real @ ( ring_1_of_int_real @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_floor__of__int) ).

thf(1356,plain,
    ! [A: int] :
      ( ( archim1031974863r_real @ ( ring_1_of_int_real @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(53,axiom,
    ! [A: real,B: finite1183840848l_num1,C: finite1183840848l_num1] :
      ( ( finite1961675766l_num1 @ A @ ( minus_249161513l_num1 @ B @ C ) )
      = ( minus_249161513l_num1 @ ( finite1961675766l_num1 @ A @ B ) @ ( finite1961675766l_num1 @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_vec_Oscale__right__diff__distrib) ).

thf(540,plain,
    ! [A: real,B: finite1183840848l_num1,C: finite1183840848l_num1] :
      ( ( finite1961675766l_num1 @ A @ ( minus_249161513l_num1 @ B @ C ) )
      = ( minus_249161513l_num1 @ ( finite1961675766l_num1 @ A @ B ) @ ( finite1961675766l_num1 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(86,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1] :
      ( ( ord_le2035778724l_num1 @ A @ B )
     => ( ord_le2035778724l_num1 @ ( minus_249161513l_num1 @ A @ C ) @ ( minus_249161513l_num1 @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_diff__strict__right__mono) ).

thf(672,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1] :
      ( ( ord_le2035778724l_num1 @ A @ B )
     => ( ord_le2035778724l_num1 @ ( minus_249161513l_num1 @ A @ C ) @ ( minus_249161513l_num1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(150,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n > $o] :
      ( ( member1352538125real_n @ A @ ring_1723899781real_n )
     => ( ! [C: int] : ( B @ ( ring_11737179077real_n @ C ) )
       => ( B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Ints__induct) ).

thf(900,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n > $o] :
      ( ( member1352538125real_n @ A @ ring_1723899781real_n )
     => ( ! [C: int] : ( B @ ( ring_11737179077real_n @ C ) )
       => ( B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(280,axiom,
    ! [A: real] : ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ ( archim1371465213g_real @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_le__of__int__ceiling) ).

thf(1282,plain,
    ! [A: real] : ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ ( archim1371465213g_real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(22,axiom,
    ( ( (=) @ finite1183840848l_num1 )
    = ( ^ [A: finite1183840848l_num1,B: finite1183840848l_num1] :
        ! [C: numeral_num1] :
          ( ( finite1106245191l_num1 @ A @ C )
          = ( finite1106245191l_num1 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_vec__eq__iff) ).

thf(419,plain,
    ( ( (=) @ finite1183840848l_num1 )
    = ( ^ [A: finite1183840848l_num1,B: finite1183840848l_num1] :
        ! [C: numeral_num1] :
          ( ( finite1106245191l_num1 @ A @ C )
          = ( finite1106245191l_num1 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(356,axiom,
    ! [A: finite1489363574real_n,B: n] : ( ord_less_eq_real @ ( real_V646646907m_real @ ( finite772340589real_n @ A @ B ) ) @ ( real_V739724485real_n @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_Finite__Cartesian__Product_Onorm__nth__le) ).

thf(1492,plain,
    ! [A: finite1489363574real_n,B: n] : ( ord_less_eq_real @ ( real_V646646907m_real @ ( finite772340589real_n @ A @ B ) ) @ ( real_V739724485real_n @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(59,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( real_V400292255l_num1 @ ( minus_249161513l_num1 @ A @ B ) )
      = ( real_V400292255l_num1 @ ( minus_249161513l_num1 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_norm__minus__commute) ).

thf(567,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( real_V400292255l_num1 @ ( minus_249161513l_num1 @ A @ B ) )
      = ( real_V400292255l_num1 @ ( minus_249161513l_num1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(51,axiom,
    ! [A: int,B: int,C: int > $o] :
      ( ( ord_less_int @ A @ B )
     => ( ( C @ A )
       => ( ~ ( C @ B )
         => ? [D: int] :
              ( ( ord_less_eq_int @ A @ D )
              & ( ord_less_eq_int @ D @ B )
              & ! [E: int] :
                  ( ( ( ord_less_eq_int @ A @ E )
                    & ( ord_less_int @ E @ D ) )
                 => ( C @ E ) )
              & ! [E: int] :
                  ( ! [F: int] :
                      ( ( ( ord_less_eq_int @ A @ F )
                        & ( ord_less_int @ F @ E ) )
                     => ( C @ F ) )
                 => ( ord_less_eq_int @ E @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_complete__interval) ).

thf(509,plain,
    ! [A: int,B: int,C: int > $o] :
      ( ( ord_less_int @ A @ B )
     => ( ( C @ A )
       => ( ~ ( C @ B )
         => ? [D: int] :
              ( ( ord_less_eq_int @ A @ D )
              & ( ord_less_eq_int @ D @ B )
              & ! [E: int] :
                  ( ( ( ord_less_eq_int @ A @ E )
                    & ( ord_less_int @ E @ D ) )
                 => ( C @ E ) )
              & ! [E: int] :
                  ( ! [F: int] :
                      ( ( ( ord_less_eq_int @ A @ F )
                        & ( ord_less_int @ F @ E ) )
                     => ( C @ F ) )
                 => ( ord_less_eq_int @ E @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(336,axiom,
    ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V646646907m_real @ A ) @ ( real_V646646907m_real @ B ) ) ) @ ( real_V646646907m_real @ ( minus_minus_real @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_norm__triangle__ineq3) ).

thf(1439,plain,
    ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V646646907m_real @ A ) @ ( real_V646646907m_real @ B ) ) ) @ ( real_V646646907m_real @ ( minus_minus_real @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(146,axiom,
    ! [A: real] : ( ord_less_eq_real @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_order__refl) ).

thf(890,plain,
    ! [A: real] : ( ord_less_eq_real @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(10,axiom,
    ! [A: $o] :
      ( ( A = $true )
      | ( A = $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mt__Numeral____Type__Onum1_J_T) ).

thf(387,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(45,axiom,
    ( ( archim1031974863r_real @ one_one_real )
    = one_one_int ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_floor__one) ).

thf(494,plain,
    ( ( archim1031974863r_real @ one_one_real )
    = one_one_int ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(70,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_antisym) ).

thf(609,plain,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(121,axiom,
    ( ( real_V646646907m_real @ one_one_real )
    = one_one_real ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_norm__one) ).

thf(799,plain,
    ( ( real_V646646907m_real @ one_one_real )
    = one_one_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(41,axiom,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ( minus_minus_int @ A @ B )
        = ( minus_minus_int @ C @ D ) )
     => ( ( ord_less_eq_int @ A @ B )
        = ( ord_less_eq_int @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_diff__eq__diff__less__eq) ).

thf(483,plain,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ( minus_minus_int @ A @ B )
        = ( minus_minus_int @ C @ D ) )
     => ( ( ord_less_eq_int @ A @ B )
        = ( ord_less_eq_int @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(97,axiom,
    ! [A: real,B: real,C: real > real,D: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_ord__le__eq__subst) ).

thf(700,plain,
    ! [A: real,B: real,C: real > real,D: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(297,axiom,
    ~ ! [A: int] :
        ( ( ring_1_of_int_real @ A )
       != ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_Areal__of__int_Am_A_061_Ax_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(1325,plain,
    ~ ! [A: int] :
        ( ( ring_1_of_int_real @ A )
       != ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(344,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V783965509real_n @ A @ B ) @ ( real_V783965509real_n @ B @ C ) ) ) @ ( real_V783965509real_n @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_abs__dist__diff__le) ).

thf(1460,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V783965509real_n @ A @ B ) @ ( real_V783965509real_n @ B @ C ) ) ) @ ( real_V783965509real_n @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(187,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
      | ( ord_less_eq_real @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_linear) ).

thf(1022,plain,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
      | ( ord_less_eq_real @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(284,axiom,
    ( real_V783965509real_n
    = ( ^ [A: finite1489363574real_n,B: finite1489363574real_n] : ( real_V739724485real_n @ ( minus_1037315151real_n @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_dist__norm) ).

thf(1293,plain,
    ( real_V783965509real_n
    = ( ^ [A: finite1489363574real_n,B: finite1489363574real_n] : ( real_V739724485real_n @ ( minus_1037315151real_n @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(240,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
      ( ( ( minus_1037315151real_n @ A @ B )
        = ( minus_1037315151real_n @ C @ D ) )
     => ( ( ord_le866583254real_n @ A @ B )
        = ( ord_le866583254real_n @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_diff__eq__diff__less__eq) ).

thf(1177,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
      ( ( ( minus_1037315151real_n @ A @ B )
        = ( minus_1037315151real_n @ C @ D ) )
     => ( ( ord_le866583254real_n @ A @ B )
        = ( ord_le866583254real_n @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(218,axiom,
    ! [A: $o,B: finite1183840848l_num1,C: finite1183840848l_num1,D: numeral_num1] :
      ( ( A
       => ( ( finite1106245191l_num1 @ ( if_Fin1668193290l_num1 @ A @ B @ C ) @ D )
          = ( finite1106245191l_num1 @ B @ D ) ) )
      & ( ~ A
       => ( ( finite1106245191l_num1 @ ( if_Fin1668193290l_num1 @ A @ B @ C ) @ D )
          = ( finite1106245191l_num1 @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_cond__component) ).

thf(1112,plain,
    ! [A: $o,B: finite1183840848l_num1,C: finite1183840848l_num1,D: numeral_num1] :
      ( ( A
       => ( ( finite1106245191l_num1 @ ( if_Fin1668193290l_num1 @ A @ B @ C ) @ D )
          = ( finite1106245191l_num1 @ B @ D ) ) )
      & ( ~ A
       => ( ( finite1106245191l_num1 @ ( if_Fin1668193290l_num1 @ A @ B @ C ) @ D )
          = ( finite1106245191l_num1 @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(228,axiom,
    ! [A: numeral_num1] :
      ( ( finite1106245191l_num1 @ one_on1961019669l_num1 @ A )
      = one_one_real ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_one__index) ).

thf(1149,plain,
    ! [A: numeral_num1] :
      ( ( finite1106245191l_num1 @ one_on1961019669l_num1 @ A )
      = one_one_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(170,axiom,
    ! [A: int] :
      ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ A ) )
      = ( ord_less_eq_int @ one_one_int @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_of__int__1__le__iff) ).

