TSTP Solution File: ITP062^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP062^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:22:32 EDT 2024

% Result   : Theorem 23.63s 6.64s
% Output   : Refutation 24.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  391
% Syntax   : Number of formulae    :  746 ( 420 unt;  38 typ;   0 def)
%            Number of atoms       : 1630 ( 686 equ;   6 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 6407 (  74   ~;  20   |;  46   &;5645   @)
%                                         (   0 <=>; 622  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :  151 ( 151   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   37 (  34 usr;  10 con; 0-4 aty)
%            Number of variables   : 1938 (  54   ^1874   !;  10   ?;1938   :)

% Comments : 
%------------------------------------------------------------------------------
thf(set_real_type,type,
    set_real: $tType ).

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

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

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

thf(genClo1161277105lle_PC_type,type,
    genClo1161277105lle_PC: nat > real > real ).

thf(genClo1144207539le_rho_type,type,
    genClo1144207539le_rho: real ).

thf(genClo1015804716orrect_type,type,
    genClo1015804716orrect: nat > real > $o ).

thf(genClo293725281kRead1_type,type,
    genClo293725281kRead1: ( nat > real ) > real > ( nat > $o ) > $o ).

thf(genClo293725282kRead2_type,type,
    genClo293725282kRead2: ( nat > real ) > ( nat > real ) > real > ( nat > $o ) > $o ).

thf(genClo2108747022bound1_type,type,
    genClo2108747022bound1: ( nat > real > real ) > $o ).

thf(genClo2108747023bound2_type,type,
    genClo2108747023bound2: ( nat > real > real ) > $o ).

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

thf(minus_minus_nat_type,type,
    minus_minus_nat: nat > nat > nat ).

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

thf(one_one_nat_type,type,
    one_one_nat: nat ).

thf(one_one_real_type,type,
    one_one_real: real ).

thf(plus_plus_nat_type,type,
    plus_plus_nat: nat > nat > nat ).

thf(plus_plus_num_type,type,
    plus_plus_num: num > num > num ).

thf(plus_plus_real_type,type,
    plus_plus_real: real > real > real ).

thf(times_times_nat_type,type,
    times_times_nat: nat > nat > nat ).

thf(times_times_num_type,type,
    times_times_num: num > num > num ).

thf(times_times_real_type,type,
    times_times_real: real > real > real ).

thf(neg_numeral_dbl_real_type,type,
    neg_numeral_dbl_real: real > real ).

thf(bit0_type,type,
    bit0: num > num ).

thf(one_type,type,
    one: num ).

thf(numeral_numeral_nat_type,type,
    numeral_numeral_nat: num > nat ).

thf(numeral_numeral_real_type,type,
    numeral_numeral_real: num > real ).

thf(ord_less_eq_nat_type,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(ord_less_eq_num_type,type,
    ord_less_eq_num: num > num > $o ).

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

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

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

thf(c_type,type,
    c: nat > real > real ).

thf(d_type,type,
    d: nat > real > real ).

thf(p_type,type,
    p: nat ).

thf(q_type,type,
    q: nat ).

thf(s_type,type,
    s: real ).

thf(t_type,type,
    t: real ).

thf(200,axiom,
    ( genClo293725282kRead2
    = ( ^ [A: nat > real,B: nat > real,C: real,D: nat > $o] :
        ! [E: nat] :
          ( ( D @ E )
         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ E ) @ ( B @ E ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_okRead2__def) ).

thf(1036,plain,
    ( genClo293725282kRead2
    = ( ^ [A: nat > real,B: nat > real,C: real,D: nat > $o] :
        ! [E: nat] :
          ( ( D @ E )
         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ E ) @ ( B @ E ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(131,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( A
        = ( plus_plus_real @ B @ C ) )
     => ( ( plus_plus_real @ D @ A )
        = ( plus_plus_real @ B @ ( plus_plus_real @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_group__cancel_Oadd2) ).

thf(809,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( A
        = ( plus_plus_real @ B @ C ) )
     => ( ( plus_plus_real @ D @ A )
        = ( plus_plus_real @ B @ ( plus_plus_real @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(325,axiom,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_add__diff__cancel) ).

thf(1454,plain,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(198,axiom,
    ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_abs__triangle__ineq4) ).

thf(1031,plain,
    ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(288,axiom,
    ! [A: num,B: num] :
      ( ( ( bit0 @ A )
        = ( bit0 @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_verit__eq__simplify_I8_J) ).

thf(1315,plain,
    ! [A: num,B: num] :
      ( ( ( bit0 @ A )
        = ( bit0 @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(168,axiom,
    genClo2108747022bound1 @ c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_rb1) ).

thf(941,plain,
    genClo2108747022bound1 @ c,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(122,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_diff__add) ).

thf(777,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(89,axiom,
    ord_less_eq_nat @ one_one_nat @ one_one_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_le__numeral__extra_I4_J) ).

thf(666,plain,
    ord_less_eq_nat @ one_one_nat @ one_one_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(6,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_diff__le__mono2) ).

thf(365,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(301,axiom,
    ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
    = ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_Eq1) ).

thf(1369,plain,
    ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
    = ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(213,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 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_add__mono) ).

thf(1083,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 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(36,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_left__add__mult__distrib) ).

thf(468,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(189,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
      = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_distrib__left) ).

thf(1005,plain,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
      = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(312,axiom,
    ord_less_eq_real @ s @ t,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_ie) ).

thf(1406,plain,
    ord_less_eq_real @ s @ t,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(110,axiom,
    ! [A: num,B: num,C: num > num,D: num] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ord_less_eq_num @ ( C @ B ) @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_order__subst2) ).

thf(730,plain,
    ! [A: num,B: num,C: num > num,D: num] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ord_less_eq_num @ ( C @ B ) @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(210,axiom,
    ! [A: num] :
      ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ A ) @ one_one_nat )
      = ( ord_less_eq_num @ A @ one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_numeral__le__one__iff) ).

thf(1068,plain,
    ! [A: num] :
      ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ A ) @ one_one_nat )
      = ( ord_less_eq_num @ A @ one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(350,axiom,
    ! [A: num] :
      ( ( plus_plus_real @ ( numeral_numeral_real @ A ) @ one_one_real )
      = ( numeral_numeral_real @ ( plus_plus_num @ A @ one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_numeral__plus__one) ).

thf(1522,plain,
    ! [A: num] :
      ( ( plus_plus_real @ ( numeral_numeral_real @ A ) @ one_one_real )
      = ( numeral_numeral_real @ ( plus_plus_num @ A @ one ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(187,axiom,
    ! [A: real] :
      ( ( minus_minus_real @ ( times_times_real @ A @ A ) @ one_one_real )
      = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( minus_minus_real @ A @ one_one_real ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_square__diff__one__factored) ).

thf(994,plain,
    ! [A: real] :
      ( ( minus_minus_real @ ( times_times_real @ A @ A ) @ one_one_real )
      = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( minus_minus_real @ A @ one_one_real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(113,axiom,
    ! [A: num,B: num] :
      ( ( ( numeral_numeral_nat @ A )
        = ( numeral_numeral_nat @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_numeral__eq__iff) ).

thf(741,plain,
    ! [A: num,B: num] :
      ( ( ( numeral_numeral_nat @ A )
        = ( numeral_numeral_nat @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(252,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
      = ( plus_plus_nat @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_mult__2) ).

thf(1205,plain,
    ! [A: nat] :
      ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
      = ( plus_plus_nat @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(273,axiom,
    ! [A: real,B: real,C: num] :
      ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ C ) )
      = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ C ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_left__diff__distrib__numeral) ).

thf(1269,plain,
    ! [A: real,B: real,C: num] :
      ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ C ) )
      = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ C ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(86,axiom,
    ! [A: num,B: num] :
      ( ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ B ) )
      = ( numeral_numeral_nat @ ( plus_plus_num @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_numeral__plus__numeral) ).

thf(655,plain,
    ! [A: num,B: num] :
      ( ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ B ) )
      = ( numeral_numeral_nat @ ( plus_plus_num @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(93,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
      = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_ab__semigroup__mult__class_Omult__ac_I1_J) ).

thf(677,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
      = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(67,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
      | ( ord_less_eq_nat @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_nat__le__linear) ).

thf(597,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
      | ( ord_less_eq_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(337,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( minus_minus_real @ A @ B )
        = C )
      = ( A
        = ( plus_plus_real @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_diff__eq__eq) ).

thf(1486,plain,
    ! [A: real,B: real,C: real] :
      ( ( ( minus_minus_real @ A @ B )
        = C )
      = ( A
        = ( plus_plus_real @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(48,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ A @ C ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_add__left__imp__eq) ).

thf(523,plain,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ A @ C ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(238,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( ord_less_eq_real @ A @ B )
        & ( C = D ) )
     => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_add__mono__thms__linordered__semiring_I3_J) ).

thf(1158,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( ord_less_eq_real @ A @ B )
        & ( C = D ) )
     => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(63,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_le__cases) ).

thf(582,plain,
    ! [A: nat,B: nat] :
      ( ~ ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(202,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
     => ( ord_less_eq_real @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_abs__le__D1) ).

thf(1041,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)],[202]) ).

thf(146,axiom,
    ! [A: num,B: num,C: nat] :
      ( ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ B ) @ C ) )
      = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ A @ B ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_add__numeral__left) ).

thf(861,plain,
    ! [A: num,B: num,C: nat] :
      ( ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ B ) @ C ) )
      = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ A @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(341,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_left__diff__distrib) ).

thf(1497,plain,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(55,axiom,
    ! [A: nat,B: num > nat,C: num,D: num] :
      ( ( ord_less_eq_nat @ A @ ( B @ C ) )
     => ( ( ord_less_eq_num @ C @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_order__subst1) ).

thf(550,plain,
    ! [A: nat,B: num > nat,C: num,D: num] :
      ( ( ord_less_eq_nat @ A @ ( B @ C ) )
     => ( ( ord_less_eq_num @ C @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(240,axiom,
    ! [A: num,B: num] :
      ( ( ( bit0 @ A )
        = ( bit0 @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_semiring__norm_I87_J) ).

thf(1164,plain,
    ! [A: num,B: num] :
      ( ( ( bit0 @ A )
        = ( bit0 @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(105,axiom,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_ab__semigroup__add__class_Oadd__ac_I1_J) ).

thf(715,plain,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(275,axiom,
    ! [A: num,B: real > num,C: real,D: real] :
      ( ( ord_less_eq_num @ A @ ( B @ C ) )
     => ( ( ord_less_eq_real @ C @ D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_order__subst1) ).

thf(1275,plain,
    ! [A: num,B: real > num,C: real,D: real] :
      ( ( ord_less_eq_num @ A @ ( B @ C ) )
     => ( ( ord_less_eq_real @ C @ D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(261,axiom,
    ! [A: nat,B: real,C: real] :
      ( ( ( genClo1015804716orrect @ A @ C )
        & ( ord_less_eq_real @ B @ C ) )
     => ( ord_less_eq_real @ ( genClo1161277105lle_PC @ A @ B ) @ ( genClo1161277105lle_PC @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_PC__monotone) ).

thf(1233,plain,
    ! [A: nat,B: real,C: real] :
      ( ( ( genClo1015804716orrect @ A @ C )
        & ( ord_less_eq_real @ B @ C ) )
     => ( ord_less_eq_real @ ( genClo1161277105lle_PC @ A @ B ) @ ( genClo1161277105lle_PC @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(170,axiom,
    ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Eq2) ).

thf(945,plain,
    ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(208,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_diff__le__eq) ).

thf(1063,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(51,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
      = ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_add_Oleft__commute) ).

thf(538,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
      = ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(164,axiom,
    ! [A: nat,B: nat,C: nat,D: nat,E: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ D ) @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ E ) )
        = ( ord_less_eq_nat @ D @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_nat__le__add__iff2) ).

thf(930,plain,
    ! [A: nat,B: nat,C: nat,D: nat,E: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ D ) @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ E ) )
        = ( ord_less_eq_nat @ D @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(132,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ A @ B )
       => ( ( ( minus_minus_nat @ B @ A )
            = C )
          = ( B
            = ( plus_plus_nat @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add) ).

