TSTP Solution File: ITP146^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP146^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:23:22 EDT 2024

% Result   : Theorem 12.45s 3.68s
% Output   : Refutation 13.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  278
% Syntax   : Number of formulae    :  525 ( 234 unt;  33 typ;   0 def)
%            Number of atoms       : 1174 ( 523 equ;   2 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 4975 (  72   ~;   4   |;  52   &;4441   @)
%                                         (   0 <=>; 406  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :   53 (  53   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   33 (  29 usr;  16 con; 0-4 aty)
%            Number of variables   :  982 (  12   ^ 966   !;   4   ?; 982   :)

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

thf(set_a_type,type,
    set_a: $tType ).

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

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

thf(auto_l612940ivl0_a_type,type,
    auto_l612940ivl0_a: ( a > a ) > set_a > a > set_real ).

thf(auto_ll_on_flow0_a_type,type,
    auto_ll_on_flow0_a: ( a > a ) > set_a > a > real > a ).

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

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

thf(uminus_uminus_a_a_type,type,
    uminus_uminus_a_a: ( a > a ) > a > a ).

thf(uminus_uminus_real_type,type,
    uminus_uminus_real: real > real ).

thf(zero_zero_real_type,type,
    zero_zero_real: real ).

thf(zero_zero_a_type,type,
    zero_zero_a: a ).

thf(initia826609931terval_type,type,
    initia826609931terval: set_real > $o ).

thf(bot_bot_set_real_type,type,
    bot_bot_set_real: set_real ).

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

thf(top_top_set_real_type,type,
    top_top_set_real: set_real ).

thf(period720806154rbit_a_type,type,
    period720806154rbit_a: ( a > a ) > set_a > a > $o ).

thf(period1305449585riod_a_type,type,
    period1305449585riod_a: ( a > a ) > set_a > a > real ).

thf(period138238489rbit_a_type,type,
    period138238489rbit_a: ( a > a ) > set_a > a > $o ).

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

thf(collect_a_type,type,
    collect_a: ( a > $o ) > set_a ).

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

thf(member_a_type,type,
    member_a: a > set_a > $o ).

thf(x_type,type,
    x: set_a ).

thf(d_type,type,
    d: real ).

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

thf(i1_type,type,
    i1: real ).

thf(i2_type,type,
    i2: real ).

thf(ss_type,type,
    ss: real ).

thf(t_type,type,
    t: real ).

thf(tt_type,type,
    tt: real ).

thf(x2_type,type,
    x2: a ).

thf(xx_type,type,
    xx: a ).

thf(134,axiom,
    ! [A: real,B: real,C: a,D: real] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( ( member_real @ D @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) ) )
       => ( member_real @ ( minus_minus_real @ ( plus_plus_real @ A @ D ) @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_general_Oexistence__ivl__trans) ).

thf(645,plain,
    ! [A: real,B: real,C: a,D: real] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( ( member_real @ D @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) ) )
       => ( member_real @ ( minus_minus_real @ ( plus_plus_real @ A @ D ) @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(188,axiom,
    ! [A: a] :
      ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
      = ( ? [B: real] :
            ( ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) )
            & ( B != zero_zero_real )
            & ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B )
              = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_rev_Oclosed__orbit__def) ).

thf(809,plain,
    ! [A: a] :
      ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
      = ( ? [B: real] :
            ( ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) )
            & ( B != zero_zero_real )
            & ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B )
              = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(44,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ C @ B ) )
      = ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_add_Oright__cancel) ).

thf(365,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)],[44]) ).

thf(81,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/sandbox2/benchmark/theBenchmark.p',fact_283_group__cancel_Oadd2) ).

thf(479,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)],[81]) ).

thf(38,axiom,
    ! [A: real] :
      ( ( ( uminus_uminus_real @ A )
        = A )
      = ( A = zero_zero_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_neg__equal__zero) ).

thf(347,plain,
    ! [A: real] :
      ( ( ( uminus_uminus_real @ A )
        = A )
      = ( A = zero_zero_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(201,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/sandbox2/benchmark/theBenchmark.p',fact_341_group__cancel_Osub1) ).

thf(846,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)],[201]) ).

thf(3,axiom,
    ! [A: a > $o,B: a > $o] :
      ( ! [C: a] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect_a @ A )
        = ( collect_a @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Collect__cong) ).

thf(249,plain,
    ! [A: a > $o,B: a > $o] :
      ( ! [C: a] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect_a @ A )
        = ( collect_a @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(232,axiom,
    ! [A: a] :
      ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ~ ! [B: real] :
            ( ( ord_less_real @ zero_zero_real @ B )
           => ~ ! [C: real] :
                  ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ ( plus_plus_real @ C @ B ) )
                  = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_rev_Oclosed__orbitE) ).