thf(964,plain,
    ! [A: int] :
      ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ A ) )
      = ( ord_less_eq_int @ one_one_int @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(34,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_int @ ( archim1031974863r_real @ A ) @ ( archim1031974863r_real @ B ) )
     => ( ord_less_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_floor__less__cancel) ).

thf(462,plain,
    ! [A: real,B: real] :
      ( ( ord_less_int @ ( archim1031974863r_real @ A ) @ ( archim1031974863r_real @ B ) )
     => ( ord_less_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(159,axiom,
    ! [A: real,B: real] :
      ( ( A != B )
     => ( ( ord_less_eq_real @ A @ B )
       => ( ord_less_real @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_order_Onot__eq__order__implies__strict) ).

thf(932,plain,
    ! [A: real,B: real] :
      ( ( A != B )
     => ( ( ord_less_eq_real @ A @ B )
       => ( ord_less_real @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(91,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V400292255l_num1 @ A ) @ ( real_V400292255l_num1 @ B ) ) @ ( real_V400292255l_num1 @ ( minus_249161513l_num1 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_norm__triangle__ineq2) ).

thf(685,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V400292255l_num1 @ A ) @ ( real_V400292255l_num1 @ B ) ) @ ( real_V400292255l_num1 @ ( minus_249161513l_num1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(176,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_diff__right__mono) ).

thf(983,plain,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(247,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V400292255l_num1 @ A ) @ ( real_V400292255l_num1 @ B ) ) ) @ ( real_V400292255l_num1 @ ( minus_249161513l_num1 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_norm__triangle__ineq3) ).

thf(1198,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V400292255l_num1 @ A ) @ ( real_V400292255l_num1 @ B ) ) ) @ ( real_V400292255l_num1 @ ( minus_249161513l_num1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(15,axiom,
    ! [A: finite964658038_int_n,B: finite964658038_int_n] :
      ( ( if_Fin1767949360_int_n @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Finite____Cartesian____Product__Ovec_It__Int__Oint_Mtf__n_J_T) ).

thf(399,plain,
    ! [A: finite964658038_int_n,B: finite964658038_int_n] :
      ( ( if_Fin1767949360_int_n @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(168,axiom,
    ! [A: finite463740460l_num1,B: finite1183840848l_num1] :
      ( ! [C: numeral_num1] : ( ord_less_eq_real @ ( real_V400292255l_num1 @ ( finite1449546019l_num1 @ A @ C ) ) @ ( real_V646646907m_real @ ( finite1106245191l_num1 @ B @ C ) ) )
     => ( ord_less_eq_real @ ( real_V316032763l_num1 @ A ) @ ( real_V400292255l_num1 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_norm__le__componentwise__cart) ).

thf(959,plain,
    ! [A: finite463740460l_num1,B: finite1183840848l_num1] :
      ( ! [C: numeral_num1] : ( ord_less_eq_real @ ( real_V400292255l_num1 @ ( finite1449546019l_num1 @ A @ C ) ) @ ( real_V646646907m_real @ ( finite1106245191l_num1 @ B @ C ) ) )
     => ( ord_less_eq_real @ ( real_V316032763l_num1 @ A ) @ ( real_V400292255l_num1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(253,axiom,
    ! [A: real,B: real,C: finite1489363574real_n] :
      ( ( finite2053577756real_n @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_1037315151real_n @ ( finite2053577756real_n @ A @ C ) @ ( finite2053577756real_n @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_vec_Oscale__left__diff__distrib) ).

thf(1213,plain,
    ! [A: real,B: real,C: finite1489363574real_n] :
      ( ( finite2053577756real_n @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_1037315151real_n @ ( finite2053577756real_n @ A @ C ) @ ( finite2053577756real_n @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(139,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ A )
        = ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_antisym__conv) ).

thf(868,plain,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ A )
        = ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(114,axiom,
    ! [A: int,B: int] :
      ( ( member_int @ A @ ring_1_Ints_int )
     => ( ( member_int @ B @ ring_1_Ints_int )
       => ( member_int @ ( minus_minus_int @ A @ B ) @ ring_1_Ints_int ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Ints__diff) ).

thf(780,plain,
    ! [A: int,B: int] :
      ( ( member_int @ A @ ring_1_Ints_int )
     => ( ( member_int @ B @ ring_1_Ints_int )
       => ( member_int @ ( minus_minus_int @ A @ B ) @ ring_1_Ints_int ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(32,axiom,
    ! [A: real,B: real] :
      ( ( A = B )
     => ( ord_less_eq_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_eq__refl) ).

thf(455,plain,
    ! [A: real,B: real] :
      ( ( A = B )
     => ( ord_less_eq_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(177,axiom,
    ! [A: int > int > $o,B: int,C: int] :
      ( ! [D: int,E: int] :
          ( ( ord_less_eq_int @ D @ E )
         => ( A @ D @ E ) )
     => ( ! [D: int,E: int] :
            ( ( A @ E @ D )
           => ( A @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_linorder__wlog) ).

thf(986,plain,
    ! [A: int > int > $o,B: int,C: int] :
      ( ! [D: int,E: int] :
          ( ( ord_less_eq_int @ D @ E )
         => ( A @ D @ E ) )
     => ( ! [D: int,E: int] :
            ( ( A @ E @ D )
           => ( A @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(268,axiom,
    member1352538125real_n @ y @ a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__C1_C_I2_J) ).

thf(1250,plain,
    member1352538125real_n @ y @ a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(358,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
     => ( ord_less_eq_int @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_abs__le__D1) ).

thf(1496,plain,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
     => ( ord_less_eq_int @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(196,axiom,
    ! [A: set_real] :
      ( ? [B: real] : ( member_real @ B @ A )
     => ( ? [B: real] :
          ! [C: real] :
            ( ( member_real @ C @ A )
           => ( ord_less_eq_real @ C @ B ) )
       => ? [B: real] :
            ( ! [C: real] :
                ( ( member_real @ C @ A )
               => ( ord_less_eq_real @ C @ B ) )
            & ! [C: real] :
                ( ! [D: real] :
                    ( ( member_real @ D @ A )
                   => ( ord_less_eq_real @ D @ C ) )
               => ( ord_less_eq_real @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_complete__real) ).

thf(1044,plain,
    ! [A: set_real] :
      ( ? [B: real] : ( member_real @ B @ A )
     => ( ? [B: real] :
          ! [C: real] :
            ( ( member_real @ C @ A )
           => ( ord_less_eq_real @ C @ B ) )
       => ? [B: real] :
            ( ! [C: real] :
                ( ( member_real @ C @ A )
               => ( ord_less_eq_real @ C @ B ) )
            & ! [C: real] :
                ( ! [D: real] :
                    ( ( member_real @ D @ A )
                   => ( ord_less_eq_real @ D @ C ) )
               => ( ord_less_eq_real @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(95,axiom,
    ! [A: finite964658038_int_n,B: n] :
      ( ( finite566214509_int_n @ ( minkow1468704075_n_int @ A ) @ B )
      = ( ring_1_of_int_int @ ( finite566214509_int_n @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_of__int__vec__nth) ).

thf(695,plain,
    ! [A: finite964658038_int_n,B: n] :
      ( ( finite566214509_int_n @ ( minkow1468704075_n_int @ A ) @ B )
      = ( ring_1_of_int_int @ ( finite566214509_int_n @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(181,axiom,
    ! [A: real,B: real] :
      ( ( finite1329045861l_num1 @ ( minus_minus_real @ A @ B ) )
      = ( minus_249161513l_num1 @ ( finite1329045861l_num1 @ A ) @ ( finite1329045861l_num1 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_vec__sub) ).

thf(1000,plain,
    ! [A: real,B: real] :
      ( ( finite1329045861l_num1 @ ( minus_minus_real @ A @ B ) )
      = ( minus_249161513l_num1 @ ( finite1329045861l_num1 @ A ) @ ( finite1329045861l_num1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(334,axiom,
    ! [A: finite337957458num1_n,B: finite1489363574real_n] :
      ( ! [C: n] : ( ord_less_eq_real @ ( real_V400292255l_num1 @ ( finite1639785033num1_n @ A @ C ) ) @ ( real_V646646907m_real @ ( finite772340589real_n @ B @ C ) ) )
     => ( ord_less_eq_real @ ( real_V1121707553num1_n @ A ) @ ( real_V739724485real_n @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_norm__le__componentwise__cart) ).

thf(1435,plain,
    ! [A: finite337957458num1_n,B: finite1489363574real_n] :
      ( ! [C: n] : ( ord_less_eq_real @ ( real_V400292255l_num1 @ ( finite1639785033num1_n @ A @ C ) ) @ ( real_V646646907m_real @ ( finite772340589real_n @ B @ C ) ) )
     => ( ord_less_eq_real @ ( real_V1121707553num1_n @ A ) @ ( real_V739724485real_n @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(87,axiom,
    ! [A: int] :
      ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ one_one_int )
      = ( ord_less_int @ A @ one_one_int ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_of__int__less__1__iff) ).

thf(675,plain,
    ! [A: int] :
      ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ one_one_int )
      = ( ord_less_int @ A @ one_one_int ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(249,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V488409631l_num1 @ A @ B ) @ ( real_V488409631l_num1 @ B @ C ) ) ) @ ( real_V488409631l_num1 @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_abs__dist__diff__le) ).

thf(1203,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V488409631l_num1 @ A @ B ) @ ( real_V488409631l_num1 @ B @ C ) ) ) @ ( real_V488409631l_num1 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(347,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( abs_abs_real @ ( real_V488409631l_num1 @ A @ B ) )
      = ( real_V488409631l_num1 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_real__abs__dist) ).

thf(1467,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( abs_abs_real @ ( real_V488409631l_num1 @ A @ B ) )
      = ( real_V488409631l_num1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(89,axiom,
    ! [A: real] :
      ( ( one_one_real = A )
      = ( A = one_one_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_one__reorient) ).

thf(680,plain,
    ! [A: real] :
      ( ( one_one_real = A )
      = ( A = one_one_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(56,axiom,
    ! [A: real,B: real > $o] :
      ( ( member_real @ A @ ( collect_real @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_mem__Collect__eq) ).

thf(548,plain,
    ! [A: real,B: real > $o] :
      ( ( member_real @ A @ ( collect_real @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(328,axiom,
    ! [A: int,B: real] :
      ( ( ord_less_eq_int @ A @ ( archim1371465213g_real @ B ) )
      = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_le__ceiling__iff) ).