thf(814,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ A @ B )
       => ( ( ( minus_minus_nat @ B @ A )
            = C )
          = ( B
            = ( plus_plus_nat @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(292,axiom,
    ! [A: real,B: real,C: real] :
      ( ( A
        = ( minus_minus_real @ B @ C ) )
      = ( ( plus_plus_real @ A @ C )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_eq__diff__eq) ).

thf(1327,plain,
    ! [A: real,B: real,C: real] :
      ( ( A
        = ( minus_minus_real @ B @ C ) )
      = ( ( plus_plus_real @ A @ C )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(115,axiom,
    ! [A: num,B: nat > num,C: nat,D: nat] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_ord__eq__le__subst) ).

thf(747,plain,
    ! [A: num,B: nat > num,C: nat,D: nat] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(159,axiom,
    ! [A: nat,B: nat,C: num] :
      ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ C ) )
      = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ C ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_distrib__right__numeral) ).

thf(913,plain,
    ! [A: nat,B: nat,C: num] :
      ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ C ) )
      = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ C ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(307,axiom,
    ! [A: real,B: real] :
      ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
      = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_abs__mult) ).

thf(1386,plain,
    ! [A: real,B: real] :
      ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
      = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(332,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
      | ( ord_less_eq_real @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_linear) ).

thf(1475,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)],[332]) ).

thf(353,axiom,
    ! [A: real] :
      ( ( times_times_real @ one_one_real @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_mult_Oleft__neutral) ).

thf(1529,plain,
    ! [A: real] :
      ( ( times_times_real @ one_one_real @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(205,axiom,
    ( ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) )
    = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_Eq4) ).

thf(1055,plain,
    ( ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) )
    = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(279,axiom,
    ! [A: nat,B: real > nat,C: real,D: real] :
      ( ( ord_less_eq_nat @ A @ ( B @ C ) )
     => ( ( ord_less_eq_real @ C @ D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_order__subst1) ).

thf(1287,plain,
    ! [A: nat,B: real > nat,C: real,D: real] :
      ( ( ord_less_eq_nat @ A @ ( B @ C ) )
     => ( ( ord_less_eq_real @ C @ D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(320,axiom,
    ! [A: nat,B: real,C: real] :
      ( ( ( genClo1015804716orrect @ A @ C )
        & ( ord_less_eq_real @ B @ C ) )
     => ( ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ C @ B ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( genClo1161277105lle_PC @ A @ C ) @ ( genClo1161277105lle_PC @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_rate__2) ).

thf(1430,plain,
    ! [A: nat,B: real,C: real] :
      ( ( ( genClo1015804716orrect @ A @ C )
        & ( ord_less_eq_real @ B @ C ) )
     => ( ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ C @ B ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( genClo1161277105lle_PC @ A @ C ) @ ( genClo1161277105lle_PC @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(293,axiom,
    ! [A: real,B: real] :
      ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
      = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_left__add__twice) ).

thf(1330,plain,
    ! [A: real,B: real] :
      ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
      = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(276,axiom,
    ! [A: real] :
      ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
      = ( times_times_real @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_abs__mult__self__eq) ).

thf(1279,plain,
    ! [A: real] :
      ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
      = ( times_times_real @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(172,axiom,
    ! [A: real,B: real] :
      ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_diff__add__cancel) ).

thf(949,plain,
    ! [A: real,B: real] :
      ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(165,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/sandbox/benchmark/theBenchmark.p',fact_230_abs__triangle__ineq2__sym) ).

thf(934,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)],[165]) ).

thf(247,axiom,
    ! [A: num] :
      ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ A ) )
      = ( numeral_numeral_real @ ( bit0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_dbl__simps_I5_J) ).

thf(1191,plain,
    ! [A: num] :
      ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ A ) )
      = ( numeral_numeral_real @ ( bit0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(157,axiom,
    ! [A: num,B: num,C: num > num,D: num] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_ord__le__eq__subst) ).

thf(902,plain,
    ! [A: num,B: num,C: num > num,D: num] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(81,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
      = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_distrib__left) ).

thf(638,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
      = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(267,axiom,
    ! [A: nat,B: real > nat,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_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_ord__eq__le__subst) ).

thf(1247,plain,
    ! [A: nat,B: real > nat,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_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(120,axiom,
    ! [A: num,B: num] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ord_less_eq_num @ B @ A )
        = ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_antisym__conv) ).

thf(770,plain,
    ! [A: num,B: num] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ord_less_eq_num @ B @ A )
        = ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(222,axiom,
    ! [A: real,B: real] :
      ( ( A = B )
     => ( ord_less_eq_real @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_eq__refl) ).

thf(1115,plain,
    ! [A: real,B: real] :
      ( ( A = B )
     => ( ord_less_eq_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(340,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_le__add__diff__inverse) ).

thf(1494,plain,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(179,axiom,
    ! [A: num] :
      ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ A ) )
      = ( numeral_numeral_real @ ( plus_plus_num @ one @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_one__plus__numeral) ).

thf(969,plain,
    ! [A: num] :
      ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ A ) )
      = ( numeral_numeral_real @ ( plus_plus_num @ one @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(70,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_comm__semiring__class_Odistrib) ).

thf(606,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(152,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( A
        = ( plus_plus_nat @ B @ C ) )
     => ( ( plus_plus_nat @ A @ D )
        = ( plus_plus_nat @ B @ ( plus_plus_nat @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_group__cancel_Oadd1) ).

thf(881,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( A
        = ( plus_plus_nat @ B @ C ) )
     => ( ( plus_plus_nat @ A @ D )
        = ( plus_plus_nat @ B @ ( plus_plus_nat @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(22,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_diff__le__mono) ).

thf(416,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(38,axiom,
    ! [A: num] :
      ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ A ) )
      = ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_one__plus__numeral__commute) ).

thf(475,plain,
    ! [A: num] :
      ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ A ) )
      = ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ one_one_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(316,axiom,
    ! [A: real] :
      ( ( times_times_real @ one_one_real @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_comm__monoid__mult__class_Omult__1) ).

thf(1418,plain,
    ! [A: real] :
      ( ( times_times_real @ one_one_real @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(229,axiom,
    ! [A: real,B: real] :
      ( ~ ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_real @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_le__cases) ).

thf(1136,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)],[229]) ).

thf(194,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_add__left__mono) ).

thf(1020,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(178,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_mult__numeral__1) ).

thf(966,plain,
    ! [A: nat] :
      ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(245,axiom,
    ! [A: real,B: real,C: real > real,D: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ ( 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/sandbox/benchmark/theBenchmark.p',fact_258_order__subst2) ).

thf(1183,plain,
    ! [A: real,B: real,C: real > real,D: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ ( 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)],[245]) ).

thf(338,axiom,
    ( ( numeral_numeral_nat @ one )
    = one_one_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_numerals_I1_J) ).

thf(1489,plain,
    ( ( numeral_numeral_nat @ one )
    = one_one_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(315,axiom,
    ! [A: nat,B: nat] :
      ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_left__add__twice) ).

thf(1415,plain,
    ! [A: nat,B: nat] :
      ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(40,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
        = ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_antisym__conv) ).

thf(492,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
        = ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(329,axiom,
    genClo1015804716orrect @ p @ t,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_corr__p) ).

thf(1465,plain,
    genClo1015804716orrect @ p @ t,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(80,axiom,
    ! [A: nat,B: nat,C: nat > num,D: num] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_num @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_order__subst2) ).

thf(634,plain,
    ! [A: nat,B: nat,C: nat > num,D: num] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_num @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(111,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( A = B )
        & ( ord_less_eq_nat @ C @ D ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_add__mono__thms__linordered__semiring_I2_J) ).

thf(734,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( A = B )
        & ( ord_less_eq_nat @ C @ D ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(175,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ C )
      = ( ( ord_less_eq_real @ ( minus_minus_real @ B @ C ) @ A )
        & ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_abs__diff__le__iff) ).

thf(956,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ C )
      = ( ( ord_less_eq_real @ ( minus_minus_real @ B @ C ) @ A )
        & ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(223,axiom,
    ! [A: num] :
      ( one
     != ( bit0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_semiring__norm_I83_J) ).

thf(1119,plain,
    ! [A: num] :
      ( one
     != ( bit0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(16,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( minus_minus_nat @ A @ B ) @ C )
      = ( minus_minus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_left__diff__distrib_H) ).

thf(396,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( minus_minus_nat @ A @ B ) @ C )
      = ( minus_minus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(49,axiom,
    ! [A: num,B: num,C: num > nat,D: nat] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_ord__le__eq__subst) ).

thf(527,plain,
    ! [A: num,B: num,C: num > nat,D: nat] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(69,axiom,
    ! [A: nat,B: nat,C: nat,D: nat,E: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D ) @ ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ E ) )
        = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ D ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_nat__diff__add__eq1) ).

thf(602,plain,
    ! [A: nat,B: nat,C: nat,D: nat,E: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D ) @ ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ E ) )
        = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ D ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(183,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
      = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_right__diff__distrib) ).

thf(981,plain,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
      = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(151,axiom,
    ! [A: num,B: nat > num,C: nat,D: nat] :
      ( ( ord_less_eq_num @ A @ ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_order__subst1) ).

thf(877,plain,
    ! [A: num,B: nat > num,C: nat,D: nat] :
      ( ( ord_less_eq_num @ A @ ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(98,axiom,
    ! [A: num,B: num] :
      ( ( times_times_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ B ) )
      = ( numeral_numeral_nat @ ( times_times_num @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_numeral__times__numeral) ).

thf(692,plain,
    ! [A: num,B: num] :
      ( ( times_times_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ B ) )
      = ( numeral_numeral_nat @ ( times_times_num @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(26,axiom,
    ( ord_less_eq_nat
    = ( ^ [A: nat,B: nat] :
        ? [C: nat] :
          ( B
          = ( plus_plus_nat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_le__iff__add) ).

thf(428,plain,
    ( ord_less_eq_nat
    = ( ^ [A: nat,B: nat] :
        ? [C: nat] :
          ( B
          = ( plus_plus_nat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(250,axiom,
    ( ( numeral_numeral_real @ one )
    = one_one_real ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_numeral__One) ).

thf(1201,plain,
    ( ( numeral_numeral_real @ one )
    = one_one_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(220,axiom,
    ! [A: real,B: nat > real,C: nat,D: nat] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_ord__eq__le__subst) ).

thf(1104,plain,
    ! [A: real,B: nat > real,C: nat,D: nat] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ 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)],[220]) ).

thf(142,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_add__right__mono) ).

thf(849,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(11,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
      = ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_diff__right__commute) ).

thf(380,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
      = ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(323,axiom,
    ! [A: real,B: real,C: real > num,D: num] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_ord__le__eq__subst) ).

thf(1438,plain,
    ! [A: real,B: real,C: real > num,D: num] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(286,axiom,
    ! [A: num,B: num] :
      ( ( ( numeral_numeral_real @ A )
        = ( numeral_numeral_real @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_numeral__eq__iff) ).

thf(1311,plain,
    ! [A: num,B: num] :
      ( ( ( numeral_numeral_real @ A )
        = ( numeral_numeral_real @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(206,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
      = ( ord_less_eq_real @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_add__le__cancel__right) ).

thf(1057,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
      = ( ord_less_eq_real @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(45,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
        = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_Nat_Oadd__diff__assoc) ).

thf(512,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
        = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(169,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = ( plus_plus_nat @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_mult__2__right) ).

thf(942,plain,
    ! [A: nat] :
      ( ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = ( plus_plus_nat @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(30,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ ( times_times_nat @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_le__cube) ).

thf(439,plain,
    ! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ ( times_times_nat @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(158,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ C @ B ) )
      = ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_add__right__cancel) ).

thf(910,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ C @ B ) )
      = ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(216,axiom,
    ! [A: real,B: real,C: num] :
      ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ C ) )
      = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ C ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_distrib__right__numeral) ).

thf(1091,plain,
    ! [A: real,B: real,C: num] :
      ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ C ) )
      = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ C ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(173,axiom,
    ord_less_eq_real @ one_one_real @ one_one_real,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_le__numeral__extra_I4_J) ).

thf(952,plain,
    ord_less_eq_real @ one_one_real @ one_one_real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(268,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_left__diff__distrib_H) ).

thf(1255,plain,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(224,axiom,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
      = ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( minus_minus_real @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_square__diff__square__factored) ).

thf(1123,plain,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
      = ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( minus_minus_real @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(256,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( A = B )
        & ( ord_less_eq_real @ C @ D ) )
     => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_add__mono__thms__linordered__semiring_I2_J) ).