thf(941,plain,
    ! [A: a] :
      ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ~ ! [B: real] :
            ( ( ord_less_real @ zero_zero_real @ B )
           => ~ ! [C: real] :
                  ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ ( plus_plus_real @ C @ B ) )
                  = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(107,axiom,
    ! [A: a] :
      ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
     => ( ( auto_l612940ivl0_a @ f @ x @ A )
        = bot_bot_set_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_local_Oexistence__ivl__empty1) ).

thf(555,plain,
    ! [A: a] :
      ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
     => ( ( auto_l612940ivl0_a @ f @ x @ A )
        = bot_bot_set_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(139,axiom,
    member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ x2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_assms_I8_J) ).

thf(666,plain,
    member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ x2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(239,axiom,
    ! [A: a] :
      ( ( period720806154rbit_a @ f @ x @ A )
     => ( ( ( f @ A )
         != zero_zero_a )
       => ( period138238489rbit_a @ f @ x @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_closed__orbit__periodic) ).

thf(962,plain,
    ! [A: a] :
      ( ( period720806154rbit_a @ f @ x @ A )
     => ( ( ( f @ A )
         != zero_zero_a )
       => ( period138238489rbit_a @ f @ x @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(77,axiom,
    ! [A: real,B: real] :
      ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_add__minus__cancel) ).

thf(468,plain,
    ! [A: real,B: real] :
      ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(245,axiom,
    ! [A: a] :
      ( ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
        = bot_bot_set_real )
      = ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
        | ~ ( member_a @ A @ x ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_local_Orev_Oexistence__ivl__empty__iff) ).

thf(977,plain,
    ! [A: a] :
      ( ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
        = bot_bot_set_real )
      = ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
        | ~ ( member_a @ A @ x ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(96,axiom,
    ( ( auto_ll_on_flow0_a @ f @ x @ xx @ tt )
    = ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_eq) ).

thf(523,plain,
    ( ( auto_ll_on_flow0_a @ f @ x @ xx @ tt )
    = ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(13,axiom,
    ( ( uminus_uminus_real @ zero_zero_real )
    = zero_zero_real ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_add_Oinverse__neutral) ).

thf(276,plain,
    ( ( uminus_uminus_real @ zero_zero_real )
    = zero_zero_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(1,conjecture,
    ( xx
    = ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ( xx
   != ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(247,plain,
    ( xx
   != ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(50,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ zero_zero_real @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_add_Ogroup__left__neutral) ).

thf(384,plain,
    ! [A: real] :
      ( ( plus_plus_real @ zero_zero_real @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(183,axiom,
    ! [A: a] :
      ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ( ( ( uminus_uminus_a_a @ f @ A )
         != zero_zero_a )
       => ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_rev_Oclosed__orbit__periodic) ).

thf(797,plain,
    ! [A: a] :
      ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ( ( ( uminus_uminus_a_a @ f @ A )
         != zero_zero_a )
       => ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(233,axiom,
    ! [A: a] :
      ( ( period720806154rbit_a @ f @ x @ A )
     => ( member_a @ A @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_closed__orbit__in__domain) ).

thf(945,plain,
    ! [A: a] :
      ( ( period720806154rbit_a @ f @ x @ A )
     => ( member_a @ A @ x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(228,axiom,
    ! [A: a,B: real] :
      ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ( ( uminus_uminus_a_a @ f @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B ) )
       != zero_zero_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_rev_Operiodic__orbit__imp__flow0__regular) ).

thf(930,plain,
    ! [A: a,B: real] :
      ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ( ( uminus_uminus_a_a @ f @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B ) )
       != zero_zero_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(141,axiom,
    ! [A: a] :
      ( ( member_a @ A @ x )
     => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_rev_Oexistence__ivl__zero) ).

thf(670,plain,
    ! [A: a] :
      ( ( member_a @ A @ x )
     => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(196,axiom,
    ! [A: real,B: real] :
      ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
      = ( minus_minus_real @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_minus__diff__eq) ).

thf(829,plain,
    ! [A: real,B: real] :
      ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
      = ( minus_minus_real @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(217,axiom,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_add__diff__cancel) ).

thf(898,plain,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(152,axiom,
    member_real @ ( uminus_uminus_real @ tt ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ xx @ tt ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_neg__tt__ex) ).