thf(1420,plain,
    ! [A: int,B: real] :
      ( ( ord_less_eq_int @ A @ ( archim1371465213g_real @ B ) )
      = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(157,axiom,
    ~ ( ord_less_real @ one_one_real @ one_one_real ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_less__numeral__extra_I4_J) ).

thf(927,plain,
    ~ ( ord_less_real @ one_one_real @ one_one_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(224,axiom,
    ( real_V400292255l_num1
    = ( ^ [A: finite1183840848l_num1] : ( real_V646646907m_real @ ( finite1106245191l_num1 @ A @ one_one_Numeral_num1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_norm__vector__1) ).

thf(1134,plain,
    ( real_V400292255l_num1
    = ( ^ [A: finite1183840848l_num1] : ( real_V646646907m_real @ ( finite1106245191l_num1 @ A @ one_one_Numeral_num1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(124,axiom,
    ! [A: real,B: real,C: real] :
      ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_diff__right__commute) ).

thf(812,plain,
    ! [A: real,B: real,C: real] :
      ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(302,axiom,
    ( ( (=) @ finite1489363574real_n )
    = ( ^ [A: finite1489363574real_n,B: finite1489363574real_n] :
        ! [C: n] :
          ( ( finite772340589real_n @ A @ C )
          = ( finite772340589real_n @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_vec__eq__iff) ).

thf(1340,plain,
    ( ( (=) @ finite1489363574real_n )
    = ( ^ [A: finite1489363574real_n,B: finite1489363574real_n] :
        ! [C: n] :
          ( ( finite772340589real_n @ A @ C )
          = ( finite772340589real_n @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(126,axiom,
    ! [A: int] :
      ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ one_one_int )
      = ( ord_less_eq_int @ A @ one_one_int ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_of__int__le__1__iff) ).

thf(823,plain,
    ! [A: int] :
      ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ one_one_int )
      = ( ord_less_eq_int @ A @ one_one_int ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(129,axiom,
    member_real @ one_one_real @ ring_1_Ints_real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_Ints__1) ).

thf(836,plain,
    member_real @ one_one_real @ ring_1_Ints_real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(38,axiom,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_int @ C @ D )
       => ( ord_less_int @ ( minus_minus_int @ A @ D ) @ ( minus_minus_int @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_diff__strict__mono) ).

thf(473,plain,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ord_less_int @ A @ B )
     => ( ( ord_less_int @ C @ D )
       => ( ord_less_int @ ( minus_minus_int @ A @ D ) @ ( minus_minus_int @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(204,axiom,
    ! [A: int,B: n] :
      ( ( finite566214509_int_n @ ( finite55766923_int_n @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_vec__component) ).

thf(1076,plain,
    ! [A: int,B: n] :
      ( ( finite566214509_int_n @ ( finite55766923_int_n @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(25,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
      = ( ord_less_int @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_zle__diff1__eq) ).

thf(426,plain,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
      = ( ord_less_int @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(235,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
     => ( ord_less_eq_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_abs__le__D1) ).

thf(1166,plain,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
     => ( ord_less_eq_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(182,axiom,
    member_int @ one_one_int @ ring_1_Ints_int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_Ints__1) ).

thf(1003,plain,
    member_int @ one_one_int @ ring_1_Ints_int,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(93,axiom,
    ! [A: int] :
      ( ( ( ring_11737179077real_n @ A )
        = one_on1253059131real_n )
      = ( A = one_one_int ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_of__int__eq__1__iff) ).

thf(690,plain,
    ! [A: int] :
      ( ( ( ring_11737179077real_n @ A )
        = one_on1253059131real_n )
      = ( A = one_one_int ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(231,axiom,
    ! [A: real,B: int] :
      ( ( archim1371465213g_real @ ( minus_minus_real @ A @ ( ring_1_of_int_real @ B ) ) )
      = ( minus_minus_int @ ( archim1371465213g_real @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_ceiling__diff__of__int) ).

thf(1156,plain,
    ! [A: real,B: int] :
      ( ( archim1371465213g_real @ ( minus_minus_real @ A @ ( ring_1_of_int_real @ B ) ) )
      = ( minus_minus_int @ ( archim1371465213g_real @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(258,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
      ( ( ord_le866583254real_n @ A @ B )
     => ( ( ord_le866583254real_n @ C @ D )
       => ( ord_le866583254real_n @ ( minus_1037315151real_n @ A @ D ) @ ( minus_1037315151real_n @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_diff__mono) ).

thf(1225,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
      ( ( ord_le866583254real_n @ A @ B )
     => ( ( ord_le866583254real_n @ C @ D )
       => ( ord_le866583254real_n @ ( minus_1037315151real_n @ A @ D ) @ ( minus_1037315151real_n @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(312,axiom,
    ! [A: $o,B: finite1489363574real_n,C: finite1489363574real_n,D: n] :
      ( ( A
       => ( ( finite772340589real_n @ ( if_Fin127821360real_n @ A @ B @ C ) @ D )
          = ( finite772340589real_n @ B @ D ) ) )
      & ( ~ A
       => ( ( finite772340589real_n @ ( if_Fin127821360real_n @ A @ B @ C ) @ D )
          = ( finite772340589real_n @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_cond__component) ).

thf(1368,plain,
    ! [A: $o,B: finite1489363574real_n,C: finite1489363574real_n,D: n] :
      ( ( A
       => ( ( finite772340589real_n @ ( if_Fin127821360real_n @ A @ B @ C ) @ D )
          = ( finite772340589real_n @ B @ D ) ) )
      & ( ~ A
       => ( ( finite772340589real_n @ ( if_Fin127821360real_n @ A @ B @ C ) @ D )
          = ( finite772340589real_n @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(275,axiom,
    ! [A: int,B: real] :
      ( ( ord_less_int @ A @ ( archim1371465213g_real @ B ) )
      = ( ord_less_real @ ( ring_1_of_int_real @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_less__ceiling__iff) ).

thf(1267,plain,
    ! [A: int,B: real] :
      ( ( ord_less_int @ A @ ( archim1371465213g_real @ B ) )
      = ( ord_less_real @ ( ring_1_of_int_real @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(353,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( member1352538125real_n @ A @ ring_1723899781real_n )
     => ( ( member1352538125real_n @ B @ ring_1723899781real_n )
       => ( member1352538125real_n @ ( minus_1037315151real_n @ A @ B ) @ ring_1723899781real_n ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Ints__diff) ).

thf(1484,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( member1352538125real_n @ A @ ring_1723899781real_n )
     => ( ( member1352538125real_n @ B @ ring_1723899781real_n )
       => ( member1352538125real_n @ ( minus_1037315151real_n @ A @ B ) @ ring_1723899781real_n ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(197,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n > $o] :
      ( ( member1352538125real_n @ A @ ( collec321817931real_n @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_mem__Collect__eq) ).

thf(1053,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n > $o] :
      ( ( member1352538125real_n @ A @ ( collec321817931real_n @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(333,axiom,
    ! [A: real] :
      ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ A ) )
        = A )
      = ( ? [B: int] :
            ( A
            = ( ring_1_of_int_real @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_of__int__floor__cancel) ).

thf(1432,plain,
    ! [A: real] :
      ( ( ( ring_1_of_int_real @ ( archim1031974863r_real @ A ) )
        = A )
      = ( ? [B: int] :
            ( A
            = ( ring_1_of_int_real @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(243,axiom,
    ! [A: finite1489363574real_n,B: real,C: n] :
      ( ( ord_less_real @ ( real_V739724485real_n @ A ) @ B )
     => ( ord_less_real @ ( abs_abs_real @ ( finite772340589real_n @ A @ C ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_norm__bound__component__lt__cart) ).

thf(1186,plain,
    ! [A: finite1489363574real_n,B: real,C: n] :
      ( ( ord_less_real @ ( real_V739724485real_n @ A ) @ B )
     => ( ord_less_real @ ( abs_abs_real @ ( finite772340589real_n @ A @ C ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(273,axiom,
    ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_abs__triangle__ineq3) ).

thf(1262,plain,
    ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(255,axiom,
    ! [A: finite1489363574real_n,B: n,C: finite1489363574real_n] : ( ord_less_eq_real @ ( real_V1934908667t_real @ ( finite772340589real_n @ A @ B ) @ ( finite772340589real_n @ C @ B ) ) @ ( real_V783965509real_n @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_dist__vec__nth__le) ).

thf(1218,plain,
    ! [A: finite1489363574real_n,B: n,C: finite1489363574real_n] : ( ord_less_eq_real @ ( real_V1934908667t_real @ ( finite772340589real_n @ A @ B ) @ ( finite772340589real_n @ C @ B ) ) @ ( real_V783965509real_n @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(256,axiom,
    ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_abs__triangle__ineq2__sym) ).

thf(1220,plain,
    ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(287,axiom,
    ! [A: int] : ( member_real @ ( ring_1_of_int_real @ A ) @ ring_1_Ints_real ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Ints__of__int) ).

thf(1300,plain,
    ! [A: int] : ( member_real @ ( ring_1_of_int_real @ A ) @ ring_1_Ints_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(341,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
      ( ( ord_le1017090250real_n @ A @ B )
     => ( ( ord_le1017090250real_n @ C @ D )
       => ( ord_le1017090250real_n @ ( minus_1037315151real_n @ A @ D ) @ ( minus_1037315151real_n @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_diff__strict__mono) ).

thf(1452,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
      ( ( ord_le1017090250real_n @ A @ B )
     => ( ( ord_le1017090250real_n @ C @ D )
       => ( ord_le1017090250real_n @ ( minus_1037315151real_n @ A @ D ) @ ( minus_1037315151real_n @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(194,axiom,
    ! [A: finite964658038_int_n,B: finite964658038_int_n] :
      ( ( ( minkow1134813771n_real @ A )
        = ( minkow1134813771n_real @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_of__int__vec__eq__iff) ).

thf(1038,plain,
    ! [A: finite964658038_int_n,B: finite964658038_int_n] :
      ( ( ( minkow1134813771n_real @ A )
        = ( minkow1134813771n_real @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(4,axiom,
    ! [A: finite964658038_int_n,B: finite964658038_int_n] :
      ( ( if_Fin1767949360_int_n @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Finite____Cartesian____Product__Ovec_It__Int__Oint_Mtf__n_J_T) ).