thf(1217,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( A = B )
        & ( ord_less_eq_real @ C @ D ) )
     => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(79,axiom,
    ! [A: num,B: num > num,C: num,D: num] :
      ( ( ord_less_eq_num @ A @ ( B @ C ) )
     => ( ( ord_less_eq_num @ C @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_order__subst1) ).

thf(630,plain,
    ! [A: num,B: num > num,C: num,D: num] :
      ( ( ord_less_eq_num @ A @ ( B @ C ) )
     => ( ( ord_less_eq_num @ C @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(263,axiom,
    ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
    = ( numeral_numeral_nat @ ( bit0 @ one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_nat__1__add__1) ).

thf(1238,plain,
    ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
    = ( numeral_numeral_nat @ ( bit0 @ one ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(160,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse) ).

thf(916,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(326,axiom,
    ! [A: num,B: num] :
      ( ( ord_less_eq_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) )
      = ( ord_less_eq_num @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_numeral__le__iff) ).

thf(1457,plain,
    ! [A: num,B: num] :
      ( ( ord_less_eq_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) )
      = ( ord_less_eq_num @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(136,axiom,
    ! [A: num,B: num,C: num] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ord_less_eq_num @ B @ C )
       => ( ord_less_eq_num @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_order_Otrans) ).

thf(830,plain,
    ! [A: num,B: num,C: num] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ord_less_eq_num @ B @ C )
       => ( ord_less_eq_num @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(212,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = C )
     => ( A
        = ( minus_minus_real @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_add__implies__diff) ).

thf(1079,plain,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = C )
     => ( A
        = ( minus_minus_real @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(117,axiom,
    ! [A: num,B: num > num,C: num,D: num] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_num @ C @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_ord__eq__le__subst) ).

thf(757,plain,
    ! [A: num,B: num > num,C: num,D: num] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_num @ C @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(226,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/sandbox/benchmark/theBenchmark.p',fact_303_order_Otrans) ).

thf(1128,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)],[226]) ).

thf(140,axiom,
    ! [A: nat] :
      ( ( one_one_nat = A )
      = ( A = one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_one__reorient) ).

thf(842,plain,
    ! [A: nat] :
      ( ( one_one_nat = A )
      = ( A = one_one_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(143,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_mult__le__mono) ).

thf(852,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(29,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ A @ C ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_add__left__imp__eq) ).

thf(435,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ A @ C ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(95,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_le__trans) ).

thf(682,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(313,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( A = B )
     => ( ( ord_less_eq_real @ ( abs_abs_real @ C ) @ D )
       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_sin__bound__lemma) ).

thf(1407,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( A = B )
     => ( ( ord_less_eq_real @ ( abs_abs_real @ C ) @ D )
       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(280,axiom,
    ! [A: num] :
      ( ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ one_one_nat )
      = ( numeral_numeral_nat @ ( plus_plus_num @ A @ one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_numeral__plus__one) ).

thf(1291,plain,
    ! [A: num] :
      ( ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ one_one_nat )
      = ( numeral_numeral_nat @ ( plus_plus_num @ A @ one ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(103,axiom,
    ( plus_plus_real
    = ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_add_Ocommute) ).

thf(710,plain,
    ( plus_plus_real
    = ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(296,axiom,
    ! [A: num,B: real > num,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_num @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_ord__eq__le__subst) ).

thf(1350,plain,
    ! [A: num,B: real > num,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_num @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(47,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
        = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right) ).

thf(519,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
        = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(73,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
     => ( ord_less_eq_nat @ A @ ( minus_minus_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_add__le__imp__le__diff) ).

thf(615,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
     => ( ord_less_eq_nat @ A @ ( minus_minus_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(259,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
      = ( times_times_real @ B @ ( times_times_real @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_mult_Oleft__commute) ).

thf(1227,plain,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
      = ( times_times_real @ B @ ( times_times_real @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(124,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
        = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_Nat_Oadd__diff__assoc2) ).

thf(783,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
        = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(309,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
      = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_mult_Oassoc) ).

thf(1397,plain,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
      = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(100,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( minus_minus_nat @ B @ A )
          = C )
        = ( B
          = ( plus_plus_nat @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_Nat_Ole__imp__diff__is__add) ).

thf(697,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( minus_minus_nat @ B @ A )
          = C )
        = ( B
          = ( plus_plus_nat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(215,axiom,
    ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
    = ( numeral_numeral_nat @ ( bit0 @ one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_one__add__one) ).

thf(1089,plain,
    ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
    = ( numeral_numeral_nat @ ( bit0 @ one ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(150,axiom,
    ! [A: num,B: nat,C: nat] :
      ( ( times_times_nat @ ( numeral_numeral_nat @ A ) @ ( plus_plus_nat @ B @ C ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ A ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_distrib__left__numeral) ).

thf(874,plain,
    ! [A: num,B: nat,C: nat] :
      ( ( times_times_nat @ ( numeral_numeral_nat @ A ) @ ( plus_plus_nat @ B @ C ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ A ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(232,axiom,
    ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Eq3) ).

thf(1143,plain,
    ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(230,axiom,
    ! [A: real] :
      ( ( times_times_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
      = ( plus_plus_real @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_mult__2__right) ).

thf(1138,plain,
    ! [A: real] :
      ( ( times_times_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
      = ( plus_plus_real @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(3,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
      = ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_diff__commute) ).

thf(356,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
      = ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(37,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ C @ B ) )
     => ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_add__right__imp__eq) ).

thf(471,plain,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ C @ B ) )
     => ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(298,axiom,
    ! [A: real,B: real,C: real,D: real,E: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
      = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_ordered__ring__class_Ole__add__iff1) ).

thf(1361,plain,
    ! [A: real,B: real,C: real,D: real,E: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
      = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(56,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
        = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_Nat_Odiff__diff__right) ).

thf(554,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
        = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(318,axiom,
    ! [A: real,B: real,C: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
      = ( minus_minus_real @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_add__diff__cancel__right) ).

thf(1424,plain,
    ! [A: real,B: real,C: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
      = ( minus_minus_real @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(255,axiom,
    ! [A: num] :
      ( ( numeral_numeral_nat @ ( bit0 @ A ) )
      = ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_numeral__Bit0) ).

thf(1214,plain,
    ! [A: num] :
      ( ( numeral_numeral_nat @ ( bit0 @ A ) )
      = ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(324,axiom,
    ! [A: num,B: num,C: num > real,D: real] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_ord__le__eq__subst) ).

thf(1446,plain,
    ! [A: num,B: num,C: num > real,D: real] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ 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)],[324]) ).

thf(193,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C )
     => ( ( ord_less_eq_real @ C @ ( plus_plus_real @ D @ B ) )
       => ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C )
         => ( ( ord_less_eq_real @ C @ ( plus_plus_real @ D @ B ) )
           => ( ord_less_eq_real @ ( minus_minus_real @ C @ B ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_add__le__add__imp__diff__le) ).

thf(1016,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C )
     => ( ( ord_less_eq_real @ C @ ( plus_plus_real @ D @ B ) )
       => ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C )
         => ( ( ord_less_eq_real @ C @ ( plus_plus_real @ D @ B ) )
           => ( ord_less_eq_real @ ( minus_minus_real @ C @ B ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(237,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/sandbox/benchmark/theBenchmark.p',fact_207_diff__right__mono) ).

thf(1155,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)],[237]) ).

thf(54,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_distrib__right) ).

thf(547,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(76,axiom,
    ! [A: num,B: num] :
      ( ~ ( ord_less_eq_num @ A @ B )
     => ( ord_less_eq_num @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_le__cases) ).

thf(622,plain,
    ! [A: num,B: num] :
      ( ~ ( ord_less_eq_num @ A @ B )
     => ( ord_less_eq_num @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(15,axiom,
    ! [A: nat,B: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_add__diff__cancel__left_H) ).

thf(393,plain,
    ! [A: nat,B: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(101,axiom,
    ! [A: nat,B: nat,C: nat,D: nat,E: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ D )
          = ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ E ) )
        = ( D
          = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_nat__eq__add__iff2) ).

thf(701,plain,
    ! [A: nat,B: nat,C: nat,D: nat,E: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ D )
          = ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ E ) )
        = ( D
          = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(282,axiom,
    ! [A: num] :
      ( one
     != ( bit0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_verit__eq__simplify_I10_J) ).

thf(1297,plain,
    ! [A: num] :
      ( one
     != ( bit0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(112,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_order_Otrans) ).

thf(738,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(272,axiom,
    ! [A: real,B: real,C: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
      = ( minus_minus_real @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_add__diff__cancel__left) ).

thf(1266,plain,
    ! [A: real,B: real,C: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
      = ( minus_minus_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(227,axiom,
    ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_abs__diff__triangle__ineq) ).

thf(1131,plain,
    ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(207,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
      = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_ring__class_Oring__distribs_I1_J) ).

thf(1060,plain,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
      = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(184,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
      = ( plus_plus_real @ ( times_times_real @ A @ ( minus_minus_real @ B @ D ) ) @ ( times_times_real @ ( minus_minus_real @ A @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_mult__diff__mult) ).

thf(984,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
      = ( plus_plus_real @ ( times_times_real @ A @ ( minus_minus_real @ B @ D ) ) @ ( times_times_real @ ( minus_minus_real @ A @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(107,axiom,
    ( times_times_nat
    = ( ^ [A: nat,B: nat] : ( times_times_nat @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_mult_Ocommute) ).

thf(721,plain,
    ( times_times_nat
    = ( ^ [A: nat,B: nat] : ( times_times_nat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(60,axiom,
    ! [A: num,B: num,C: num > nat,D: nat] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ord_less_eq_nat @ ( C @ B ) @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_order__subst2) ).

thf(569,plain,
    ! [A: num,B: num,C: num > nat,D: nat] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ord_less_eq_nat @ ( C @ B ) @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(42,axiom,
    ! [A: num,B: num] :
      ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ B ) )
      = ( ord_less_eq_num @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_numeral__le__iff) ).

thf(503,plain,
    ! [A: num,B: num] :
      ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ B ) )
      = ( ord_less_eq_num @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(351,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
     => ( ord_less_eq_real @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_add__le__imp__le__left) ).

thf(1525,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
     => ( ord_less_eq_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(271,axiom,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
      = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_add__diff__eq) ).

thf(1263,plain,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
      = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(188,axiom,
    ! [A: nat,B: nat,C: nat > real,D: real] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_ord__le__eq__subst) ).

thf(997,plain,
    ! [A: nat,B: nat,C: nat > real,D: real] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ 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)],[188]) ).

thf(294,axiom,
    ! [A: real] :
      ( ( times_times_real @ A @ one_one_real )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_mult_Ocomm__neutral) ).

thf(1333,plain,
    ! [A: real] :
      ( ( times_times_real @ A @ one_one_real )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(289,axiom,
    ! [A: num] :
      ~ ( ord_less_eq_num @ ( bit0 @ A ) @ one ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_semiring__norm_I69_J) ).

thf(1318,plain,
    ! [A: num] :
      ~ ( ord_less_eq_num @ ( bit0 @ A ) @ one ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(265,axiom,
    ! [A: real,B: real,C: real] :
      ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
      = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_diff__add__eq__diff__diff__swap) ).

thf(1241,plain,
    ! [A: real,B: real,C: real] :
      ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
      = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(52,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_le__add__diff__inverse) ).

thf(541,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(118,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
     => ( ord_less_eq_nat @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_add__le__imp__le__left) ).

thf(765,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
     => ( ord_less_eq_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(347,axiom,
    ( genClo293725281kRead1
    = ( ^ [A: nat > real,B: real,C: nat > $o] :
        ! [D: nat,E: nat] :
          ( ( ( C @ D )
            & ( C @ E ) )
         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ D ) @ ( A @ E ) ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_okRead1__def) ).

thf(1515,plain,
    ( genClo293725281kRead1
    = ( ^ [A: nat > real,B: real,C: nat > $o] :
        ! [D: nat,E: nat] :
          ( ( ( C @ D )
            & ( C @ E ) )
         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ D ) @ ( A @ E ) ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(174,axiom,
    ! [A: num,B: num,C: real] :
      ( ( plus_plus_real @ ( numeral_numeral_real @ A ) @ ( plus_plus_real @ ( numeral_numeral_real @ B ) @ C ) )
      = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ A @ B ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_add__numeral__left) ).