thf(709,plain,
    member_real @ ( uminus_uminus_real @ tt ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ xx @ tt ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(17,axiom,
    ! [A: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
      = ( ord_less_real @ A @ zero_zero_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_double__add__less__zero__iff__single__add__less__zero) ).

thf(288,plain,
    ! [A: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
      = ( ord_less_real @ A @ zero_zero_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(67,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
      = zero_zero_real ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_add_Oright__inverse) ).

thf(436,plain,
    ! [A: real] :
      ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
      = zero_zero_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(136,axiom,
    ! [A: real,B: a] :
      ( ( ( ( member_real @ A @ top_top_set_real )
          & ( member_a @ B @ x ) )
       => ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( minus_minus_real @ A @ A ) )
          = B ) )
      & ( ~ ( ( member_real @ A @ top_top_set_real )
            & ( member_a @ B @ x ) )
       => ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( minus_minus_real @ A @ A ) )
          = zero_zero_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_general_Oflow__initial__time__if) ).

thf(651,plain,
    ! [A: real,B: a] :
      ( ( ( ( member_real @ A @ top_top_set_real )
          & ( member_a @ B @ x ) )
       => ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( minus_minus_real @ A @ A ) )
          = B ) )
      & ( ~ ( ( member_real @ A @ top_top_set_real )
            & ( member_a @ B @ x ) )
       => ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( minus_minus_real @ A @ A ) )
          = zero_zero_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(157,axiom,
    ! [A: a,B: real] :
      ( ( period138238489rbit_a @ f @ x @ A )
     => ( ( f @ ( auto_ll_on_flow0_a @ f @ x @ A @ B ) )
       != zero_zero_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_periodic__orbit__imp__flow0__regular) ).

thf(724,plain,
    ! [A: a,B: real] :
      ( ( period138238489rbit_a @ f @ x @ A )
     => ( ( f @ ( auto_ll_on_flow0_a @ f @ x @ A @ B ) )
       != zero_zero_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(112,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( member_real @ A @ top_top_set_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_rev_Ogeneral_Omem__existence__ivl__subset) ).

thf(570,plain,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( member_real @ A @ top_top_set_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(46,axiom,
    ! [A: a,B: a > $o] :
      ( ( member_a @ A @ ( collect_a @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_mem__Collect__eq) ).

thf(372,plain,
    ! [A: a,B: a > $o] :
      ( ( member_a @ A @ ( collect_a @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(89,axiom,
    ! [A: a,B: real] :
      ( ( member_a @ A @ x )
     => ( ( ( uminus_uminus_a_a @ f @ A )
          = zero_zero_a )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_rev_Ofixpoint__sol_I2_J) ).

thf(504,plain,
    ! [A: a,B: real] :
      ( ( member_a @ A @ x )
     => ( ( ( uminus_uminus_a_a @ f @ A )
          = zero_zero_a )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(229,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_local_Orev_Oflow__in__domain) ).

thf(934,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) @ x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(185,axiom,
    ! [A: a] :
      ( ~ ( member_a @ A @ x )
     => ( ( auto_l612940ivl0_a @ f @ x @ A )
        = bot_bot_set_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_local_Oexistence__ivl__undefined) ).

thf(802,plain,
    ! [A: a] :
      ( ~ ( member_a @ A @ x )
     => ( ( auto_l612940ivl0_a @ f @ x @ A )
        = bot_bot_set_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(37,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
      = ( ord_less_real @ zero_zero_real @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_less__add__same__cancel1) ).

thf(344,plain,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
      = ( ord_less_real @ zero_zero_real @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(108,axiom,
    ! [A: real,B: a,C: real] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( ( member_real @ C @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
       => ( member_real @ ( minus_minus_real @ C @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_rev_Odiff__existence__ivl__trans) ).

thf(559,plain,
    ! [A: real,B: a,C: real] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( ( member_real @ C @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
       => ( member_real @ ( minus_minus_real @ C @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(213,axiom,
    ! [A: real] :
      ( ( minus_minus_real @ A @ zero_zero_real )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_diff__zero) ).

thf(881,plain,
    ! [A: real] :
      ( ( minus_minus_real @ A @ zero_zero_real )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(71,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ zero_zero_real @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_add_Oleft__neutral) ).

thf(448,plain,
    ! [A: real] :
      ( ( plus_plus_real @ zero_zero_real @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(7,axiom,
    ! [A: real] :
      ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
      = ( ord_less_real @ zero_zero_real @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_neg__less__pos) ).

thf(261,plain,
    ! [A: real] :
      ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
      = ( ord_less_real @ zero_zero_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(16,axiom,
    ! [A: real,B: real,C: real] :
      ( ( A
        = ( plus_plus_real @ B @ C ) )
     => ( ( uminus_uminus_real @ A )
        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_group__cancel_Oneg1) ).