thf(370,plain,
    ! [A: finite964658038_int_n,B: finite964658038_int_n] :
      ( ( if_Fin1767949360_int_n @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(207,axiom,
    ! [A: int,B: int > $o] :
      ( ( member_int @ A @ ring_1_Ints_int )
     => ( ! [C: int] : ( B @ ( ring_1_of_int_int @ C ) )
       => ( B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_Ints__induct) ).

thf(1085,plain,
    ! [A: int,B: int > $o] :
      ( ( member_int @ A @ ring_1_Ints_int )
     => ( ! [C: int] : ( B @ ( ring_1_of_int_int @ C ) )
       => ( B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(62,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1,D: finite1183840848l_num1] :
      ( ( ( minus_249161513l_num1 @ A @ B )
        = ( minus_249161513l_num1 @ C @ D ) )
     => ( ( ord_le2035778724l_num1 @ A @ B )
        = ( ord_le2035778724l_num1 @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_diff__eq__diff__less) ).

thf(576,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: finite1183840848l_num1,D: finite1183840848l_num1] :
      ( ( ( minus_249161513l_num1 @ A @ B )
        = ( minus_249161513l_num1 @ C @ D ) )
     => ( ( ord_le2035778724l_num1 @ A @ B )
        = ( ord_le2035778724l_num1 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(281,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) )
      = ( ord_less_eq_int @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_of__int__le__iff) ).

thf(1284,plain,
    ! [A: int,B: int] :
      ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) )
      = ( ord_less_eq_int @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(331,axiom,
    ( real_V400292255l_num1
    = ( ^ [A: finite1183840848l_num1] : ( abs_abs_real @ ( finite1106245191l_num1 @ A @ one_one_Numeral_num1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_norm__real) ).

thf(1427,plain,
    ( real_V400292255l_num1
    = ( ^ [A: finite1183840848l_num1] : ( abs_abs_real @ ( finite1106245191l_num1 @ A @ one_one_Numeral_num1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(361,axiom,
    ! [A: int] :
      ( ( archim1371465213g_real @ ( ring_1_of_int_real @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_ceiling__of__int) ).

thf(1504,plain,
    ! [A: int] :
      ( ( archim1371465213g_real @ ( ring_1_of_int_real @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(210,axiom,
    ! [A: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim1371465213g_real @ A ) @ ( archim1031974863r_real @ A ) ) @ one_one_int ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_ceiling__diff__floor__le__1) ).

thf(1094,plain,
    ! [A: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim1371465213g_real @ A ) @ ( archim1031974863r_real @ A ) ) @ one_one_int ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(71,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( minus_minus_real @ A @ B )
        = ( minus_minus_real @ C @ D ) )
     => ( ( A = B )
        = ( C = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_diff__eq__diff__eq) ).

thf(612,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( minus_minus_real @ A @ B )
        = ( minus_minus_real @ C @ D ) )
     => ( ( A = B )
        = ( C = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(142,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( member1413569767l_num1 @ A @ ring_11529266783l_num1 )
     => ( ( member1413569767l_num1 @ B @ ring_11529266783l_num1 )
       => ( member1413569767l_num1 @ ( minus_249161513l_num1 @ A @ B ) @ ring_11529266783l_num1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Ints__diff) ).

thf(876,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( member1413569767l_num1 @ A @ ring_11529266783l_num1 )
     => ( ( member1413569767l_num1 @ B @ ring_11529266783l_num1 )
       => ( member1413569767l_num1 @ ( minus_249161513l_num1 @ A @ B ) @ ring_11529266783l_num1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(136,axiom,
    ! [A: numeral_num1 > int > $o] :
      ( ( ! [B: numeral_num1] :
          ? [C: int] : ( A @ B @ C ) )
      = ( ? [B: finite2063899472l_num1] :
          ! [C: numeral_num1] : ( A @ C @ ( finite1800583751l_num1 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_lambda__skolem) ).

thf(859,plain,
    ! [A: numeral_num1 > int > $o] :
      ( ( ! [B: numeral_num1] :
          ? [C: int] : ( A @ B @ C ) )
      = ( ? [B: finite2063899472l_num1] :
          ! [C: numeral_num1] : ( A @ C @ ( finite1800583751l_num1 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(307,axiom,
    ! [A: real,B: int] :
      ( ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ B )
      = ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_ceiling__le__iff) ).

thf(1353,plain,
    ! [A: real,B: int] :
      ( ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ B )
      = ( ord_less_eq_real @ A @ ( ring_1_of_int_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(67,axiom,
    ! [A: int] :
      ( ( ( ring_1_of_int_int @ A )
        = one_one_int )
      = ( A = one_one_int ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_of__int__eq__1__iff) ).

thf(600,plain,
    ! [A: int] :
      ( ( ( ring_1_of_int_int @ A )
        = one_one_int )
      = ( A = one_one_int ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(77,axiom,
    ! [A: int,B: int,C: int > $o] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( C @ B )
       => ( ! [D: int] :
              ( ( ord_less_eq_int @ D @ B )
             => ( ( C @ D )
               => ( C @ ( minus_minus_int @ D @ one_one_int ) ) ) )
         => ( C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_int__le__induct) ).

thf(627,plain,
    ! [A: int,B: int,C: int > $o] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( C @ B )
       => ( ! [D: int] :
              ( ( ord_less_eq_int @ D @ B )
             => ( ( C @ D )
               => ( C @ ( minus_minus_int @ D @ one_one_int ) ) ) )
         => ( C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(31,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_int @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_ord__le__eq__trans) ).

thf(450,plain,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_int @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(241,axiom,
    ! [A: int] :
      ( ( ring_1_of_int_int @ ( abs_abs_int @ A ) )
      = ( abs_abs_int @ ( ring_1_of_int_int @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_of__int__abs) ).

thf(1180,plain,
    ! [A: int] :
      ( ( ring_1_of_int_int @ ( abs_abs_int @ A ) )
      = ( abs_abs_int @ ( ring_1_of_int_int @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(295,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: n] :
      ( ( finite772340589real_n @ ( minus_1037315151real_n @ A @ B ) @ C )
      = ( minus_minus_real @ ( finite772340589real_n @ A @ C ) @ ( finite772340589real_n @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_vector__minus__component) ).

thf(1321,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: n] :
      ( ( finite772340589real_n @ ( minus_1037315151real_n @ A @ B ) @ C )
      = ( minus_minus_real @ ( finite772340589real_n @ A @ C ) @ ( finite772340589real_n @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(64,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) )
      = ( ord_less_eq_int @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_of__int__le__iff) ).

thf(581,plain,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) )
      = ( ord_less_eq_int @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(108,axiom,
    ! [A: n] :
      ( ( finite566214509_int_n @ one_on1516019131_int_n @ A )
      = one_one_int ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_one__index) ).

thf(759,plain,
    ! [A: n] :
      ( ( finite566214509_int_n @ one_on1516019131_int_n @ A )
      = one_one_int ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(254,axiom,
    ! [A: finite1489363574real_n,B: n] : ( ord_less_eq_real @ ( abs_abs_real @ ( finite772340589real_n @ A @ B ) ) @ ( real_V739724485real_n @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_component__le__norm__cart) ).

thf(1216,plain,
    ! [A: finite1489363574real_n,B: n] : ( ord_less_eq_real @ ( abs_abs_real @ ( finite772340589real_n @ A @ B ) ) @ ( real_V739724485real_n @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(221,axiom,
    ! [A: real,B: real] :
      ( ( A != B )
     => ( ~ ( ord_less_real @ A @ B )
       => ( ord_less_real @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_linorder__neqE__linordered__idom) ).

thf(1126,plain,
    ! [A: real,B: real] :
      ( ( A != B )
     => ( ~ ( ord_less_real @ A @ B )
       => ( ord_less_real @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(244,axiom,
    ! [A: real,B: real] :
      ( ( abs_abs_real @ ( real_V1934908667t_real @ A @ B ) )
      = ( real_V1934908667t_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_real__abs__dist) ).

thf(1189,plain,
    ! [A: real,B: real] :
      ( ( abs_abs_real @ ( real_V1934908667t_real @ A @ B ) )
      = ( real_V1934908667t_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(318,axiom,
    ! [A: real,B: finite1489363574real_n,C: finite1489363574real_n] :
      ( ( finite2053577756real_n @ A @ ( minus_1037315151real_n @ B @ C ) )
      = ( minus_1037315151real_n @ ( finite2053577756real_n @ A @ B ) @ ( finite2053577756real_n @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_vector__ssub__ldistrib) ).

thf(1390,plain,
    ! [A: real,B: finite1489363574real_n,C: finite1489363574real_n] :
      ( ( finite2053577756real_n @ A @ ( minus_1037315151real_n @ B @ C ) )
      = ( minus_1037315151real_n @ ( finite2053577756real_n @ A @ B ) @ ( finite2053577756real_n @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(3,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( ord_le1724070576l_num1 @ ( abs_ab948591917l_num1 @ ( minus_249161513l_num1 @ ( abs_ab948591917l_num1 @ A ) @ ( abs_ab948591917l_num1 @ B ) ) ) @ ( abs_ab948591917l_num1 @ ( minus_249161513l_num1 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_abs__triangle__ineq3) ).

thf(368,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( ord_le1724070576l_num1 @ ( abs_ab948591917l_num1 @ ( minus_249161513l_num1 @ ( abs_ab948591917l_num1 @ A ) @ ( abs_ab948591917l_num1 @ B ) ) ) @ ( abs_ab948591917l_num1 @ ( minus_249161513l_num1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(216,axiom,
    ! [A: finite1183840848l_num1,B: finite463740460l_num1] :
      ( ! [C: numeral_num1] : ( ord_less_eq_real @ ( real_V646646907m_real @ ( finite1106245191l_num1 @ A @ C ) ) @ ( real_V400292255l_num1 @ ( finite1449546019l_num1 @ B @ C ) ) )
     => ( ord_less_eq_real @ ( real_V400292255l_num1 @ A ) @ ( real_V316032763l_num1 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_norm__le__componentwise__cart) ).