thf(953,plain,
    ! [A: num,B: num,C: real] :
      ( ( plus_plus_real @ ( numeral_numeral_real @ A ) @ ( plus_plus_real @ ( numeral_numeral_real @ B ) @ C ) )
      = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ A @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(163,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
        = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2) ).

thf(926,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
        = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(214,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( plus_plus_real @ ( times_times_real @ C @ B ) @ D ) )
      = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ C ) @ B ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_combine__common__factor) ).

thf(1086,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( plus_plus_real @ ( times_times_real @ C @ B ) @ D ) )
      = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ C ) @ B ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(167,axiom,
    ! [A: num] :
      ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ A ) )
      = ( plus_plus_real @ ( numeral_numeral_real @ A ) @ one_one_real ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_one__plus__numeral__commute) ).

thf(938,plain,
    ! [A: num] :
      ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ A ) )
      = ( plus_plus_real @ ( numeral_numeral_real @ A ) @ one_one_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(330,axiom,
    ord_less_eq_real @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_PC__ie) ).

thf(1466,plain,
    ord_less_eq_real @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(57,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( A
        = ( plus_plus_real @ B @ C ) )
     => ( ( plus_plus_real @ A @ D )
        = ( plus_plus_real @ B @ ( plus_plus_real @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_group__cancel_Oadd1) ).

thf(558,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( A
        = ( plus_plus_real @ B @ C ) )
     => ( ( plus_plus_real @ A @ D )
        = ( plus_plus_real @ B @ ( plus_plus_real @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(211,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/sandbox/benchmark/theBenchmark.p',fact_270_ord__eq__le__subst) ).

thf(1071,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)],[211]) ).

thf(246,axiom,
    ! [A: num,B: num,C: num > real,D: real] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ord_less_eq_real @ ( C @ B ) @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_order__subst2) ).

thf(1187,plain,
    ! [A: num,B: num,C: num > real,D: real] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ord_less_eq_real @ ( C @ B ) @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ 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)],[246]) ).

thf(92,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_mult__le__mono2) ).

thf(674,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(196,axiom,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_add__diff__cancel__left_H) ).

thf(1026,plain,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(241,axiom,
    ! [A: real,B: num > real,C: num,D: num] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_num @ C @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_ord__eq__le__subst) ).

thf(1167,plain,
    ! [A: real,B: num > real,C: num,D: num] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_num @ C @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ 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)],[241]) ).

thf(121,axiom,
    ! [A: num,B: num] :
      ( ( A = B )
     => ( ord_less_eq_num @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_eq__refl) ).

thf(773,plain,
    ! [A: num,B: num] :
      ( ( A = B )
     => ( ord_less_eq_num @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(127,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ord_less_eq_nat @ A @ B )
        & ( ord_less_eq_nat @ C @ D ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_add__mono__thms__linordered__semiring_I1_J) ).

thf(794,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ord_less_eq_nat @ A @ B )
        & ( ord_less_eq_nat @ C @ D ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(65,axiom,
    ! [A: nat,B: nat] :
      ( ( one_one_nat
        = ( times_times_nat @ A @ B ) )
      = ( ( A = one_one_nat )
        & ( B = one_one_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_nat__1__eq__mult__iff) ).

thf(586,plain,
    ! [A: nat,B: nat] :
      ( ( one_one_nat
        = ( times_times_nat @ A @ B ) )
      = ( ( A = one_one_nat )
        & ( B = one_one_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(88,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ C @ B ) )
     => ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_add__right__imp__eq) ).

thf(662,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ C @ B ) )
     => ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(106,axiom,
    ! [A: real,B: real > $o] :
      ( ( member_real @ A @ ( collect_real @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_mem__Collect__eq) ).

thf(718,plain,
    ! [A: real,B: real > $o] :
      ( ( member_real @ A @ ( collect_real @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(154,axiom,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_ord__eq__le__subst) ).

thf(888,plain,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(283,axiom,
    ! [A: nat,B: real,C: real] :
      ( ( ( ord_less_eq_real @ B @ C )
        & ( genClo1015804716orrect @ A @ C ) )
     => ( genClo1015804716orrect @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_correct__closed) ).

thf(1301,plain,
    ! [A: nat,B: real,C: real] :
      ( ( ( ord_less_eq_real @ B @ C )
        & ( genClo1015804716orrect @ A @ C ) )
     => ( genClo1015804716orrect @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(61,axiom,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_is__num__normalize_I1_J) ).

thf(573,plain,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(303,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/sandbox/benchmark/theBenchmark.p',fact_24_abs__triangle__ineq2) ).

thf(1374,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)],[303]) ).

thf(234,axiom,
    ! [A: real] :
      ( ( times_times_real @ A @ one_one_real )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_mult_Oright__neutral) ).

thf(1146,plain,
    ! [A: real] :
      ( ( times_times_real @ A @ one_one_real )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(27,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_le__refl) ).

thf(430,plain,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(64,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
     => ( ord_less_eq_nat @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_add__le__imp__le__right) ).

thf(584,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
     => ( ord_less_eq_nat @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(133,axiom,
    ! [A: nat,B: nat,C: nat,D: nat,E: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ D ) @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ E ) )
        = ( minus_minus_nat @ D @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_nat__diff__add__eq2) ).

thf(819,plain,
    ! [A: nat,B: nat,C: nat,D: nat,E: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ D ) @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ E ) )
        = ( minus_minus_nat @ D @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(181,axiom,
    ! [A: num,B: num,C: real] :
      ( ( times_times_real @ ( numeral_numeral_real @ A ) @ ( times_times_real @ ( numeral_numeral_real @ B ) @ C ) )
      = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ A @ B ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_mult__numeral__left__semiring__numeral) ).

thf(975,plain,
    ! [A: num,B: num,C: real] :
      ( ( times_times_real @ ( numeral_numeral_real @ A ) @ ( times_times_real @ ( numeral_numeral_real @ B ) @ C ) )
      = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ A @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(24,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
      = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_diff__diff__left) ).

thf(423,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
      = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(18,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
      = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_diff__diff__add) ).

thf(402,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
      = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(308,axiom,
    ! [A: real,B: real,C: real > nat,D: nat] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_ord__le__eq__subst) ).

thf(1389,plain,
    ! [A: real,B: real,C: real > nat,D: nat] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(135,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( ord_less_eq_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_eq__refl) ).

thf(826,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( ord_less_eq_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(311,axiom,
    ! [A: num,B: real,C: real] :
      ( ( times_times_real @ ( numeral_numeral_real @ A ) @ ( minus_minus_real @ B @ C ) )
      = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ A ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_right__diff__distrib__numeral) ).

thf(1403,plain,
    ! [A: num,B: real,C: real] :
      ( ( times_times_real @ ( numeral_numeral_real @ A ) @ ( minus_minus_real @ B @ C ) )
      = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ A ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(349,axiom,
    ( ( numeral_numeral_nat @ one )
    = one_one_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_numeral__One) ).

thf(1520,plain,
    ( ( numeral_numeral_nat @ one )
    = one_one_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(21,axiom,
    ! [A: nat,B: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_diff__add__inverse2) ).

thf(413,plain,
    ! [A: nat,B: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(82,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
      = ( ord_less_eq_nat @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_nat__add__left__cancel__le) ).

thf(641,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
      = ( ord_less_eq_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(343,axiom,
    ! [A: real,B: real,C: real,D: real,E: real] :
      ( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ C )
        = ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
      = ( C
        = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_eq__add__iff2) ).

thf(1503,plain,
    ! [A: real,B: real,C: real,D: real,E: real] :
      ( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ C )
        = ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
      = ( C
        = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(166,axiom,
    ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_abs__triangle__ineq) ).

thf(936,plain,
    ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(302,axiom,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_diff__add__eq) ).

thf(1371,plain,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(161,axiom,
    ! [A: nat,B: nat,C: nat,D: nat,E: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D ) @ ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ E ) )
        = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ D ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_nat__le__add__iff1) ).

thf(919,plain,
    ! [A: nat,B: nat,C: nat,D: nat,E: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D ) @ ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ E ) )
        = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ D ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(269,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
      = ( ord_less_eq_real @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_add__le__cancel__left) ).

thf(1258,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
      = ( ord_less_eq_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(258,axiom,
    ! [A: real] :
      ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_mult__numeral__1) ).

thf(1224,plain,
    ! [A: real] :
      ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(72,axiom,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_order__subst1) ).

thf(611,plain,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(125,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
        = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc) ).

thf(787,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
        = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(248,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
      = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_right__diff__distrib_H) ).

thf(1194,plain,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
      = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(277,axiom,
    ! [A: real,B: real] :
      ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
      = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_abs__add__abs) ).

thf(1282,plain,
    ! [A: real,B: real] :
      ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
      = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(10,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
      = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_diff__mult__distrib2) ).

thf(377,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
      = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(233,axiom,
    ( ( abs_abs_real @ one_one_real )
    = one_one_real ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_abs__1) ).

thf(1144,plain,
    ( ( abs_abs_real @ one_one_real )
    = one_one_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(285,axiom,
    ! [A: real,B: real,C: real > num,D: num] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_num @ ( C @ B ) @ D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_order__subst2) ).

thf(1307,plain,
    ! [A: real,B: real,C: real > num,D: num] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_num @ ( C @ B ) @ D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(242,axiom,
    ( ( (=) @ real )
    = ( ^ [A: real,B: real] :
          ( ( ord_less_eq_real @ A @ B )
          & ( ord_less_eq_real @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_eq__iff) ).

thf(1175,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)],[242]) ).

thf(191,axiom,
    ! [A: real] :
      ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A )
      = ( plus_plus_real @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_mult__2) ).

thf(1011,plain,
    ! [A: real] :
      ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A )
      = ( plus_plus_real @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(23,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ A @ C )
       => ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
          = ( ord_less_eq_nat @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_le__diff__iff) ).

thf(419,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ A @ C )
       => ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
          = ( ord_less_eq_nat @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(5,axiom,
    ! [A: nat,B: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_add__diff__cancel__right_H) ).

thf(362,plain,
    ! [A: nat,B: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(59,axiom,
    ( plus_plus_nat
    = ( ^ [A: nat,B: nat] : ( plus_plus_nat @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_add_Ocommute) ).

thf(567,plain,
    ( plus_plus_nat
    = ( ^ [A: nat,B: nat] : ( plus_plus_nat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(44,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_le__antisym) ).

thf(509,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(203,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/sandbox/benchmark/theBenchmark.p',fact_311_complete__real) ).

thf(1043,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)],[203]) ).

thf(68,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_add__mono) ).

thf(599,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(304,axiom,
    ( times_times_real
    = ( ^ [A: real,B: real] : ( times_times_real @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_mult_Ocommute) ).

thf(1376,plain,
    ( times_times_real
    = ( ^ [A: real,B: real] : ( times_times_real @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(145,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
      = ( ord_less_eq_nat @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_add__le__cancel__left) ).

thf(858,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
      = ( ord_less_eq_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(50,axiom,
    ! [A: num,B: num,C: nat] :
      ( ( times_times_nat @ ( numeral_numeral_nat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ B ) @ C ) )
      = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ A @ B ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_mult__numeral__left__semiring__numeral) ).

thf(535,plain,
    ! [A: num,B: num,C: nat] :
      ( ( times_times_nat @ ( numeral_numeral_nat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ B ) @ C ) )
      = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ A @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(71,axiom,
    ! [A: num,B: num] :
      ( ( ord_less_eq_num @ A @ B )
      | ( ord_less_eq_num @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_linear) ).

thf(609,plain,
    ! [A: num,B: num] :
      ( ( ord_less_eq_num @ A @ B )
      | ( ord_less_eq_num @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(291,axiom,
    ( genClo2108747022bound1
    = ( ^ [A: nat > real > real] :
        ! [B: nat,C: real,D: real] :
          ( ( ( genClo1015804716orrect @ B @ D )
            & ( ord_less_eq_real @ C @ D ) )
         => ( ord_less_eq_real @ ( minus_minus_real @ ( A @ B @ D ) @ ( A @ B @ C ) ) @ ( times_times_real @ ( minus_minus_real @ D @ C ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_rho__bound1__def) ).