thf(284,plain,
    ! [A: real,B: real,C: real] :
      ( ( A
        = ( plus_plus_real @ B @ C ) )
     => ( ( uminus_uminus_real @ A )
        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(172,axiom,
    ! [A: a] :
      ( ( member_real @ zero_zero_real @ top_top_set_real )
     => ( ( member_a @ A @ x )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_local_Orev_Oflow__initial__time) ).

thf(770,plain,
    ! [A: a] :
      ( ( member_real @ zero_zero_real @ top_top_set_real )
     => ( ( member_a @ A @ x )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(29,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
      = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_minus__less__iff) ).

thf(321,plain,
    ! [A: real,B: real] :
      ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
      = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(40,axiom,
    ! [A: real,B: real] :
      ( ( ( plus_plus_real @ A @ B )
        = A )
      = ( B = zero_zero_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_add__cancel__left__right) ).

thf(353,plain,
    ! [A: real,B: real] :
      ( ( ( plus_plus_real @ A @ B )
        = A )
      = ( B = zero_zero_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(122,axiom,
    ! [A: real,B: a,C: real] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ B ) )
       => ( member_real @ ( minus_minus_real @ C @ A ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_diff__existence__ivl__trans) ).

thf(602,plain,
    ! [A: real,B: a,C: real] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ B ) )
       => ( member_real @ ( minus_minus_real @ C @ A ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(211,axiom,
    ! [A: a] :
      ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_rev_Operiodic__orbit__period_I1_J) ).

thf(877,plain,
    ! [A: a] :
      ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(160,axiom,
    ! [A: a] :
      ( ( period720806154rbit_a @ f @ x @ A )
     => ( ( auto_l612940ivl0_a @ f @ x @ A )
        = top_top_set_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_closed__orbit__global__existence) ).

thf(734,plain,
    ! [A: a] :
      ( ( period720806154rbit_a @ f @ x @ A )
     => ( ( auto_l612940ivl0_a @ f @ x @ A )
        = top_top_set_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(20,axiom,
    ! [A: real] :
      ~ ( ord_less_real @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_verit__comp__simplify1_I1_J) ).

thf(293,plain,
    ! [A: real] :
      ~ ( ord_less_real @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(207,axiom,
    ! [A: real,B: real] :
      ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
      = ( minus_minus_real @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_uminus__add__conv__diff) ).

thf(866,plain,
    ! [A: real,B: real] :
      ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
      = ( minus_minus_real @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(173,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_rev_Oflow0__defined) ).

thf(774,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) @ x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(64,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( ord_less_real @ A @ B )
        & ( ord_less_real @ C @ D ) )
     => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_add__mono__thms__linordered__field_I5_J) ).

thf(428,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( ord_less_real @ A @ B )
        & ( ord_less_real @ C @ D ) )
     => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(26,axiom,
    ! [A: real,B: real] :
      ( ( A
        = ( plus_plus_real @ B @ A ) )
      = ( B = zero_zero_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_add__cancel__right__left) ).

thf(312,plain,
    ! [A: real,B: real] :
      ( ( A
        = ( plus_plus_real @ B @ A ) )
      = ( B = zero_zero_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(19,axiom,
    ord_less_real @ zero_zero_real @ i1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_i2_I2_J) ).

thf(292,plain,
    ord_less_real @ zero_zero_real @ i1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(68,axiom,
    ! [A: real] :
      ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_add_Oinverse__inverse) ).

thf(439,plain,
    ! [A: real] :
      ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(144,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/sandbox2/benchmark/theBenchmark.p',fact_333_diff__diff__eq2) ).

thf(678,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)],[144]) ).

thf(11,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ zero_zero_real @ A )
     => ( ( ord_less_real @ B @ C )
       => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_pos__add__strict) ).

thf(270,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ zero_zero_real @ A )
     => ( ( ord_less_real @ B @ C )
       => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(137,axiom,
    ! [A: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ f @ x @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_mvar_Ointerval__axioms) ).

thf(661,plain,
    ! [A: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ f @ x @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(104,axiom,
    ! [A: a] :
      ( ( period720806154rbit_a @ f @ x @ A )
      = ( ? [B: real] :
            ( ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ A ) )
            & ( B != zero_zero_real )
            & ( ( auto_ll_on_flow0_a @ f @ x @ A @ B )
              = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_closed__orbit__def) ).