thf(1108,plain,
    ! [A: finite1183840848l_num1,B: finite463740460l_num1] :
      ( ! [C: numeral_num1] : ( ord_less_eq_real @ ( real_V646646907m_real @ ( finite1106245191l_num1 @ A @ C ) ) @ ( real_V400292255l_num1 @ ( finite1449546019l_num1 @ B @ C ) ) )
     => ( ord_less_eq_real @ ( real_V400292255l_num1 @ A ) @ ( real_V316032763l_num1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(174,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_real @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_ord__le__eq__trans) ).

thf(976,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_real @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(151,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ B @ A )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_dual__order_Oantisym) ).

thf(903,plain,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ B @ A )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(278,axiom,
    ! [A: int] :
      ( ( member_int @ A @ ring_1_Ints_int )
     => ( member_int @ ( abs_abs_int @ A ) @ ring_1_Ints_int ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Ints__abs) ).

thf(1276,plain,
    ! [A: int] :
      ( ( member_int @ A @ ring_1_Ints_int )
     => ( member_int @ ( abs_abs_int @ A ) @ ring_1_Ints_int ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(270,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
      ( ( ( minus_1037315151real_n @ A @ B )
        = ( minus_1037315151real_n @ C @ D ) )
     => ( ( A = B )
        = ( C = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_diff__eq__diff__eq) ).

thf(1253,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n,D: finite1489363574real_n] :
      ( ( ( minus_1037315151real_n @ A @ B )
        = ( minus_1037315151real_n @ C @ D ) )
     => ( ( A = B )
        = ( C = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(169,axiom,
    ! [A: real,B: real] :
      ( ( real_V1934908667t_real @ ( minus_minus_real @ A @ B ) @ A )
      = ( real_V646646907m_real @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_dist__diff_I2_J) ).

thf(961,plain,
    ! [A: real,B: real] :
      ( ( real_V1934908667t_real @ ( minus_minus_real @ A @ B ) @ A )
      = ( real_V646646907m_real @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(363,axiom,
    ! [A: real] :
      ( ( member_real @ A @ ring_1_Ints_real )
     => ( member_real @ ( abs_abs_real @ A ) @ ring_1_Ints_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Ints__abs) ).

thf(1508,plain,
    ! [A: real] :
      ( ( member_real @ A @ ring_1_Ints_real )
     => ( member_real @ ( abs_abs_real @ A ) @ ring_1_Ints_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(352,axiom,
    ! [A: real] :
      ( ( abs_abs_real @ ( abs_abs_real @ A ) )
      = ( abs_abs_real @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_abs__idempotent) ).

thf(1481,plain,
    ! [A: real] :
      ( ( abs_abs_real @ ( abs_abs_real @ A ) )
      = ( abs_abs_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(265,axiom,
    ! [A: real] :
      ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ A ) )
        = A )
      = ( ? [B: int] :
            ( A
            = ( ring_1_of_int_real @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_of__int__ceiling__cancel) ).

thf(1244,plain,
    ! [A: real] :
      ( ( ( ring_1_of_int_real @ ( archim1371465213g_real @ A ) )
        = A )
      = ( ? [B: int] :
            ( A
            = ( ring_1_of_int_real @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(116,axiom,
    ! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n] :
      ( ( member1352538125real_n @ A @ B )
     => ( ( member1352538125real_n @ C @ B )
       => ( ( A = C )
          = ( ! [D: finite1489363574real_n] :
                ( ( member1352538125real_n @ D @ B )
               => ( ( real_V783965509real_n @ A @ D )
                  = ( real_V783965509real_n @ C @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_metric__eq__thm) ).

thf(786,plain,
    ! [A: finite1489363574real_n,B: set_Fi1058188332real_n,C: finite1489363574real_n] :
      ( ( member1352538125real_n @ A @ B )
     => ( ( member1352538125real_n @ C @ B )
       => ( ( A = C )
          = ( ! [D: finite1489363574real_n] :
                ( ( member1352538125real_n @ D @ B )
               => ( ( real_V783965509real_n @ A @ D )
                  = ( real_V783965509real_n @ C @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(179,axiom,
    ! [A: real] :
      ( ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ one_one_int )
      = ( ord_less_eq_real @ A @ one_one_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_ceiling__le__one) ).

thf(995,plain,
    ! [A: real] :
      ( ( ord_less_eq_int @ ( archim1371465213g_real @ A ) @ one_one_int )
      = ( ord_less_eq_real @ A @ one_one_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(84,axiom,
    ( ord_le1724070576l_num1
    = ( ^ [A: finite1183840848l_num1,B: finite1183840848l_num1] :
        ! [C: numeral_num1] : ( ord_less_eq_real @ ( finite1106245191l_num1 @ A @ C ) @ ( finite1106245191l_num1 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_less__eq__vec__def) ).

thf(667,plain,
    ( ord_le1724070576l_num1
    = ( ^ [A: finite1183840848l_num1,B: finite1183840848l_num1] :
        ! [C: numeral_num1] : ( ord_less_eq_real @ ( finite1106245191l_num1 @ A @ C ) @ ( finite1106245191l_num1 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(158,axiom,
    ! [A: real,B: real] :
      ( ( member_real @ A @ ring_1_Ints_real )
     => ( ( member_real @ B @ ring_1_Ints_real )
       => ( member_real @ ( minus_minus_real @ A @ B ) @ ring_1_Ints_real ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_Ints__diff) ).

thf(929,plain,
    ! [A: real,B: real] :
      ( ( member_real @ A @ ring_1_Ints_real )
     => ( ( member_real @ B @ ring_1_Ints_real )
       => ( member_real @ ( minus_minus_real @ A @ B ) @ ring_1_Ints_real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(290,axiom,
    ! [A: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim1371465213g_real @ A ) ) @ one_one_real ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_of__int__ceiling__diff__one__le) ).

thf(1308,plain,
    ! [A: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim1371465213g_real @ A ) ) @ one_one_real ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(365,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V739724485real_n @ A ) @ ( real_V739724485real_n @ B ) ) ) @ ( real_V739724485real_n @ ( minus_1037315151real_n @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_norm__triangle__ineq3) ).

thf(1513,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V739724485real_n @ A ) @ ( real_V739724485real_n @ B ) ) ) @ ( real_V739724485real_n @ ( minus_1037315151real_n @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(101,axiom,
    ( real_V488409631l_num1
    = ( ^ [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( real_V400292255l_num1 @ ( minus_249161513l_num1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_dist__norm) ).

thf(716,plain,
    ( real_V488409631l_num1
    = ( ^ [A: finite1183840848l_num1,B: finite1183840848l_num1] : ( real_V400292255l_num1 @ ( minus_249161513l_num1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(233,axiom,
    ( ( ring_1_of_int_real @ one_one_int )
    = one_one_real ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_of__int__1) ).

thf(1161,plain,
    ( ( ring_1_of_int_real @ one_one_int )
    = one_one_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(74,axiom,
    ! [A: real,B: real] :
      ( ~ ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_real @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_le__cases) ).

thf(620,plain,
    ! [A: real,B: real] :
      ( ~ ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_real @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(30,axiom,
    ! [A: set_real] :
      ( ( collect_real
        @ ^ [B: real] : ( member_real @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Collect__mem__eq) ).

thf(447,plain,
    ! [A: set_real] :
      ( ( collect_real
        @ ^ [B: real] : ( member_real @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(27,axiom,
    ! [A: int,B: int] :
      ( ( A = B )
     => ( ord_less_eq_int @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_eq__refl) ).

thf(432,plain,
    ! [A: int,B: int] :
      ( ( A = B )
     => ( ord_less_eq_int @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(320,axiom,
    ! [A: finite2063899472l_num1,B: numeral_num1] :
      ( ( finite1106245191l_num1 @ ( minkow19073400691_real @ A ) @ B )
      = ( ring_1_of_int_real @ ( finite1800583751l_num1 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_of__int__vec__nth) ).

thf(1395,plain,
    ! [A: finite2063899472l_num1,B: numeral_num1] :
      ( ( finite1106245191l_num1 @ ( minkow19073400691_real @ A ) @ B )
      = ( ring_1_of_int_real @ ( finite1800583751l_num1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(314,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( real_V783965509real_n @ ( minus_1037315151real_n @ A @ B ) @ A )
      = ( real_V739724485real_n @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_dist__diff_I2_J) ).

thf(1380,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( real_V783965509real_n @ ( minus_1037315151real_n @ A @ B ) @ A )
      = ( real_V739724485real_n @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(17,axiom,
    ! [A: real] : ( ord_less_eq_int @ ( archim1031974863r_real @ A ) @ ( archim1371465213g_real @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_floor__le__ceiling) ).

thf(405,plain,
    ! [A: real] : ( ord_less_eq_int @ ( archim1031974863r_real @ A ) @ ( archim1371465213g_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(138,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( ( finite1106245191l_num1 @ A )
        = ( finite1106245191l_num1 @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_vec__nth__inject) ).

thf(865,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( ( finite1106245191l_num1 @ A )
        = ( finite1106245191l_num1 @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(19,axiom,
    ! [A: real,B: real] :
      ( ( real_V1934908667t_real @ A @ ( minus_minus_real @ A @ B ) )
      = ( real_V646646907m_real @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_dist__diff_I1_J) ).

thf(410,plain,
    ! [A: real,B: real] :
      ( ( real_V1934908667t_real @ A @ ( minus_minus_real @ A @ B ) )
      = ( real_V646646907m_real @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(171,axiom,
    ! [A: numeral_num1] :
      ( ( real_V400292255l_num1 @ ( finite15144922381_real @ A @ one_one_real ) )
      = one_one_real ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_norm__axis__1) ).

thf(967,plain,
    ! [A: numeral_num1] :
      ( ( real_V400292255l_num1 @ ( finite15144922381_real @ A @ one_one_real ) )
      = one_one_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(267,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] : ( ord_le866583254real_n @ ( minus_1037315151real_n @ ( abs_ab1599551059real_n @ A ) @ ( abs_ab1599551059real_n @ B ) ) @ ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_abs__triangle__ineq2) ).

thf(1248,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] : ( ord_le866583254real_n @ ( minus_1037315151real_n @ ( abs_ab1599551059real_n @ A ) @ ( abs_ab1599551059real_n @ B ) ) @ ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(117,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) )
      = ( ord_less_int @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_of__int__less__iff) ).

thf(790,plain,
    ! [A: int,B: int] :
      ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) )
      = ( ord_less_int @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(5,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( if_Fin1668193290l_num1 @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mt__Numeral____Type__Onum1_J_T) ).