thf(1325,plain,
    ( genClo2108747022bound1
    = ( ^ [A: nat > real > real] :
        ! [B: nat,C: real,D: real] :
          ( ( ( genClo1015804716orrect @ B @ D )
            & ( ord_less_eq_real @ C @ D ) )
         => ( ord_less_eq_real @ ( minus_minus_real @ ( A @ B @ D ) @ ( A @ B @ C ) ) @ ( times_times_real @ ( minus_minus_real @ D @ C ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(197,axiom,
    ( ( neg_numeral_dbl_real @ one_one_real )
    = ( numeral_numeral_real @ ( bit0 @ one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_dbl__simps_I3_J) ).

thf(1029,plain,
    ( ( neg_numeral_dbl_real @ one_one_real )
    = ( numeral_numeral_real @ ( bit0 @ one ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(235,axiom,
    ! [A: num] :
      ( ( one_one_real
        = ( numeral_numeral_real @ A ) )
      = ( one = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_one__eq__numeral__iff) ).

thf(1149,plain,
    ! [A: num] :
      ( ( one_one_real
        = ( numeral_numeral_real @ A ) )
      = ( one = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(327,axiom,
    ! [A: num,B: num] :
      ( ( ord_less_eq_num @ ( bit0 @ A ) @ ( bit0 @ B ) )
      = ( ord_less_eq_num @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_semiring__norm_I71_J) ).

thf(1460,plain,
    ! [A: num,B: num] :
      ( ( ord_less_eq_num @ ( bit0 @ A ) @ ( bit0 @ B ) )
      = ( ord_less_eq_num @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(34,axiom,
    ! [A: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_one__le__numeral) ).

thf(462,plain,
    ! [A: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(221,axiom,
    ! [A: num] :
      ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ A ) )
      = ( numeral_numeral_nat @ ( plus_plus_num @ one @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_one__plus__numeral) ).

thf(1112,plain,
    ! [A: num] :
      ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ A ) )
      = ( numeral_numeral_nat @ ( plus_plus_num @ one @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(129,axiom,
    ! [A: nat,B: nat,C: nat > num,D: num] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_ord__le__eq__subst) ).

thf(799,plain,
    ! [A: nat,B: nat,C: nat > num,D: num] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(239,axiom,
    ( genClo2108747023bound2
    = ( ^ [A: nat > real > real] :
        ! [B: nat,C: real,D: real] :
          ( ( ( genClo1015804716orrect @ B @ D )
            & ( ord_less_eq_real @ C @ D ) )
         => ( ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ D @ C ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( A @ B @ D ) @ ( A @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_rho__bound2__def) ).

thf(1162,plain,
    ( genClo2108747023bound2
    = ( ^ [A: nat > real > real] :
        ! [B: nat,C: real,D: real] :
          ( ( ( genClo1015804716orrect @ B @ D )
            & ( ord_less_eq_real @ C @ D ) )
         => ( ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ D @ C ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( A @ B @ D ) @ ( A @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(243,axiom,
    ! [A: real] :
      ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_mult__numeral__1__right) ).

thf(1177,plain,
    ! [A: real] :
      ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(306,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( A
        = ( plus_plus_real @ B @ C ) )
     => ( ( minus_minus_real @ A @ D )
        = ( plus_plus_real @ B @ ( minus_minus_real @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_group__cancel_Osub1) ).

thf(1381,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( A
        = ( plus_plus_real @ B @ C ) )
     => ( ( minus_minus_real @ A @ D )
        = ( plus_plus_real @ B @ ( minus_minus_real @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(96,axiom,
    ! [A: real] :
      ( ( one_one_real = A )
      = ( A = one_one_real ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_one__reorient) ).

thf(685,plain,
    ! [A: real] :
      ( ( one_one_real = A )
      = ( A = one_one_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(17,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_diff__diff__cancel) ).

thf(399,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(176,axiom,
    ! [A: nat,B: nat,C: nat > real,D: real] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_real @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_order__subst2) ).

thf(959,plain,
    ! [A: nat,B: nat,C: nat > real,D: real] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_real @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ 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)],[176]) ).

thf(99,axiom,
    ( ( (=) @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( ord_less_eq_nat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_eq__iff) ).

thf(695,plain,
    ( ( (=) @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( ord_less_eq_nat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(123,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
      = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_mult_Oassoc) ).

thf(780,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
      = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(32,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
        = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2) ).

thf(455,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
        = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(58,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
     => ( ( ord_less_eq_nat @ C @ ( plus_plus_nat @ D @ B ) )
       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
         => ( ( ord_less_eq_nat @ C @ ( plus_plus_nat @ D @ B ) )
           => ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_add__le__add__imp__diff__le) ).

thf(563,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
     => ( ( ord_less_eq_nat @ C @ ( plus_plus_nat @ D @ B ) )
       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
         => ( ( ord_less_eq_nat @ C @ ( plus_plus_nat @ D @ B ) )
           => ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(322,axiom,
    ! [A: real,B: real,C: real] :
      ( ( A
        = ( minus_minus_real @ B @ C ) )
      = ( B
        = ( plus_plus_real @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_eq__diff__eq_H) ).

thf(1435,plain,
    ! [A: real,B: real,C: real] :
      ( ( A
        = ( minus_minus_real @ B @ C ) )
      = ( B
        = ( plus_plus_real @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(333,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_mult__numeral__1__right) ).

thf(1477,plain,
    ! [A: nat] :
      ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(299,axiom,
    ! [A: num,B: num] :
      ( ( times_times_num @ ( bit0 @ A ) @ ( bit0 @ B ) )
      = ( bit0 @ ( bit0 @ ( times_times_num @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_semiring__norm_I13_J) ).

thf(1364,plain,
    ! [A: num,B: num] :
      ( ( times_times_num @ ( bit0 @ A ) @ ( bit0 @ B ) )
      = ( bit0 @ ( bit0 @ ( times_times_num @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(87,axiom,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_order__subst2) ).

thf(658,plain,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(209,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 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_add__mono__thms__linordered__semiring_I1_J) ).

thf(1066,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 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(148,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_add__left__mono) ).

thf(868,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(284,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
      = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_ab__semigroup__mult__class_Omult__ac_I1_J) ).

thf(1304,plain,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
      = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(25,axiom,
    ( ( (=) @ num )
    = ( ^ [A: num,B: num] :
          ( ( ord_less_eq_num @ A @ B )
          & ( ord_less_eq_num @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_eq__iff) ).

thf(426,plain,
    ( ( (=) @ num )
    = ( ^ [A: num,B: num] :
          ( ( ord_less_eq_num @ A @ B )
          & ( ord_less_eq_num @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(331,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/sandbox/benchmark/theBenchmark.p',fact_279_ord__le__eq__subst) ).

thf(1467,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)],[331]) ).

thf(94,axiom,
    ( neg_numeral_dbl_real
    = ( ^ [A: real] : ( plus_plus_real @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_dbl__def) ).

thf(680,plain,
    ( neg_numeral_dbl_real
    = ( ^ [A: real] : ( plus_plus_real @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(84,axiom,
    ! [A: nat,B: nat,C: nat,D: nat,E: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D )
          = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ E ) )
        = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ D )
          = E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_nat__eq__add__iff1) ).

thf(648,plain,
    ! [A: nat,B: nat,C: nat,D: nat,E: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D )
          = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ E ) )
        = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ D )
          = E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(345,axiom,
    ! [A: real] :
      ( ( abs_abs_real @ ( abs_abs_real @ A ) )
      = ( abs_abs_real @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_abs__idempotent) ).

thf(1509,plain,
    ! [A: real] :
      ( ( abs_abs_real @ ( abs_abs_real @ A ) )
      = ( abs_abs_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(1,conjecture,
    ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(355,plain,
    ~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(134,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ A @ one_one_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_mult_Oright__neutral) ).

thf(823,plain,
    ! [A: nat] :
      ( ( times_times_nat @ A @ one_one_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(138,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
      = ( ord_less_eq_nat @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_add__le__cancel__right) ).

thf(836,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
      = ( ord_less_eq_nat @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(251,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C )
     => ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_add__le__imp__le__diff) ).

thf(1203,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C )
     => ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(253,axiom,
    ! [A: real,B: real > real,C: real,D: real] :
      ( ( ord_less_eq_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/sandbox/benchmark/theBenchmark.p',fact_249_order__subst1) ).

thf(1208,plain,
    ! [A: real,B: real > real,C: real,D: real] :
      ( ( ord_less_eq_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)],[253]) ).

thf(66,axiom,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_ord__le__eq__subst) ).

thf(589,plain,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(74,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_le__add__diff__inverse2) ).

thf(617,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(46,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ A @ one_one_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_mult_Ocomm__neutral) ).

thf(516,plain,
    ! [A: nat] :
      ( ( times_times_nat @ A @ one_one_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(104,axiom,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_add_Oassoc) ).

thf(712,plain,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(144,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_antisym) ).

thf(855,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(102,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( A
        = ( plus_plus_nat @ B @ C ) )
     => ( ( plus_plus_nat @ D @ A )
        = ( plus_plus_nat @ B @ ( plus_plus_nat @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_group__cancel_Oadd2) ).

thf(705,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( A
        = ( plus_plus_nat @ B @ C ) )
     => ( ( plus_plus_nat @ D @ A )
        = ( plus_plus_nat @ B @ ( plus_plus_nat @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(310,axiom,
    ! [A: real,B: real] :
      ( ( A = B )
      | ~ ( ord_less_eq_real @ A @ B )
      | ~ ( ord_less_eq_real @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_verit__la__disequality) ).

thf(1400,plain,
    ! [A: real,B: real] :
      ( ( A = B )
      | ~ ( ord_less_eq_real @ A @ B )
      | ~ ( ord_less_eq_real @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(20,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ B )
       => ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ B @ C ) )
          = ( ord_less_eq_nat @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_le__diff__iff_H) ).

thf(409,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ B )
       => ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ B @ C ) )
          = ( ord_less_eq_nat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(260,axiom,
    ! [A: real] :
      ( ( abs_abs_real @ ( abs_abs_real @ A ) )
      = ( abs_abs_real @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_abs__abs) ).

thf(1230,plain,
    ! [A: real] :
      ( ( abs_abs_real @ ( abs_abs_real @ A ) )
      = ( abs_abs_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(336,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
     => ( ord_less_eq_real @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_add__le__imp__le__right) ).

thf(1484,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
     => ( ord_less_eq_real @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(321,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/sandbox/benchmark/theBenchmark.p',fact_209_diff__mono) ).

thf(1432,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)],[321]) ).

thf(126,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_add_Oassoc) ).

thf(791,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(31,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ord_less_eq_nat @ A @ B )
       => ~ ( ord_less_eq_nat @ B @ C ) )
     => ( ( ( ord_less_eq_nat @ B @ A )
         => ~ ( ord_less_eq_nat @ A @ C ) )
       => ( ( ( ord_less_eq_nat @ A @ C )
           => ~ ( ord_less_eq_nat @ C @ B ) )
         => ( ( ( ord_less_eq_nat @ C @ B )
             => ~ ( ord_less_eq_nat @ B @ A ) )
           => ( ( ( ord_less_eq_nat @ B @ C )
               => ~ ( ord_less_eq_nat @ C @ A ) )
             => ~ ( ( ord_less_eq_nat @ C @ A )
                 => ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_le__cases3) ).

thf(441,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ord_less_eq_nat @ A @ B )
       => ~ ( ord_less_eq_nat @ B @ C ) )
     => ( ( ( ord_less_eq_nat @ B @ A )
         => ~ ( ord_less_eq_nat @ A @ C ) )
       => ( ( ( ord_less_eq_nat @ A @ C )
           => ~ ( ord_less_eq_nat @ C @ B ) )
         => ( ( ( ord_less_eq_nat @ C @ B )
             => ~ ( ord_less_eq_nat @ B @ A ) )
           => ( ( ( ord_less_eq_nat @ B @ C )
               => ~ ( ord_less_eq_nat @ C @ A ) )
             => ~ ( ( ord_less_eq_nat @ C @ A )
                 => ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(262,axiom,
    ! [A: num] :
      ( ( ord_less_eq_num @ A @ one )
      = ( A = one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_le__num__One__iff) ).