thf(546,plain,
    ! [A: a] :
      ( ( period720806154rbit_a @ f @ x @ A )
      = ( ? [B: real] :
            ( ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ A ) )
            & ( B != zero_zero_real )
            & ( ( auto_ll_on_flow0_a @ f @ x @ A @ B )
              = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(226,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_rev_Ogeneral_Oflow__in__domain) ).

thf(925,plain,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) @ x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(169,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/sandbox2/benchmark/theBenchmark.p',fact_335_add__diff__eq) ).

thf(761,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)],[169]) ).

thf(49,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
      = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_less__minus__iff) ).

thf(381,plain,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
      = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(154,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/sandbox2/benchmark/theBenchmark.p',fact_202_add__diff__cancel__right) ).

thf(714,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)],[154]) ).

thf(215,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ ( minus_minus_real @ B @ C ) )
      = ( ord_less_real @ ( plus_plus_real @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_less__diff__eq) ).

thf(894,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ ( minus_minus_real @ B @ C ) )
      = ( ord_less_real @ ( plus_plus_real @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(164,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( member_real @ A @ top_top_set_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_local_Omem__existence__ivl__subset) ).

thf(746,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( member_real @ A @ top_top_set_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(175,axiom,
    ! [A: a] :
      ( ( member_a @ A @ x )
     => ( ( ( uminus_uminus_a_a @ f @ A )
          = zero_zero_a )
       => ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_rev_Ofixed__point__imp__closed__orbit__period__zero_I1_J) ).

thf(778,plain,
    ! [A: a] :
      ( ( member_a @ A @ x )
     => ( ( ( uminus_uminus_a_a @ f @ A )
          = zero_zero_a )
       => ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(236,axiom,
    ! [A: a] :
      ( ( period138238489rbit_a @ f @ x @ A )
     => ( ( auto_ll_on_flow0_a @ f @ x @ A @ ( period1305449585riod_a @ f @ x @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_periodic__orbit__period_I2_J) ).

thf(952,plain,
    ! [A: a] :
      ( ( period138238489rbit_a @ f @ x @ A )
     => ( ( auto_ll_on_flow0_a @ f @ x @ A @ ( period1305449585riod_a @ f @ x @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(193,axiom,
    ! [A: real,B: a,C: real] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) ) )
       => ( member_real @ ( plus_plus_real @ A @ C ) @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_local_Oexistence__ivl__trans) ).

thf(820,plain,
    ! [A: real,B: a,C: real] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) ) )
       => ( member_real @ ( plus_plus_real @ A @ C ) @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(53,axiom,
    ! [A: real,B: real] :
      ( ( A
        = ( plus_plus_real @ A @ B ) )
      = ( B = zero_zero_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_add__cancel__right__right) ).

thf(392,plain,
    ! [A: real,B: real] :
      ( ( A
        = ( plus_plus_real @ A @ B ) )
      = ( B = zero_zero_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(149,axiom,
    ! [A: a] :
      ( ( member_a @ A @ x )
     => ( ( ( f @ A )
          = zero_zero_a )
       => ( period720806154rbit_a @ f @ x @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_fixed__point__imp__closed__orbit__period__zero_I1_J) ).

thf(693,plain,
    ! [A: a] :
      ( ( member_a @ A @ x )
     => ( ( ( f @ A )
          = zero_zero_a )
       => ( period720806154rbit_a @ f @ x @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(179,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( member_real @ ( minus_minus_real @ zero_zero_real @ A ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_local_Oexistence__ivl__reverse) ).

thf(788,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( member_real @ ( minus_minus_real @ zero_zero_real @ A ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(190,axiom,
    ord_less_real @ zero_zero_real @ tt,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_tt_I1_J) ).

thf(815,plain,
    ord_less_real @ zero_zero_real @ tt,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(223,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
      = ( ord_less_real @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_diff__gt__0__iff__gt) ).

thf(916,plain,
    ! [A: real,B: real] :
      ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
      = ( ord_less_real @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(4,axiom,
    ! [A: real > $o,B: real > $o] :
      ( ! [C: real] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect_real @ A )
        = ( collect_real @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Collect__cong) ).

thf(252,plain,
    ! [A: real > $o,B: real > $o] :
      ( ! [C: real] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect_real @ A )
        = ( collect_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(212,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_local_Oflow__in__domain) ).

thf(879,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) @ x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(32,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ zero_zero_real @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_comm__monoid__add__class_Oadd__0) ).

thf(329,plain,
    ! [A: real] :
      ( ( plus_plus_real @ zero_zero_real @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(85,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_verit__negate__coefficient_I2_J) ).