thf(373,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( if_Fin1668193290l_num1 @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(68,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ B @ C )
       => ( ord_less_eq_int @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_order__trans) ).

thf(603,plain,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ B @ C )
       => ( ord_less_eq_int @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(50,axiom,
    ! [A: numeral_num1,B: real] :
      ( ( finite1106245191l_num1 @ ( finite15144922381_real @ A @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_axis__nth) ).

thf(506,plain,
    ! [A: numeral_num1,B: real] :
      ( ( finite1106245191l_num1 @ ( finite15144922381_real @ A @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(300,axiom,
    ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_abs__triangle__ineq2) ).

thf(1335,plain,
    ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(192,axiom,
    ! [A: n > int > $o] :
      ( ( ! [B: n] :
          ? [C: int] : ( A @ B @ C ) )
      = ( ? [B: finite964658038_int_n] :
          ! [C: n] : ( A @ C @ ( finite566214509_int_n @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_lambda__skolem) ).

thf(1033,plain,
    ! [A: n > int > $o] :
      ( ( ! [B: n] :
          ? [C: int] : ( A @ B @ C ) )
      = ( ? [B: finite964658038_int_n] :
          ! [C: n] : ( A @ C @ ( finite566214509_int_n @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(128,axiom,
    ! [A: int,B: real > int,C: real,D: real] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_real @ C @ D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_int @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_ord__eq__le__subst) ).

thf(828,plain,
    ! [A: int,B: real > int,C: real,D: real] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_real @ C @ D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_int @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(349,axiom,
    ! [A: finite1183840848l_num1,B: numeral_num1] : ( ord_less_eq_real @ ( abs_abs_real @ ( finite1106245191l_num1 @ A @ B ) ) @ ( real_V400292255l_num1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_component__le__norm__cart) ).

thf(1473,plain,
    ! [A: finite1183840848l_num1,B: numeral_num1] : ( ord_less_eq_real @ ( abs_abs_real @ ( finite1106245191l_num1 @ A @ B ) ) @ ( real_V400292255l_num1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(120,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_diff__strict__right__mono) ).

thf(796,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(154,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ord_less_eq_int @ ( minus_minus_int @ C @ B ) @ ( minus_minus_int @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_diff__left__mono) ).

thf(918,plain,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ord_less_eq_int @ ( minus_minus_int @ C @ B ) @ ( minus_minus_int @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(122,axiom,
    ! [A: real,B: real,C: real > int,D: int] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_int @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_ord__le__eq__subst) ).

thf(801,plain,
    ! [A: real,B: real,C: real > int,D: int] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_int @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(238,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] : ( ord_le866583254real_n @ ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ ( abs_ab1599551059real_n @ A ) @ ( abs_ab1599551059real_n @ B ) ) ) @ ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_abs__triangle__ineq3) ).

thf(1172,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] : ( ord_le866583254real_n @ ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ ( abs_ab1599551059real_n @ A ) @ ( abs_ab1599551059real_n @ B ) ) ) @ ( abs_ab1599551059real_n @ ( minus_1037315151real_n @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(149,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ B @ C )
       => ( ord_less_eq_int @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_order_Otrans) ).

thf(897,plain,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ B @ C )
       => ( ord_less_eq_int @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(110,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ord_less_int @ ( minus_minus_int @ C @ B ) @ ( minus_minus_int @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_diff__strict__left__mono) ).

thf(767,plain,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_int @ A @ B )
     => ( ord_less_int @ ( minus_minus_int @ C @ B ) @ ( minus_minus_int @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(198,axiom,
    ! [A: finite1183840848l_num1,B: numeral_num1,C: finite1183840848l_num1] : ( ord_less_eq_real @ ( real_V1934908667t_real @ ( finite1106245191l_num1 @ A @ B ) @ ( finite1106245191l_num1 @ C @ B ) ) @ ( real_V488409631l_num1 @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_dist__vec__nth__le) ).

thf(1056,plain,
    ! [A: finite1183840848l_num1,B: numeral_num1,C: finite1183840848l_num1] : ( ord_less_eq_real @ ( real_V1934908667t_real @ ( finite1106245191l_num1 @ A @ B ) @ ( finite1106245191l_num1 @ C @ B ) ) @ ( real_V488409631l_num1 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(83,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_diff__right__mono) ).

thf(664,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(262,axiom,
    ! [A: real,B: real] :
      ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
      = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_abs__minus__commute) ).

thf(1236,plain,
    ! [A: real,B: real] :
      ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
      = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(35,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: real] :
      ( ( ord_less_real @ ( real_V488409631l_num1 @ A @ B ) @ C )
     => ( ord_less_real @ ( real_V488409631l_num1 @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_dist__commute__lessI) ).

thf(464,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1,C: real] :
      ( ( ord_less_real @ ( real_V488409631l_num1 @ A @ B ) @ C )
     => ( ord_less_real @ ( real_V488409631l_num1 @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(222,axiom,
    ( ord_le1202326448l_num1
    = ( ^ [A: finite2063899472l_num1,B: finite2063899472l_num1] :
        ! [C: numeral_num1] : ( ord_less_eq_int @ ( finite1800583751l_num1 @ A @ C ) @ ( finite1800583751l_num1 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_less__eq__vec__def) ).

thf(1129,plain,
    ( ord_le1202326448l_num1
    = ( ^ [A: finite2063899472l_num1,B: finite2063899472l_num1] :
        ! [C: numeral_num1] : ( ord_less_eq_int @ ( finite1800583751l_num1 @ A @ C ) @ ( finite1800583751l_num1 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(229,axiom,
    ( real_V783965509real_n
    = ( ^ [A: finite1489363574real_n,B: finite1489363574real_n] : ( real_V783965509real_n @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_dist__commute) ).

thf(1152,plain,
    ( real_V783965509real_n
    = ( ^ [A: finite1489363574real_n,B: finite1489363574real_n] : ( real_V783965509real_n @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(186,axiom,
    ! [A: n,B: int] :
      ( ( finite566214509_int_n @ ( finite1888777460_n_int @ A @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_axis__nth) ).

thf(1019,plain,
    ! [A: n,B: int] :
      ( ( finite566214509_int_n @ ( finite1888777460_n_int @ A @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(33,axiom,
    ! [A: numeral_num1] :
      ( ( finite1800583751l_num1 @ one_on601734293l_num1 @ A )
      = one_one_int ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_one__index) ).

thf(459,plain,
    ! [A: numeral_num1] :
      ( ( finite1800583751l_num1 @ one_on601734293l_num1 @ A )
      = one_one_int ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(178,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_order__class_Oorder_Oantisym) ).

thf(992,plain,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(133,axiom,
    ! [A: int,B: numeral_num1] :
      ( ( finite1800583751l_num1 @ ( finite1470207077l_num1 @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_vec__component) ).

thf(850,plain,
    ! [A: int,B: numeral_num1] :
      ( ( finite1800583751l_num1 @ ( finite1470207077l_num1 @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(183,axiom,
    ! [A: $o,B: finite964658038_int_n,C: finite964658038_int_n,D: n] :
      ( ( A
       => ( ( finite566214509_int_n @ ( if_Fin1767949360_int_n @ A @ B @ C ) @ D )
          = ( finite566214509_int_n @ B @ D ) ) )
      & ( ~ A
       => ( ( finite566214509_int_n @ ( if_Fin1767949360_int_n @ A @ B @ C ) @ D )
          = ( finite566214509_int_n @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_cond__component) ).

thf(1004,plain,
    ! [A: $o,B: finite964658038_int_n,C: finite964658038_int_n,D: n] :
      ( ( A
       => ( ( finite566214509_int_n @ ( if_Fin1767949360_int_n @ A @ B @ C ) @ D )
          = ( finite566214509_int_n @ B @ D ) ) )
      & ( ~ A
       => ( ( finite566214509_int_n @ ( if_Fin1767949360_int_n @ A @ B @ C ) @ D )
          = ( finite566214509_int_n @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(140,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( ord_less_eq_int @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_dual__order_Ostrict__implies__order) ).

thf(871,plain,
    ! [A: int,B: int] :
      ( ( ord_less_int @ A @ B )
     => ( ord_less_eq_int @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(48,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: real] :
      ( ( ord_less_real @ ( real_V783965509real_n @ A @ B ) @ C )
     => ( ord_less_real @ ( real_V783965509real_n @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_dist__commute__lessI) ).

thf(501,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: real] :
      ( ( ord_less_real @ ( real_V783965509real_n @ A @ B ) @ C )
     => ( ord_less_real @ ( real_V783965509real_n @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(76,axiom,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_order__class_Oorder_Oantisym) ).

thf(624,plain,
    ! [A: int,B: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(131,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( minus_minus_real @ A @ B )
        = ( minus_minus_real @ C @ D ) )
     => ( ( ord_less_eq_real @ A @ B )
        = ( ord_less_eq_real @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_diff__eq__diff__less__eq) ).

thf(839,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( minus_minus_real @ A @ B )
        = ( minus_minus_real @ C @ D ) )
     => ( ( ord_less_eq_real @ A @ B )
        = ( ord_less_eq_real @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(42,axiom,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ C @ A )
       => ( ord_less_eq_int @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_dual__order_Otrans) ).

thf(486,plain,
    ! [A: int,B: int,C: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ C @ A )
       => ( ord_less_eq_int @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(37,axiom,
    ! [A: real,B: set_real,C: real] :
      ( ( member_real @ A @ B )
     => ( ( member_real @ C @ B )
       => ( ( A = C )
          = ( ! [D: real] :
                ( ( member_real @ D @ B )
               => ( ( real_V1934908667t_real @ A @ D )
                  = ( real_V1934908667t_real @ C @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_metric__eq__thm) ).

thf(469,plain,
    ! [A: real,B: set_real,C: real] :
      ( ( member_real @ A @ B )
     => ( ( member_real @ C @ B )
       => ( ( A = C )
          = ( ! [D: real] :
                ( ( member_real @ D @ B )
               => ( ( real_V1934908667t_real @ A @ D )
                  = ( real_V1934908667t_real @ C @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(160,axiom,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ C @ D )
       => ( ord_less_eq_int @ ( minus_minus_int @ A @ D ) @ ( minus_minus_int @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_diff__mono) ).