thf(1235,plain,
    ! [A: num] :
      ( ( ord_less_eq_num @ A @ one )
      = ( A = one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(62,axiom,
    ! [A: nat > $o,B: nat,C: nat] :
      ( ( A @ B )
     => ( ! [D: nat] :
            ( ( A @ D )
           => ( ord_less_eq_nat @ D @ C ) )
       => ? [D: nat] :
            ( ( A @ D )
            & ! [E: nat] :
                ( ( A @ E )
               => ( ord_less_eq_nat @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_Nat_Oex__has__greatest__nat) ).

thf(576,plain,
    ! [A: nat > $o,B: nat,C: nat] :
      ( ( A @ B )
     => ( ! [D: nat] :
            ( ( A @ D )
           => ( ord_less_eq_nat @ D @ C ) )
       => ? [D: nat] :
            ( ( A @ D )
            & ! [E: nat] :
                ( ( A @ E )
               => ( ord_less_eq_nat @ E @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(4,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( minus_minus_nat @ A @ B ) @ C )
      = ( minus_minus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_diff__mult__distrib) ).

thf(359,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( minus_minus_nat @ A @ B ) @ C )
      = ( minus_minus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(278,axiom,
    ! [A: num] : ( ord_less_eq_num @ one @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_semiring__norm_I68_J) ).

thf(1285,plain,
    ! [A: num] : ( ord_less_eq_num @ one @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(295,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/sandbox/benchmark/theBenchmark.p',fact_306_le__cases3) ).

thf(1336,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)],[295]) ).

thf(53,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_add__left__cancel) ).

thf(544,plain,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(201,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/sandbox/benchmark/theBenchmark.p',fact_206_diff__eq__diff__less__eq) ).

thf(1038,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)],[201]) ).

thf(8,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
      = ( minus_minus_nat @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_add__diff__cancel__right) ).

thf(370,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
      = ( minus_minus_nat @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(297,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/sandbox/benchmark/theBenchmark.p',fact_171_diff__right__commute) ).

thf(1358,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)],[297]) ).

thf(114,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ C @ B ) )
      = ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_add_Oright__cancel) ).

thf(744,plain,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ C @ B ) )
      = ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(231,axiom,
    ( ( plus_plus_real @ one_one_real @ one_one_real )
    = ( numeral_numeral_real @ ( bit0 @ one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_one__add__one) ).

thf(1141,plain,
    ( ( plus_plus_real @ one_one_real @ one_one_real )
    = ( numeral_numeral_real @ ( bit0 @ one ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(195,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/sandbox/benchmark/theBenchmark.p',fact_208_diff__left__mono) ).

thf(1023,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)],[195]) ).

thf(257,axiom,
    ! [A: num,B: num] :
      ( ( times_times_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) )
      = ( numeral_numeral_real @ ( times_times_num @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_numeral__times__numeral) ).

thf(1221,plain,
    ! [A: num,B: num] :
      ( ( times_times_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) )
      = ( numeral_numeral_real @ ( times_times_num @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(147,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ~ ! [C: nat] :
            ( B
           != ( plus_plus_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_less__eqE) ).

thf(864,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ~ ! [C: nat] :
            ( B
           != ( plus_plus_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(319,axiom,
    ! [A: num] :
      ( ( numeral_numeral_real @ ( bit0 @ A ) )
      = ( plus_plus_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_numeral__Bit0) ).

thf(1427,plain,
    ! [A: num] :
      ( ( numeral_numeral_real @ ( bit0 @ A ) )
      = ( plus_plus_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(109,axiom,
    ! [A: num,B: num] :
      ( ( A = B )
      | ~ ( ord_less_eq_num @ A @ B )
      | ~ ( ord_less_eq_num @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_verit__la__disequality) ).

thf(727,plain,
    ! [A: num,B: num] :
      ( ( A = B )
      | ~ ( ord_less_eq_num @ A @ B )
      | ~ ( ord_less_eq_num @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(190,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_ring__class_Oring__distribs_I2_J) ).

thf(1008,plain,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(274,axiom,
    ! [A: num] :
      ( ( plus_plus_num @ one @ A )
      = ( plus_plus_num @ A @ one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_add__One__commute) ).

thf(1272,plain,
    ! [A: num] :
      ( ( plus_plus_num @ one @ A )
      = ( plus_plus_num @ A @ one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(204,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_comm__semiring__class_Odistrib) ).

thf(1052,plain,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(344,axiom,
    ! [A: num] :
      ( ( times_times_num @ one @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_semiring__norm_I12_J) ).

thf(1506,plain,
    ! [A: num] :
      ( ( times_times_num @ one @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(13,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ A @ C )
       => ( ( minus_minus_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
          = ( minus_minus_nat @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_Nat_Odiff__diff__eq) ).

thf(386,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ A @ C )
       => ( ( minus_minus_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
          = ( minus_minus_nat @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(217,axiom,
    ! [A: real,B: real,C: real,D: real,E: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
      = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_ordered__ring__class_Ole__add__iff2) ).

thf(1094,plain,
    ! [A: real,B: real,C: real,D: real,E: real] :
      ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
      = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(182,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ ( minus_minus_real @ B @ C ) )
      = ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_le__diff__eq) ).

thf(978,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ ( minus_minus_real @ B @ C ) )
      = ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(264,axiom,
    ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__092_060open_062_It_A_N_As_J_A_K_A_I1_A_N_A_092_060rho_062_J_A_092_060le_062_AD_Aq_At_A_N_AD_Aq_As_092_060close_062) ).

thf(1240,plain,
    ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(186,axiom,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_distrib__right) ).

thf(991,plain,
    ! [A: real,B: real,C: real] :
      ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
      = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(141,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( A = B )
        & ( C = D ) )
     => ( ( plus_plus_real @ A @ C )
        = ( plus_plus_real @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_add__mono__thms__linordered__semiring_I4_J) ).

thf(845,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( A = B )
        & ( C = D ) )
     => ( ( plus_plus_real @ A @ C )
        = ( plus_plus_real @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(317,axiom,
    ! [A: num] :
      ( ( ( numeral_numeral_nat @ A )
        = one_one_nat )
      = ( A = one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_numeral__eq__one__iff) ).

thf(1421,plain,
    ! [A: num] :
      ( ( ( numeral_numeral_nat @ A )
        = one_one_nat )
      = ( A = one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(78,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ one_one_nat @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_mult_Oleft__neutral) ).

thf(627,plain,
    ! [A: nat] :
      ( ( times_times_nat @ one_one_nat @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(244,axiom,
    ! [A: real,B: real] :
      ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
      = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_abs__minus__commute) ).

thf(1180,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)],[244]) ).

thf(91,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ C @ B ) )
      = ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_add__right__cancel) ).

thf(671,plain,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ C @ B ) )
      = ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(290,axiom,
    ! [A: real,B: nat > real,C: nat,D: nat] :
      ( ( ord_less_eq_real @ A @ ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_order__subst1) ).

thf(1321,plain,
    ! [A: real,B: nat > real,C: nat,D: nat] :
      ( ( ord_less_eq_real @ A @ ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ 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)],[290]) ).

thf(97,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
        = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc) ).

thf(688,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
        = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(348,axiom,
    ! [A: num] :
      ( ( abs_abs_real @ ( numeral_numeral_real @ A ) )
      = ( numeral_numeral_real @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_abs__numeral) ).

thf(1517,plain,
    ! [A: num] :
      ( ( abs_abs_real @ ( numeral_numeral_real @ A ) )
      = ( numeral_numeral_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(225,axiom,
    ! [A: real] : ( ord_less_eq_real @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_order__refl) ).

thf(1126,plain,
    ! [A: real] : ( ord_less_eq_real @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(7,axiom,
    ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_diff__le__self) ).

thf(368,plain,
    ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(41,axiom,
    ! [A: nat,B: num > nat,C: num,D: num] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_num @ C @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_ord__eq__le__subst) ).

thf(495,plain,
    ! [A: nat,B: num > nat,C: num,D: num] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_num @ C @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(314,axiom,
    ! [A: num,B: num] :
      ( ( plus_plus_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) )
      = ( numeral_numeral_real @ ( plus_plus_num @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_numeral__plus__numeral) ).

thf(1412,plain,
    ! [A: num,B: num] :
      ( ( plus_plus_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) )
      = ( numeral_numeral_real @ ( plus_plus_num @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(177,axiom,
    ! [A: real,B: real,C: real] :
      ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_diff__diff__add) ).

thf(963,plain,
    ! [A: real,B: real,C: real] :
      ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(155,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_add__left__cancel) ).

thf(896,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(335,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_real @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_antisym) ).

thf(1481,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)],[335]) ).

thf(85,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_combine__common__factor) ).

thf(652,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(14,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
      = ( minus_minus_nat @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_add__diff__cancel__left) ).

thf(390,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
      = ( minus_minus_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(266,axiom,
    ! [A: num] :
      ( ( times_times_num @ A @ one )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_semiring__norm_I11_J) ).

thf(1244,plain,
    ! [A: num] :
      ( ( times_times_num @ A @ one )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(171,axiom,
    ! [A: num] :
      ( ( times_times_num @ ( bit0 @ one ) @ A )
      = ( bit0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_num__double) ).

thf(946,plain,
    ! [A: num] :
      ( ( times_times_num @ ( bit0 @ one ) @ A )
      = ( bit0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(219,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_add__right__mono) ).

thf(1101,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(339,axiom,
    ! [A: num,B: real,C: real] :
      ( ( times_times_real @ ( numeral_numeral_real @ A ) @ ( plus_plus_real @ B @ C ) )
      = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ A ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_distrib__left__numeral) ).

thf(1491,plain,
    ! [A: num,B: real,C: real] :
      ( ( times_times_real @ ( numeral_numeral_real @ A ) @ ( plus_plus_real @ B @ C ) )
      = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ A ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(39,axiom,
    ! [A: num,B: num,C: num] :
      ( ( ( ord_less_eq_num @ A @ B )
       => ~ ( ord_less_eq_num @ B @ C ) )
     => ( ( ( ord_less_eq_num @ B @ A )
         => ~ ( ord_less_eq_num @ A @ C ) )
       => ( ( ( ord_less_eq_num @ A @ C )
           => ~ ( ord_less_eq_num @ C @ B ) )
         => ( ( ( ord_less_eq_num @ C @ B )
             => ~ ( ord_less_eq_num @ B @ A ) )
           => ( ( ( ord_less_eq_num @ B @ C )
               => ~ ( ord_less_eq_num @ C @ A ) )
             => ~ ( ( ord_less_eq_num @ C @ A )
                 => ~ ( ord_less_eq_num @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_le__cases3) ).

thf(478,plain,
    ! [A: num,B: num,C: num] :
      ( ( ( ord_less_eq_num @ A @ B )
       => ~ ( ord_less_eq_num @ B @ C ) )
     => ( ( ( ord_less_eq_num @ B @ A )
         => ~ ( ord_less_eq_num @ A @ C ) )
       => ( ( ( ord_less_eq_num @ A @ C )
           => ~ ( ord_less_eq_num @ C @ B ) )
         => ( ( ( ord_less_eq_num @ C @ B )
             => ~ ( ord_less_eq_num @ B @ A ) )
           => ( ( ( ord_less_eq_num @ B @ C )
               => ~ ( ord_less_eq_num @ C @ A ) )
             => ~ ( ( ord_less_eq_num @ C @ A )
                 => ~ ( ord_less_eq_num @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(254,axiom,
    ! [A: nat,B: real,C: real] :
      ( ( ( genClo1015804716orrect @ A @ C )
        & ( ord_less_eq_real @ B @ C ) )
     => ( ord_less_eq_real @ ( minus_minus_real @ ( genClo1161277105lle_PC @ A @ C ) @ ( genClo1161277105lle_PC @ A @ B ) ) @ ( times_times_real @ ( minus_minus_real @ C @ B ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_rate__1) ).

thf(1212,plain,
    ! [A: nat,B: real,C: real] :
      ( ( ( genClo1015804716orrect @ A @ C )
        & ( ord_less_eq_real @ B @ C ) )
     => ( ord_less_eq_real @ ( minus_minus_real @ ( genClo1161277105lle_PC @ A @ C ) @ ( genClo1161277105lle_PC @ A @ B ) ) @ ( times_times_real @ ( minus_minus_real @ C @ B ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(12,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
      = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_right__diff__distrib_H) ).

thf(383,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
      = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(156,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ one_one_nat @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_comm__monoid__mult__class_Omult__1) ).

thf(899,plain,
    ! [A: nat] :
      ( ( times_times_nat @ one_one_nat @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(90,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( ord_less_eq_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_eq__imp__le) ).