thf(493,plain,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(153,axiom,
    ! [A: real,B: a,C: real] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( ( member_real @ C @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( plus_plus_real @ A @ C ) )
          = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_local_Orev_Oflow__trans) ).

thf(710,plain,
    ! [A: real,B: a,C: real] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( ( member_real @ C @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( plus_plus_real @ A @ C ) )
          = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(200,axiom,
    ! [A: real,B: real,C: a] :
      ( ( A != B )
     => ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ C ) )
       => ( ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ C ) )
         => ( ( ( auto_ll_on_flow0_a @ f @ x @ C @ A )
              = ( auto_ll_on_flow0_a @ f @ x @ C @ B ) )
           => ( period720806154rbit_a @ f @ x @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_closed__orbitI) ).

thf(842,plain,
    ! [A: real,B: real,C: a] :
      ( ( A != B )
     => ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ C ) )
       => ( ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ C ) )
         => ( ( ( auto_ll_on_flow0_a @ f @ x @ C @ A )
              = ( auto_ll_on_flow0_a @ f @ x @ C @ B ) )
           => ( period720806154rbit_a @ f @ x @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(110,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( ( member_a @ C @ x )
       => ( ! [D: real,E: real,F: a] :
              ( ( member_a @ F @ x )
             => ( ( f @ F )
                = ( f @ F ) ) )
         => ( ( top_top_set_real = top_top_set_real )
           => ( ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) )
              = ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_flow__shift__autonomous2) ).

thf(566,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(82,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ A @ zero_zero_real )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_add_Oright__neutral) ).

thf(484,plain,
    ! [A: real] :
      ( ( plus_plus_real @ A @ zero_zero_real )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(30,axiom,
    ! [A: set_a] :
      ( ( collect_a
        @ ^ [B: a] : ( member_a @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Collect__mem__eq) ).

thf(324,plain,
    ! [A: set_a] :
      ( ( collect_a
        @ ^ [B: a] : ( member_a @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(244,axiom,
    ! [A: real,B: real,C: real] :
      ( ( A
        = ( minus_minus_real @ B @ C ) )
      = ( ( plus_plus_real @ A @ C )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_eq__diff__eq) ).

thf(974,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)],[244]) ).

thf(210,axiom,
    ! [A: real] :
      ( ( minus_minus_real @ zero_zero_real @ A )
      = ( uminus_uminus_real @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_diff__0) ).

thf(874,plain,
    ! [A: real] :
      ( ( minus_minus_real @ zero_zero_real @ A )
      = ( uminus_uminus_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(41,axiom,
    ! [A: real] :
      ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
      = ( ord_less_real @ zero_zero_real @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_linordered__ab__group__add__class_Ozero__less__double__add__iff__zero__less__single__add) ).

thf(356,plain,
    ! [A: real] :
      ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
      = ( ord_less_real @ zero_zero_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(208,axiom,
    ! [A: real,B: a] :
      ( ~ ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( ( auto_ll_on_flow0_a @ f @ x @ B @ A )
        = zero_zero_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_local_Oflow__undefined0) ).

thf(869,plain,
    ! [A: real,B: a] :
      ( ~ ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( ( auto_ll_on_flow0_a @ f @ x @ B @ A )
        = zero_zero_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(177,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( minus_minus_real @ A @ B )
        = ( minus_minus_real @ C @ D ) )
     => ( ( A = B )
        = ( C = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_diff__eq__diff__eq) ).

thf(783,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)],[177]) ).

thf(204,axiom,
    ! [A: real] :
      ( ( minus_minus_real @ A @ zero_zero_real )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_diff__0__right) ).

thf(857,plain,
    ! [A: real] :
      ( ( minus_minus_real @ A @ zero_zero_real )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(246,axiom,
    ( ( (=) @ real )
    = ( ^ [A: real,B: real] :
          ( ( minus_minus_real @ A @ B )
          = zero_zero_real ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_eq__iff__diff__eq__0) ).

thf(980,plain,
    ( ( (=) @ real )
    = ( ^ [A: real,B: real] :
          ( ( minus_minus_real @ A @ B )
          = zero_zero_real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(56,axiom,
    ! [A: real] :
      ( ( ( plus_plus_real @ A @ A )
        = zero_zero_real )
      = ( A = zero_zero_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_linordered__ab__group__add__class_Odouble__zero) ).

thf(403,plain,
    ! [A: real] :
      ( ( ( plus_plus_real @ A @ A )
        = zero_zero_real )
      = ( A = zero_zero_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(78,axiom,
    ( plus_plus_real
    = ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_add_Ocommute) ).