thf(935,plain,
    ! [A: int,B: int,C: int,D: int] :
      ( ( ord_less_eq_int @ A @ B )
     => ( ( ord_less_eq_int @ C @ D )
       => ( ord_less_eq_int @ ( minus_minus_int @ A @ D ) @ ( minus_minus_int @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(81,axiom,
    ( ( (=) @ real )
    = ( ^ [A: real,B: real] :
          ( ( ord_less_eq_real @ A @ B )
          & ( ord_less_eq_real @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_eq__iff) ).

thf(659,plain,
    ( ( (=) @ real )
    = ( ^ [A: real,B: real] :
          ( ( ord_less_eq_real @ A @ B )
          & ( ord_less_eq_real @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(54,axiom,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( real_V488409631l_num1 @ A @ ( minus_249161513l_num1 @ A @ B ) )
      = ( real_V400292255l_num1 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_dist__diff_I1_J) ).

thf(543,plain,
    ! [A: finite1183840848l_num1,B: finite1183840848l_num1] :
      ( ( real_V488409631l_num1 @ A @ ( minus_249161513l_num1 @ A @ B ) )
      = ( real_V400292255l_num1 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(113,axiom,
    ! [A: real,B: real,C: real] :
      ( ( A = B )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ord_less_eq_real @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_ord__eq__le__trans) ).

thf(775,plain,
    ! [A: real,B: real,C: real] :
      ( ( A = B )
     => ( ( ord_less_eq_real @ B @ C )
       => ( ord_less_eq_real @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(106,axiom,
    ( real_V1934908667t_real
    = ( ^ [A: real,B: real] : ( real_V646646907m_real @ ( minus_minus_real @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_dist__norm) ).

thf(755,plain,
    ( real_V1934908667t_real
    = ( ^ [A: real,B: real] : ( real_V646646907m_real @ ( minus_minus_real @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(208,axiom,
    ! [A: int] :
      ( ( one_one_int = A )
      = ( A = one_one_int ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_one__reorient) ).

thf(1088,plain,
    ! [A: int] :
      ( ( one_one_int = A )
      = ( A = one_one_int ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(340,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
      ( ( ord_le866583254real_n @ A @ B )
     => ( ord_le866583254real_n @ ( minus_1037315151real_n @ C @ B ) @ ( minus_1037315151real_n @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_diff__left__mono) ).

thf(1449,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n,C: finite1489363574real_n] :
      ( ( ord_le866583254real_n @ A @ B )
     => ( ord_le866583254real_n @ ( minus_1037315151real_n @ C @ B ) @ ( minus_1037315151real_n @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(46,axiom,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( if_Fin127821360real_n @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_T) ).

thf(496,plain,
    ! [A: finite1489363574real_n,B: finite1489363574real_n] :
      ( ( if_Fin127821360real_n @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(98,axiom,
    ! [A: real,B: real] :
      ( ( real_V646646907m_real @ ( minus_minus_real @ A @ B ) )
      = ( real_V646646907m_real @ ( minus_minus_real @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_norm__minus__commute) ).

thf(708,plain,
    ! [A: real,B: real] :
      ( ( real_V646646907m_real @ ( minus_minus_real @ A @ B ) )
      = ( real_V646646907m_real @ ( minus_minus_real @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(327,axiom,
    ! [A: int,B: int] :
      ( ( real_V1934908667t_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) )
      = ( ring_1_of_int_real @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_dist__of__int) ).