thf(667,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( ord_less_eq_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(281,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/sandbox/benchmark/theBenchmark.p',fact_173_diff__eq__diff__eq) ).

thf(1294,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)],[281]) ).

thf(228,axiom,
    ! [A: num,B: num] :
      ( ( plus_plus_num @ ( bit0 @ A ) @ ( bit0 @ B ) )
      = ( bit0 @ ( plus_plus_num @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_semiring__norm_I6_J) ).

thf(1133,plain,
    ! [A: num,B: num] :
      ( ( plus_plus_num @ ( bit0 @ A ) @ ( bit0 @ B ) )
      = ( bit0 @ ( plus_plus_num @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(75,axiom,
    ! [A: num] : ( ord_less_eq_num @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_order__refl) ).

thf(620,plain,
    ! [A: num] : ( ord_less_eq_num @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(346,axiom,
    ! [A: num] :
      ( ( ( numeral_numeral_real @ A )
        = one_one_real )
      = ( A = one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_numeral__eq__one__iff) ).

thf(1512,plain,
    ! [A: num] :
      ( ( ( numeral_numeral_real @ A )
        = one_one_real )
      = ( A = one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(28,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
      = ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_mult_Oleft__commute) ).

thf(432,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
      = ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(137,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_ab__semigroup__add__class_Oadd__ac_I1_J) ).

thf(833,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(218,axiom,
    ! [A: num] :
      ( ( bit0 @ A )
     != one ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_semiring__norm_I85_J) ).

thf(1097,plain,
    ! [A: num] :
      ( ( bit0 @ A )
     != one ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(19,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ A @ C )
       => ( ( ( minus_minus_nat @ B @ A )
            = ( minus_minus_nat @ C @ A ) )
          = ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_eq__diff__iff) ).

thf(405,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ A @ C )
       => ( ( ( minus_minus_nat @ B @ A )
            = ( minus_minus_nat @ C @ A ) )
          = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(352,axiom,
    ( ( abs_abs_real @ one_one_real )
    = one_one_real ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_abs__one) ).

thf(1527,plain,
    ( ( abs_abs_real @ one_one_real )
    = one_one_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(334,axiom,
    genClo2108747023bound2 @ d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_rb2) ).

thf(1480,plain,
    genClo2108747023bound2 @ d,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(9,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = C )
     => ( A
        = ( minus_minus_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_add__implies__diff) ).

thf(373,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = C )
     => ( A
        = ( minus_minus_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(287,axiom,
    genClo1015804716orrect @ q @ t,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_corr__q) ).

thf(1314,plain,
    genClo1015804716orrect @ q @ t,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(43,axiom,
    ! [A: nat,B: nat] :
      ( ( ( times_times_nat @ A @ B )
        = one_one_nat )
      = ( ( A = one_one_nat )
        & ( B = one_one_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_nat__mult__eq__1__iff) ).

thf(506,plain,
    ! [A: nat,B: nat] :
      ( ( ( times_times_nat @ A @ B )
        = one_one_nat )
      = ( ( A = one_one_nat )
        & ( B = one_one_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(130,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
      | ( ord_less_eq_nat @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_linear) ).

thf(807,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
      | ( ord_less_eq_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(119,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
      | ~ ( ord_less_eq_nat @ A @ B )
      | ~ ( ord_less_eq_nat @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_verit__la__disequality) ).

thf(767,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
      | ~ ( ord_less_eq_nat @ A @ B )
      | ~ ( ord_less_eq_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(128,axiom,
    ! [A: num,B: num] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ord_less_eq_num @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_antisym) ).

thf(796,plain,
    ! [A: num,B: num] :
      ( ( ord_less_eq_num @ A @ B )
     => ( ( ord_less_eq_num @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(153,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_order__refl) ).

thf(886,plain,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(199,axiom,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_add__diff__cancel__right_H) ).

thf(1033,plain,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(249,axiom,
    ! [A: real,B: real,C: real > nat,D: nat] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_nat @ ( C @ B ) @ D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_order__subst2) ).

thf(1197,plain,
    ! [A: real,B: real,C: real > nat,D: nat] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_eq_nat @ ( C @ B ) @ D )
       => ( ! [E: real,F: real] :
              ( ( ord_less_eq_real @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(185,axiom,
    ! [A: real,B: num > real,C: num,D: num] :
      ( ( ord_less_eq_real @ A @ ( B @ C ) )
     => ( ( ord_less_eq_num @ C @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ E @ F )
             => ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_order__subst1) ).

thf(987,plain,
    ! [A: real,B: num > real,C: num,D: num] :
      ( ( ord_less_eq_real @ A @ ( B @ C ) )
     => ( ( ord_less_eq_num @ C @ D )
       => ( ! [E: num,F: num] :
              ( ( ord_less_eq_num @ 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)],[185]) ).

thf(35,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ord_less_eq_nat @ A @ B )
        & ( C = D ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_add__mono__thms__linordered__semiring_I3_J) ).

thf(464,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ord_less_eq_nat @ A @ B )
        & ( C = D ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(270,axiom,
    ( ( plus_plus_num @ one @ one )
    = ( bit0 @ one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_semiring__norm_I2_J) ).

thf(1261,plain,
    ( ( plus_plus_num @ one @ one )
    = ( bit0 @ one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(236,axiom,
    ! [A: num] :
      ( ( one_one_nat
        = ( numeral_numeral_nat @ A ) )
      = ( one = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_one__eq__numeral__iff) ).

thf(1152,plain,
    ! [A: num] :
      ( ( one_one_nat
        = ( numeral_numeral_nat @ A ) )
      = ( one = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(354,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( plus_plus_real @ ( minus_minus_real @ B @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_le__add__diff__inverse2) ).

thf(1532,plain,
    ! [A: real,B: real] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( plus_plus_real @ ( minus_minus_real @ B @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(305,axiom,
    ! [A: real,B: real,C: real] :
      ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
      = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_diff__diff__eq2) ).

thf(1378,plain,
    ! [A: real,B: real,C: real] :
      ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
      = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(83,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
        = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2) ).

thf(644,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
        = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(33,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_mult__le__mono1) ).

thf(459,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(149,axiom,
    ! [A: set_real] :
      ( ( collect_real
        @ ^ [B: real] : ( member_real @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Collect__mem__eq) ).

thf(871,plain,
    ! [A: set_real] :
      ( ( collect_real
        @ ^ [B: real] : ( member_real @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(77,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_le__add__diff) ).

thf(624,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(139,axiom,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
      = ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_add_Oleft__commute) ).

thf(839,plain,
    ! [A: real,B: real,C: real] :
      ( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
      = ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(342,axiom,
    ! [A: num] :
      ( ( ord_less_eq_real @ ( numeral_numeral_real @ A ) @ one_one_real )
      = ( ord_less_eq_num @ A @ one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_numeral__le__one__iff) ).

thf(1500,plain,
    ! [A: num] :
      ( ( ord_less_eq_real @ ( numeral_numeral_real @ A ) @ one_one_real )
      = ( ord_less_eq_num @ A @ one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(108,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( A = B )
        & ( C = D ) )
     => ( ( plus_plus_nat @ A @ C )
        = ( plus_plus_nat @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add__mono__thms__linordered__semiring_I4_J) ).

thf(723,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( A = B )
        & ( C = D ) )
     => ( ( plus_plus_nat @ A @ C )
        = ( plus_plus_nat @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(300,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/sandbox/benchmark/theBenchmark.p',fact_25_abs__triangle__ineq3) ).

thf(1367,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)],[300]) ).

thf(162,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_add_Oleft__cancel) ).

thf(923,plain,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(328,axiom,
    ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_abs__ge__self) ).

thf(1463,plain,
    ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(116,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_le__square) ).

thf(755,plain,
    ! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(192,axiom,
    ! [A: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_one__le__numeral) ).

thf(1014,plain,
    ! [A: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(180,axiom,
    ! [A: real,B: real,C: real,D: real,E: real] :
      ( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ C )
        = ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
      = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C )
        = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_eq__add__iff1) ).