thf(471,plain,
    ( plus_plus_real
    = ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(214,axiom,
    ! [A: a] :
      ( ( ( ( member_real @ zero_zero_real @ top_top_set_real )
          & ( member_a @ A @ x ) )
       => ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
          = A ) )
      & ( ~ ( ( member_real @ zero_zero_real @ top_top_set_real )
            & ( member_a @ A @ x ) )
       => ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
          = zero_zero_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_local_Oflow__initial__time__if) ).

thf(884,plain,
    ! [A: a] :
      ( ( ( ( member_real @ zero_zero_real @ top_top_set_real )
          & ( member_a @ A @ x ) )
       => ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
          = A ) )
      & ( ~ ( ( member_real @ zero_zero_real @ top_top_set_real )
            & ( member_a @ A @ x ) )
       => ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
          = zero_zero_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(101,axiom,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B )
      = ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_minus__diff__commute) ).

thf(537,plain,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B )
      = ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(133,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( member_real @ A @ top_top_set_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_general_Omem__existence__ivl__subset) ).

thf(642,plain,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( member_real @ A @ top_top_set_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(131,axiom,
    ! [A: real,B: real,C: a] :
      ( ( A != B )
     => ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
       => ( ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
         => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ A )
              = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ B ) )
           => ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_rev_Oclosed__orbitI) ).

thf(637,plain,
    ! [A: real,B: real,C: a] :
      ( ( A != B )
     => ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
       => ( ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
         => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ A )
              = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ B ) )
           => ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(218,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_real @ ( minus_minus_real @ C @ B ) @ ( minus_minus_real @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_diff__strict__left__mono) ).

thf(901,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_real @ ( minus_minus_real @ C @ B ) @ ( minus_minus_real @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(80,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/sandbox2/benchmark/theBenchmark.p',fact_295_ab__semigroup__add__class_Oadd__ac_I1_J) ).

thf(476,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)],[80]) ).

thf(93,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( member_a @ C @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_general_Omem__existence__ivl__iv__defined_I2_J) ).

thf(515,plain,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( member_a @ C @ x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(221,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ ( minus_minus_real @ A @ A ) @ ( auto_l612940ivl0_a @ f @ x @ B ) )
      = ( ( member_real @ A @ top_top_set_real )
        & ( member_a @ B @ x ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_general_Oexistence__ivl__initial__time__iff) ).

thf(911,plain,
    ! [A: real,B: a] :
      ( ( member_real @ ( minus_minus_real @ A @ A ) @ ( auto_l612940ivl0_a @ f @ x @ B ) )
      = ( ( member_real @ A @ top_top_set_real )
        & ( member_a @ B @ x ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(123,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( ( ( auto_ll_on_flow0_a @ f @ x @ B @ A )
          = B )
       => ( member_real @ ( uminus_uminus_real @ A ) @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_recurrence__time__flip__sign_I1_J) ).

thf(605,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( ( ( auto_ll_on_flow0_a @ f @ x @ B @ A )
          = B )
       => ( member_real @ ( uminus_uminus_real @ A ) @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(181,axiom,
    ! [A: a] :
      ( ( member_a @ A @ x )
     => ( ( ( f @ A )
          = zero_zero_a )
       => ( ( auto_l612940ivl0_a @ f @ x @ A )
          = top_top_set_real ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_fixpoint__sol_I1_J) ).

thf(792,plain,
    ! [A: a] :
      ( ( member_a @ A @ x )
     => ( ( ( f @ A )
          = zero_zero_a )
       => ( ( auto_l612940ivl0_a @ f @ x @ A )
          = top_top_set_real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(186,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( minus_minus_real @ A @ B )
        = C )
      = ( A
        = ( plus_plus_real @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_diff__eq__eq) ).

thf(805,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)],[186]) ).

thf(90,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( member_real @ ( minus_minus_real @ zero_zero_real @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_local_Orev_Oexistence__ivl__reverse) ).

thf(508,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( member_real @ ( minus_minus_real @ zero_zero_real @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(55,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/sandbox2/benchmark/theBenchmark.p',fact_285_group__cancel_Oadd1) ).

thf(398,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)],[55]) ).

thf(59,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
      = ( ord_less_real @ zero_zero_real @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_less__add__same__cancel2) ).

thf(412,plain,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
      = ( ord_less_real @ zero_zero_real @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(240,axiom,
    ! [A: real,B: real,C: a] :
      ( ~ ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) )
        = zero_zero_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_rev_Ogeneral_Oflow__undefined0) ).