thf(1417,plain,
    ! [A: int,B: int] :
      ( ( real_V1934908667t_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) )
      = ( ring_1_of_int_real @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(1516,plain,
    $false,
    inference(e,[status(thm)],[1036,1337,1411,1024,1168,1105,1315,1295,1110,645,892,1501,809,909,1031,1200,762,1406,683,1290,1443,379,1305,1437,1041,873,1205,384,1310,698,945,1063,538,1342,747,1507,1222,1441,973,1359,1386,1475,436,1228,565,1366,1409,1287,570,1298,1313,1455,1462,949,1330,1264,853,1247,421,1494,1362,1100,606,1347,1013,770,1398,881,416,1489,924,1302,376,1136,1383,1183,480,492,1465,981,687,1377,396,998,1345,1447,956,1074,678,661,1470,366,1163,942,439,546,793,894,1091,952,862,1174,598,1487,424,429,815,407,693,1423,879,1457,1159,1210,1079,757,1195,551,842,1350,1234,615,1121,1498,1425,1096,388,1138,783,499,1270,1259,884,753,669,476,642,1414,489,970,1028,1082,1016,1207,1099,1478,1231,1131,1192,1060,1429,622,837,1324,393,503,1393,1318,938,1241,921,1170,1071,1026,718,773,794,906,1278,1146,1103,1273,856,573,750,1510,1251,618,402,1388,579,1403,1124,1256,413,584,1154,826,711,641,391,382,713,1058,1239,1332,466,947,1356,540,672,900,1282,419,1492,567,509,1439,890,387,494,609,799,483,700,1325,1460,1022,1293,1177,1112,1149,964,462,932,685,983,1198,399,959,1213,868,780,455,986,1250,1496,1044,695,1000,1435,675,1203,1467,680,548,1420,927,1134,812,1340,823,836,473,1076,426,1166,1003,690,1156,1225,1368,1267,1484,1053,1432,1186,1262,1218,1220,1300,1452,1038,370,1085,576,1284,1427,1504,1094,612,876,859,1353,600,627,450,1180,1321,581,759,1216,1126,1189,1390,368,1108,976,903,1276,1253,961,1508,1481,1244,786,995,667,929,1308,1513,716,1161,620,447,432,1395,1380,405,865,410,967,1248,790,373,603,506,1335,1033,828,1473,796,918,801,1172,897,767,1056,664,1236,464,1129,1152,1019,459,992,850,1004,871,501,624,839,486,469,935,659,543,775,755,1088,1449,496,708,1417]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ITP118^1 : TPTP v8.2.0. Released v7.5.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n006.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sat May 18 16:20:54 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.03/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.81/1.11  % [INFO] 	 Parsing done (234ms). 
% 1.81/1.12  % [INFO] 	 Running in sequential loop mode. 
% 2.44/1.33  % [INFO] 	 eprover registered as external prover. 
% 2.44/1.33  % [INFO] 	 cvc4 registered as external prover. 
% 2.44/1.33  % [INFO] 	 Scanning for conjecture ... 
% 2.60/1.43  % [INFO] 	 Found a conjecture (or negated_conjecture) and 363 axioms. Running axiom selection ... 
% 2.95/1.53  % [INFO] 	 Axiom selection finished. Selected 363 axioms (removed 0 axioms). 
% 3.55/1.68  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.78/1.70  % [INFO] 	 Type checking passed. 
% 3.78/1.70  % [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 ... 
% 15.54/4.55  % External prover 'e' found a proof!
% 15.54/4.55  % [INFO] 	 Killing All external provers ... 
% 15.54/4.55  % Time passed: 4023ms (effective reasoning time: 3435ms)
% 15.54/4.55  % 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)>
% 15.82/4.57  % Axioms used in derivation (363): fact_145_dist__commute__lessI, fact_272_le__of__int__ceiling, fact_47_Ints__abs, fact_333_order_Otrans, fact_240_abs__le__D1, fact_323_ord__le__eq__trans, fact_178_abs__one, fact_273_norm__bound__component__le__cart, fact_92_mem__Collect__eq, fact_102_of__int__eq__1__iff, fact_282_norm__triangle__ineq2, fact_260_abs__triangle__ineq2, fact_8_of__int__abs, fact_211_le__numeral__extra_I4_J, fact_85_axis__nth, fact_56_Ints__cases, fact_156_real__norm__def, fact_349_ord__eq__le__subst, fact_275_component__le__norm__cart, fact_299_complete__interval, fact_67_vec__nth__inject, fact_10_of__int__diff, fact_314_linorder__wlog, fact_305_vector__one__nth, fact_48_Ints__abs, fact_209_less__eq__real__def, fact_97_of__int__less__iff, fact_210_le__numeral__extra_I4_J, fact_228_diff__right__mono, fact_58_diff__right__commute, fact_232_diff__left__mono, fact_332_order_Otrans, fact_99_one__index, fact_37_vec__eq__iff, fact_264_norm__le__componentwise__cart, fact_277_dist__real, fact_217_int__le__induct, fact_161_diff__strict__mono, fact_160_norm__bound__component__lt__cart, fact_229_diff__left__mono, fact_345_ord__le__eq__subst, fact_52_Ints__induct, fact_251_abs__triangle__ineq2__sym, help_If_1_1_If_001t__Finite____Cartesian____Product__Ovec_It__Int__Oint_Mtf__n_J_T, fact_281_norm__triangle__ineq2, fact_105_of__int__1, fact_318_order__trans, fact_79__C1_C_I3_J, fact_133_floor__diff__one, fact_286_metric__eq__thm, fact_173_diff__strict__right__mono, fact_84_axis__nth, fact_180_Ints__1, fact_130_dist__diff_I1_J, fact_162_diff__strict__mono, fact_65_diff__eq__diff__eq, fact_0__C1_C_I2_J, fact_150_dist__commute, fact_40_assms, fact_335_le__cases, fact_111_ceiling__one, fact_45_Ints__diff, fact_203_of__int__1__le__iff, fact_307_complete__real, fact_331_le__cases3, fact_13_of__int__diff, fact_250_abs__triangle__ineq2__sym, fact_98_one__index, fact_107_of__int__1, fact_32_lambda__skolem, fact_290_dist__vec__nth__le, fact_301_order_Onot__eq__order__implies__strict, fact_248_ceiling__diff__floor__le__1, fact_20_of__int__vec__nth, fact_195_le__ceiling__iff, fact_59_diff__right__commute, fact_257_abs__triangle__ineq3, fact_112_floor__of__int, fact_327_order__class_Oorder_Oeq__iff, fact_46_Ints__diff, fact_51_Ints__of__int, fact_75_vec__sub, fact_18_of__int__vec__nth, fact_219_le__floor__iff, fact_4_vector__minus__component, fact_340_antisym, fact_205_one__le__floor, fact_179_dist__real__def, fact_188_of__int__floor__cancel, fact_234_diff__mono, fact_223_diff__eq__diff__less__eq, fact_213_less__eq__vec__def, fact_76_vec__sub, fact_55_Ints__cases, fact_27_abs__idempotent, fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_Areal__of__int_Am_A_061_Ax_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_329_antisym__conv, fact_36_vec__eq__iff, fact_159_norm__bound__component__lt__cart, fact_294_ceiling__correct, fact_143_linorder__neqE__linordered__idom, fact_252_abs__triangle__ineq2__sym, fact_176_diff__strict__right__mono, fact_146_dist__commute__lessI, fact_280_norm__triangle__ineq2, fact_54_Ints__induct, fact_192_real__abs__dist, fact_254_abs__triangle__ineq3, fact_350_ord__eq__le__subst, fact_86_vec_Oscale__left__diff__distrib, fact_283_abs__dist__diff__le, fact_78_vector__sub__rdistrib, fact_225_diff__right__mono, fact_325_ord__eq__le__trans, fact_90_abs__1, fact_292_norm__triangle__ineq3, fact_338_linear, fact_70_cond__component, fact_131_floor__less__one, fact_142_dist__norm, fact_221_diff__eq__diff__less__eq, fact_208_floor__mono, fact_230_diff__left__mono, fact_100_one__index, fact_300_eucl__less__le__not__le, fact_60_diff__right__commute, fact_136_one__reorient, fact_216_int__less__induct, fact_298_complete__interval, fact_181_Ints__1, fact_104_of__int__eq__1__iff, fact_220_ceiling__le__iff, fact_50_Ints__of__int, fact_271_of__int__floor__le, fact_165_diff__eq__diff__less, fact_236_diff__mono, fact_89_norm__axis__1, fact_343_eq__iff, help_If_2_1_If_001t__Finite____Cartesian____Product__Ovec_It__Int__Oint_Mtf__n_J_T, fact_118_vector__ssub__ldistrib, help_If_1_1_If_001t__Finite____Cartesian____Product__Ovec_It__Int__Oint_Mt__Numeral____Type__Onum1_J_T, fact_141_dist__norm, fact_22_of__int__eq__iff, fact_119_vector__ssub__ldistrib, fact_117_vec__component, help_If_3_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mt__Numeral____Type__Onum1_J_T, fact_81_ceiling__diff__of__int, fact_134_ceiling__diff__one, fact_25_abs__abs, fact_306_vector__one__nth, fact_166_diff__eq__diff__less, fact_348_ord__eq__le__subst, fact_245_dist__vector__1, fact_140_dist__norm, fact_196_ceiling__split, fact_19_of__int__vec__nth, fact_14__092_060open_062x_A_E_Ai_A_N_Ay_A_E_Ai_A_092_060in_062_A_092_060int_062_092_060close_062, fact_110_floor__one, fact_115_vec__component, fact_139_less__ceiling__iff, fact_261_abs__triangle__ineq2, fact_116_vec__component, fact_43_Ints__diff, fact_316_dual__order_Orefl, help_If_2_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_T, fact_246_dist__vector__1, fact_96_of__int__less__iff, fact_120_of__int__1__less__iff, fact_128_dist__diff_I1_J, fact_326_order__class_Oorder_Oeq__iff, fact_137_one__reorient, fact_152_floor__less__cancel, fact_26_abs__idempotent, fact_319_order__trans, fact_287_metric__eq__thm, fact_31_abs__minus__commute, fact_302_order_Onot__eq__order__implies__strict, fact_149_dist__commute, fact_34_lambda__skolem, fact_344_ord__le__eq__subst, fact_174_diff__strict__right__mono, fact_352_forall__1, fact_153_norm__minus__commute, fact_17_of__int__vec__nth, fact_308_dual__order_Oantisym, fact_163_diff__strict__mono, fact_171_diff__strict__left__mono, fact_138_floor__less__iff, fact_262_norm__le__componentwise__cart, fact_24_abs__abs, fact_39_vec__eq__iff, fact_12_of__int__diff, fact_263_norm__le__componentwise__cart, fact_11_of__int__diff, help_If_2_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mt__Numeral____Type__Onum1_J_T, fact_182_Ints__1, fact_6_vector__minus__component, fact_87_vec_Oscale__left__diff__distrib, fact_125_dist__diff_I2_J, fact_235_diff__mono, fact_334_le__cases, fact_83_axis__nth, fact_66_vec__nth__inject, fact_285_abs__dist__diff__le, fact_311_dual__order_Oeq__iff, fact_5_vector__minus__component, fact_53_Ints__induct, fact_346_ord__le__eq__subst, fact_72_cond__component, fact_49_Ints__of__int, fact_322_ord__le__eq__trans, fact_249_ceiling__less__iff, fact_189_real__of__int__floor__gt__diff__one, fact_201_of__int__le__1__iff, fact_122_of__int__less__1__iff, fact_193_less__numeral__extra_I4_J, fact_158_ex__of__int__less, help_If_1_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mt__Numeral____Type__Onum1_J_T, fact_16_of__int__vec__nth, fact_304_dual__order_Ostrict__implies__order, fact_202_of__int__le__1__iff, fact_68_vec__nth__inject, fact_7_vector__minus__component, fact_259_abs__triangle__ineq2, fact_342_eq__iff, fact_243_ex__le__of__int, fact_258_abs__triangle__ineq2, fact_336_eq__refl, fact_73_cond__component, fact_151_ceiling__less__cancel, fact_309_dual__order_Oantisym, fact_265_norm__le__componentwise__cart, fact_114_vec__component, fact_9_of__int__abs, fact_274_norm__bound__component__le__cart, fact_337_eq__refl, fact_215_less__eq__vec__def, fact_303_dual__order_Ostrict__implies__order, fact_320_order__class_Oorder_Oantisym, fact_95_Collect__mem__eq, fact_93_mem__Collect__eq, fact_255_abs__triangle__ineq3, fact_88_floor__diff__of__int, fact_77_vector__sub__rdistrib, fact_155_norm__minus__commute, fact_1__C1_C_I1_J, fact_15_of__int__vec__nth, fact_231_diff__left__mono, help_If_2_1_If_001t__Finite____Cartesian____Product__Ovec_It__Int__Oint_Mt__Numeral____Type__Onum1_J_T, fact_339_linear, fact_186_Ints__eq__abs__less1, fact_288_metric__eq__thm, fact_164_diff__strict__mono, help_If_1_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_T, fact_206_ceiling__le__one, fact_69_vec__nth__inject, fact_347_ord__le__eq__subst, fact_313_dual__order_Otrans, fact_194_less__numeral__extra_I4_J, fact_212_less__eq__vec__def, fact_123_of__int__less__1__iff, fact_237_abs__ge__self, fact_94_Collect__mem__eq, fact_296_order__refl, fact_157_ex__less__of__int, fact_177_abs__one, fact_266_norm__le__componentwise__cart, fact_330_le__cases3, fact_293_norm__triangle__ineq3, fact_154_norm__minus__commute, fact_351_ord__eq__le__subst, fact_291_norm__triangle__ineq3, fact_80_norm__of__int, fact_324_ord__eq__le__trans, fact_103_of__int__eq__1__iff, fact_191_real__abs__dist, fact_207_ceiling__mono, fact_279_of__int__ceiling__diff__one__le, fact_233_diff__mono, fact_268_Finite__Cartesian__Product_Onorm__nth__le, fact_63_diff__eq__diff__eq, fact_23_of__int__eq__iff, fact_218_ceiling__le, fact_35_lambda__skolem, fact_241_norm__vector__1, fact_91_abs__1, fact_185_Ints__eq__abs__less1, fact_109_abs__norm__cancel, fact_38_vec__eq__iff, fact_190_real__abs__dist, fact_198_of__int__le__iff, fact_144_linorder__neqE__linordered__idom, fact_29_abs__minus__commute, fact_204_of__int__1__le__iff, fact_297_order__refl, fact_167_diff__eq__diff__less, fact_244_dist__vector__1, fact_183_vec_Oscale__right__diff__distrib, fact_187_of__int__ceiling__cancel, fact_284_abs__dist__diff__le, fact_270_real__of__int__floor__ge__diff__one, fact_41_of__int__vec__eq__iff, fact_267_norm__le__componentwise__cart, fact_199_of__int__le__iff, fact_242_norm__vector__1, fact_135_one__reorient, fact_253_abs__triangle__ineq2__sym, fact_172_diff__strict__left__mono, fact_353_ex__1, fact_71_cond__component, fact_44_Ints__diff, fact_74_dist__of__int, fact_108_abs__norm__cancel, fact_321_order__class_Oorder_Oantisym, fact_57_Ints__cases, fact_312_dual__order_Otrans, fact_278_floor__le__ceiling, fact_269_Finite__Cartesian__Product_Onorm__nth__le, fact_82_axis__nth, fact_132_one__less__ceiling, fact_197_ceiling__eq__iff, fact_124_norm__one, fact_28_abs__minus__commute, fact_113_ceiling__of__int, fact_276_component__le__norm__cart, fact_64_diff__eq__diff__eq, fact_317_dual__order_Orefl, fact_247_norm__real, fact_341_antisym, fact_175_diff__strict__right__mono, fact_101_one__index, fact_21_of__int__eq__iff, fact_214_less__eq__vec__def, fact_169_diff__strict__left__mono, fact_127_dist__diff_I2_J, fact_106_of__int__1, fact_170_diff__strict__left__mono, fact_328_antisym__conv, fact_238_abs__ge__self, fact_147_dist__commute__lessI, fact_184_vec_Oscale__right__diff__distrib, fact_256_abs__triangle__ineq3, fact_168_diff__eq__diff__less, fact_310_dual__order_Oeq__iff, fact_222_diff__eq__diff__less__eq, fact_61_diff__right__commute, fact_315_linorder__wlog, fact_295_ceiling__unique, fact_289_dist__vec__nth__le, fact_33_lambda__skolem, fact_227_diff__right__mono, fact_226_diff__right__mono, fact_148_dist__commute, fact_42_of__int__vec__eq__iff, fact_129_dist__diff_I1_J, fact_2_m, fact_200_zle__diff1__eq, fact_62_diff__eq__diff__eq, fact_121_of__int__1__less__iff, fact_224_diff__eq__diff__less__eq, fact_239_abs__le__D1, fact_30_abs__minus__commute, fact_126_dist__diff_I2_J
% 15.82/4.57  % No. of inferences in proof: 730
% 15.82/4.57  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4023 ms resp. 3435 ms w/o parsing
% 16.80/4.82  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.80/4.83  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------