thf(972,plain,
    ! [A: real,B: real,C: real,D: real,E: real] :
      ( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ C )
        = ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
      = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C )
        = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(1574,plain,
    $false,
    inference(cvc4,[status(thm)],[1036,809,1454,1031,1315,941,777,666,365,1369,1083,468,1005,1406,730,1068,1522,994,741,1205,1269,655,677,597,1486,523,1158,582,1041,861,1497,550,1164,715,1275,1233,945,1063,538,930,814,1327,747,913,1386,1475,1529,1055,1287,1430,1330,1279,949,934,1191,902,638,1247,770,1115,1494,969,606,881,416,475,1418,1136,1020,966,1183,1489,1415,492,1465,634,734,956,1119,396,527,602,981,877,692,428,1201,1104,849,380,1438,1311,1057,512,942,439,910,1091,952,1255,1123,1217,630,1238,916,1457,830,1079,757,1128,842,852,435,682,1407,1291,710,1350,519,615,1227,783,1397,697,1089,874,1143,1138,356,471,1361,554,1424,1214,1446,1016,1155,547,622,393,701,1297,738,1266,1131,1060,984,721,569,503,1525,1263,997,1333,1318,1241,541,765,1515,953,926,1086,938,1466,558,1071,1187,674,1026,1167,773,794,586,662,718,888,1301,573,1374,1146,430,584,819,975,423,402,1389,826,1403,1520,413,641,1503,936,1371,919,1258,1224,611,787,1194,1282,377,1144,1307,1175,1011,419,362,567,509,1043,599,1376,858,535,609,1325,1029,1149,1460,462,1112,799,1162,1177,1381,685,399,959,695,780,455,563,1435,1477,1364,658,1066,868,1304,426,1467,680,648,1509,355,823,836,1203,1208,589,617,516,712,855,705,1400,409,1230,1484,1432,791,441,1235,576,359,1285,1336,544,1038,370,1358,744,1141,1023,1221,864,1427,727,1008,1272,1052,1506,386,1094,978,1240,991,845,1421,627,1180,671,1321,688,1517,1126,368,495,1412,963,896,1481,652,390,1244,946,1101,1491,478,1212,383,899,667,1294,1133,620,1512,432,833,1097,405,1527,1480,373,1314,506,807,767,796,886,1033,1197,987,464,1261,1152,1532,1378,644,459,871,624,839,1500,723,1367,923,1463,755,1014,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : ITP062^1 : TPTP v8.2.0. Released v7.5.0.
% 0.13/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n010.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 17:00:09 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.95/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.70/1.15  % [INFO] 	 Parsing done (285ms). 
% 2.04/1.16  % [INFO] 	 Running in sequential loop mode. 
% 2.71/1.39  % [INFO] 	 eprover registered as external prover. 
% 2.71/1.40  % [INFO] 	 cvc4 registered as external prover. 
% 2.93/1.40  % [INFO] 	 Scanning for conjecture ... 
% 3.10/1.49  % [INFO] 	 Found a conjecture (or negated_conjecture) and 352 axioms. Running axiom selection ... 
% 3.42/1.59  % [INFO] 	 Axiom selection finished. Selected 352 axioms (removed 0 axioms). 
% 4.11/1.80  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 4.42/1.82  % [INFO] 	 Type checking passed. 
% 4.42/1.82  % [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 ... 
% 23.63/6.63  % External prover 'cvc4' found a proof!
% 23.63/6.63  % [INFO] 	 Killing All external provers ... 
% 23.63/6.63  % Time passed: 6100ms (effective reasoning time: 5463ms)
% 23.63/6.63  % 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)>
% 23.63/6.64  % Axioms used in derivation (352): fact_67_le__add__diff__inverse2, fact_34_abs__abs, fact_299_eq__refl, fact_320_left__add__mult__distrib, fact_178_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2, fact_213_left__diff__distrib_H, fact_41_mult_Oleft__neutral, fact_9_Eq2, fact_196_one__le__numeral, fact_27_numeral__eq__iff, fact_252_order__subst1, fact_301_le__cases, fact_316_nat__le__add__iff1, fact_210_right__diff__distrib_H, fact_93_one__reorient, fact_126_add__mono, fact_65_semiring__norm_I68_J, fact_106_add_Oleft__commute, fact_245_nat__1__add__1, fact_154_diff__eq__eq, fact_193_eq__add__iff1, fact_1_rb1, fact_175_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add, fact_161_square__diff__one__factored, fact_42_mult_Oleft__neutral, fact_335_diff__le__mono2, fact_62_semiring__norm_I11_J, fact_292_antisym, fact_4_Eq4, fact_223_mult__2__right, fact_109_add__right__imp__eq, fact_311_complete__real, fact_240_order__refl, fact_302_le__cases, fact_287_ord__le__eq__subst, fact_242_semiring__norm_I6_J, fact_347_diff__mult__distrib2, fact_338_mult__le__mono2, fact_231_sin__bound__lemma, fact_189_le__diff__eq, fact_110_add__right__imp__eq, fact_334_le__diff__iff_H, fact_194_numeral__Bit0, fact_100_add_Oassoc, fact_253_order__subst1, fact_308_le__cases3, fact_235_mult__diff__mult, fact_163_mult_Oleft__commute, fact_119_le__iff__add, fact_184_add__le__add__imp__diff__le, fact_201_ordered__ring__class_Ole__add__iff2, fact_350_Nat_Ole__imp__diff__is__add, fact_206_diff__eq__diff__less__eq, fact_198_abs__triangle__ineq, fact_328_Nat_Oadd__diff__assoc, fact_349_diff__commute, fact_243_semiring__norm_I2_J, fact_150_diff__add__eq, fact_183_le__add__diff, fact_22_numeral__le__iff, fact_176_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse, fact_227_mult__numeral__1__right, fact_38_add__le__cancel__left, fact_122_less__eqE, fact_17_mult__numeral__left__semiring__numeral, fact_218_abs__mult, fact_89_ab__semigroup__add__class_Oadd__ac_I1_J, fact_8_corr__p, fact_113_one__plus__numeral__commute, fact_111_le__num__One__iff, fact_120_add__right__mono, fact_33_abs__idempotent, fact_55_diff__add__cancel, fact_271_ord__eq__le__subst, fact_78_num__double, fact_182_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2, fact_214_right__diff__distrib, fact_281_ord__le__eq__subst, fact_76_numeral__eq__one__iff, fact_155_group__cancel_Osub1, fact_283_ord__le__eq__subst, fact_112_one__plus__numeral__commute, fact_69_le__add__diff__inverse, fact_244_dbl__simps_I5_J, fact_160_abs__one, fact_179_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2, fact_291_antisym, fact_32_semiring__norm_I87_J, fact_247_numerals_I1_J, fact_262_order__subst2, fact_229_mult__numeral__1, fact_294_linear, fact_132_add__mono__thms__linordered__semiring_I3_J, fact_323_nat__add__left__cancel__le, fact_307_le__cases3, fact_135_distrib__right, fact_344_le__trans, fact_40_mult_Oright__neutral, fact_59_mem__Collect__eq, fact_268_verit__la__disequality, fact_195_numeral__Bit0, fact_212_left__diff__distrib_H, fact_43_numeral__plus__numeral, fact_174_rho__bound2__def, fact_149_diff__add__eq__diff__diff__swap, fact_16_semiring__norm_I83_J, fact_60_Collect__mem__eq, fact_204_abs__triangle__ineq4, fact_233_rate__2, fact_286_ord__le__eq__subst, fact_277_ord__eq__le__subst, fact_107_add__left__imp__eq, fact_300_le__cases, fact_141_ring__class_Oring__distribs_I1_J, fact_251_order__subst1, fact_5_Eq3, fact_18_mult__numeral__left__semiring__numeral, fact_104_add_Ocommute, fact_191_square__diff__square__factored, fact_288_eq__iff, fact_125_add__mono, fact_73_distrib__left__numeral, fact_158_comm__monoid__mult__class_Omult__1, fact_146_add__implies__diff, fact_332_diff__le__mono, fact_68_le__add__diff__inverse, fact_312_PC__monotone, fact_257_order__subst1, fact_58_abs__1, fact_310_antisym__conv, fact_203_abs__diff__triangle__ineq, fact_180_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc, fact_254_order__subst1, fact_133_combine__common__factor, fact_232_rate__1, fact_256_order__subst1, fact_219_abs__minus__commute, fact_305_order_Otrans, fact_152_add__diff__eq, fact_57_abs__add__abs, fact_10__092_060open_062_It_A_N_As_J_A_K_A_I1_A_N_A_092_060rho_062_J_A_092_060le_062_AD_Aq_At_A_N_AD_Aq_As_092_060close_062, fact_86_numeral__le__one__iff, fact_147_diff__diff__add, fact_84_one__add__one, fact_282_ord__le__eq__subst, fact_134_combine__common__factor, fact_88_ab__semigroup__add__class_Oadd__ac_I1_J, fact_138_distrib__left, fact_315_nat__eq__add__iff2, fact_64_semiring__norm_I71_J, fact_230_abs__triangle__ineq2__sym, fact_280_ord__le__eq__subst, fact_37_add__le__cancel__left, fact_148_diff__diff__add, fact_317_nat__le__add__iff2, fact_72_distrib__left__numeral, fact_156_mult_Ocomm__neutral, fact_340_mult__le__mono, fact_216_abs__ge__self, fact_313_verit__eq__simplify_I10_J, fact_82_numeral__plus__one, fact_101_add_Oleft__cancel, fact_269_verit__la__disequality, fact_25_abs__triangle__ineq3, fact_75_one__eq__numeral__iff, fact_0_rb2, fact_153_eq__diff__eq, fact_85_one__add__one, fact_49_add__diff__cancel__right, fact_190_diff__le__eq, fact_172_diff__right__commute, fact_177_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right, fact_348_diff__mult__distrib, fact_205_abs__diff__le__iff, fact_202_ordered__ring__class_Ole__add__iff1, fact_11_left__diff__distrib__numeral, fact_322_nat__mult__eq__1__iff, fact_143_le__numeral__extra_I4_J, fact_258_order__subst2, fact_24_abs__triangle__ineq2, fact_215_left__diff__distrib, fact_327_Nat_Oadd__diff__assoc2, fact_26_numeral__eq__iff, fact_209_diff__mono, fact_274_ord__eq__le__subst, fact_165_mult_Ocommute, fact_289_eq__iff, fact_87_numeral__le__one__iff, fact_246_add__One__commute, fact_115_add__le__imp__le__right, fact_168_mult_Oassoc, fact_309_antisym__conv, fact_234_dbl__simps_I3_J, fact_159_comm__monoid__mult__class_Omult__1, fact_6_corr__q, fact_171_diff__right__commute, fact_61_semiring__norm_I13_J, fact_98_group__cancel_Oadd2, fact_285_ord__le__eq__subst, fact_114_correct__closed, fact_255_order__subst1, fact_295_linear, fact_35_add__le__cancel__right, fact_20_numeral__times__numeral, fact_241_eq__diff__eq_H, fact_318_nat__diff__add__eq1, fact_186_diff__add, fact_63_semiring__norm_I12_J, fact_144_le__numeral__extra_I4_J, fact_326_Nat_Odiff__diff__right, fact_173_diff__eq__diff__eq, fact_331_Nat_Odiff__diff__eq, fact_44_numeral__plus__numeral, fact_30_add__right__cancel, fact_53_add__diff__cancel__left, fact_324_diff__diff__cancel, fact_102_add_Oright__cancel, fact_217_abs__le__D1, fact_129_add__mono__thms__linordered__semiring_I2_J, fact_239_order__refl, fact_336_Nat_Oex__has__greatest__nat, fact_97_group__cancel_Oadd2, fact_71_distrib__right__numeral, fact_50_add__diff__cancel__right, fact_226_mult__numeral__1__right, fact_15_semiring__norm_I85_J, fact_341_le__antisym, fact_279_ord__le__eq__subst, fact_237_okRead1__def, fact_140_comm__semiring__class_Odistrib, fact_80_one__plus__numeral, fact_105_add_Oleft__commute, fact_21_numeral__le__iff, fact_121_add__right__mono, fact_54_add__diff__cancel__left, fact_337_nat__le__linear, fact_108_add__left__imp__eq, fact_66_le__add__diff__inverse2, fact_304_order_Otrans, fact_23_okRead2__def, fact_52_add__diff__cancel__left_H, fact_225_mult__2, fact_275_ord__eq__le__subst, fact_199_numeral__One, fact_192_eq__add__iff2, fact_128_add__mono__thms__linordered__semiring_I1_J, fact_170_ab__semigroup__mult__class_Omult__ac_I1_J, fact_303_order_Otrans, fact_181_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc, fact_197_one__le__numeral, fact_130_add__mono__thms__linordered__semiring_I2_J, fact_3_Eq1, fact_123_add__left__mono, fact_200_numeral__One, fact_272_ord__eq__le__subst, fact_259_order__subst2, fact_103_add_Ocommute, fact_325_diff__diff__left, fact_345_le__refl, fact_261_order__subst2, fact_263_order__subst2, fact_314_nat__eq__add__iff1, fact_187_add__le__imp__le__diff, fact_330_le__diff__iff, fact_260_order__subst2, fact_164_mult_Oleft__commute, fact_95_group__cancel_Oadd1, fact_139_comm__semiring__class_Odistrib, fact_124_add__left__mono, fact_45_add__numeral__left, fact_248_dbl__def, fact_28_add__left__cancel, fact_7_PC__ie, fact_14_abs__mult__self__eq, fact_116_add__le__imp__le__right, fact_136_distrib__right, fact_151_diff__diff__eq2, fact_346_le__cube, fact_296_linear, fact_298_eq__refl, fact_51_add__diff__cancel__left_H, fact_249_order__subst1, fact_290_eq__iff, fact_238_order__refl, fact_70_distrib__right__numeral, fact_31_add__right__cancel, fact_92_add__mono__thms__linordered__semiring_I4_J, fact_166_mult_Ocommute, fact_264_order__subst2, fact_145_add__implies__diff, fact_81_one__plus__numeral, fact_266_order__subst2, fact_236_verit__eq__simplify_I8_J, fact_12_right__diff__distrib__numeral, fact_118_add__le__imp__le__left, fact_29_add__left__cancel, fact_351_diff__add__inverse2, fact_157_mult_Ocomm__neutral, fact_339_mult__le__mono1, fact_270_ord__eq__le__subst, fact_96_group__cancel_Oadd1, fact_56_add__diff__cancel, fact_39_mult_Oright__neutral, fact_220_left__add__twice, fact_46_add__numeral__left, fact_321_nat__1__eq__mult__iff, fact_83_numeral__plus__one, fact_142_ring__class_Oring__distribs_I2_J, fact_342_le__square, fact_137_distrib__left, fact_273_ord__eq__le__subst, fact_188_add__le__imp__le__diff, fact_319_nat__diff__add__eq2, fact_306_le__cases3, fact_224_mult__2, fact_297_eq__refl, fact_265_order__subst2, fact_13_abs__numeral, fact_222_mult__2__right, fact_221_left__add__twice, fact_167_mult_Oassoc, fact_79_semiring__norm_I69_J, fact_207_diff__right__mono, fact_91_add__mono__thms__linordered__semiring_I4_J, fact_90_is__num__normalize_I1_J, fact_162_rho__bound1__def, fact_2_ie, fact_267_verit__la__disequality, fact_211_right__diff__distrib_H, fact_117_add__le__imp__le__left, fact_36_add__le__cancel__right, fact_48_add__diff__cancel__right_H, fact_99_add_Oassoc, fact_293_antisym, fact_208_diff__left__mono, fact_276_ord__eq__le__subst, fact_343_eq__imp__le, fact_329_eq__diff__iff, fact_333_diff__le__self, fact_185_add__le__add__imp__diff__le, fact_250_order__subst1, fact_19_numeral__times__numeral, fact_127_add__mono__thms__linordered__semiring_I1_J, fact_169_ab__semigroup__mult__class_Omult__ac_I1_J, fact_94_one__reorient, fact_278_ord__eq__le__subst, fact_228_mult__numeral__1, fact_47_add__diff__cancel__right_H, fact_77_numeral__eq__one__iff, fact_74_one__eq__numeral__iff, fact_131_add__mono__thms__linordered__semiring_I3_J, fact_284_ord__le__eq__subst
% 23.63/6.64  % No. of inferences in proof: 708
% 23.63/6.64  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6100 ms resp. 5463 ms w/o parsing
% 24.56/6.88  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.56/6.88  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------