thf(965,plain,
    ! [A: real,B: real,C: a] :
      ( ~ ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) )
        = zero_zero_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(63,axiom,
    ! [A: real,B: real] :
      ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_minus__add__cancel) ).

thf(425,plain,
    ! [A: real,B: real] :
      ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(8,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ord_less_real @ A @ B )
     => ( ( ord_less_real @ C @ D )
       => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_add__strict__mono) ).

thf(264,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ord_less_real @ A @ B )
     => ( ( ord_less_real @ C @ D )
       => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(113,axiom,
    ! [A: a,B: real] :
      ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B )
      = ( auto_ll_on_flow0_a @ f @ x @ A @ ( uminus_uminus_real @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_rev__eq__flow) ).

thf(573,plain,
    ! [A: a,B: real] :
      ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B )
      = ( auto_ll_on_flow0_a @ f @ x @ A @ ( uminus_uminus_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(21,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_add__left__cancel) ).

thf(296,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)],[21]) ).

thf(47,axiom,
    ! [A: real] :
      ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
      = ( ord_less_real @ A @ zero_zero_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_neg__0__less__iff__less) ).

thf(375,plain,
    ! [A: real] :
      ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
      = ( ord_less_real @ A @ zero_zero_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(92,axiom,
    ! [A: a] :
      ( ( period138238489rbit_a @ f @ x @ A )
     => ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_periodic__orbit__period_I1_J) ).

thf(513,plain,
    ! [A: a] :
      ( ( period138238489rbit_a @ f @ x @ A )
     => ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(65,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_add_Oleft__cancel) ).

thf(430,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)],[65]) ).

thf(163,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) @ ( minus_minus_real @ zero_zero_real @ A ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_local_Orev_Oflows__reverse) ).

thf(743,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) @ ( minus_minus_real @ zero_zero_real @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(15,axiom,
    ! [A: real] :
      ( ( zero_zero_real
        = ( uminus_uminus_real @ A ) )
      = ( zero_zero_real = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_neg__0__equal__iff__equal) ).

thf(281,plain,
    ! [A: real] :
      ( ( zero_zero_real
        = ( uminus_uminus_real @ A ) )
      = ( zero_zero_real = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(109,axiom,
    ! [A: real,B: real,C: a,D: real] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( ( member_real @ D @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) ) )
       => ( ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ ( plus_plus_real @ A @ D ) @ B ) )
          = ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_general_Oflow__trans) ).

thf(562,plain,
    ! [A: real,B: real,C: a,D: real] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( ( member_real @ D @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) ) )
       => ( ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ ( plus_plus_real @ A @ D ) @ B ) )
          = ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(219,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ top_top_set_real )
     => ( ( member_a @ B @ x )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( minus_minus_real @ A @ A ) )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_rev_Ogeneral_Oflow__initial__time) ).

thf(904,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ top_top_set_real )
     => ( ( member_a @ B @ x )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( minus_minus_real @ A @ A ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(115,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( plus_plus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
       => ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_local_Orev_Oexistence__ivl__trans_H) ).

thf(579,plain,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( plus_plus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
       => ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(18,axiom,
    ord_less_real @ i1 @ i2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_i2_I3_J) ).

thf(291,plain,
    ord_less_real @ i1 @ i2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(132,axiom,
    member_real @ tt @ ( auto_l612940ivl0_a @ f @ x @ xx ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_tt__ex) ).

thf(641,plain,
    member_real @ tt @ ( auto_l612940ivl0_a @ f @ x @ xx ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(52,axiom,
    ord_less_real @ zero_zero_real @ d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_d) ).

thf(391,plain,
    ord_less_real @ zero_zero_real @ d,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(87,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/sandbox2/benchmark/theBenchmark.p',fact_331_diff__add__eq) ).

thf(498,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)],[87]) ).

thf(34,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_add__strict__right__mono) ).

thf(335,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(224,axiom,
    ! [A: a] :
      ( ( member_real @ zero_zero_real @ top_top_set_real )
     => ( ( member_a @ A @ x )
       => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_local_Orev_Oexistence__ivl__initial__time) ).

thf(919,plain,
    ! [A: a] :
      ( ( member_real @ zero_zero_real @ top_top_set_real )
     => ( ( member_a @ A @ x )
       => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(234,axiom,
    ! [A: real] :
      ( ( minus_minus_real @ A @ A )
      = zero_zero_real ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_cancel__comm__monoid__add__class_Odiff__cancel) ).

thf(947,plain,
    ! [A: real] :
      ( ( minus_minus_real @ A @ A )
      = zero_zero_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(39,axiom,
    ! [A: real] :
      ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_verit__minus__simplify_I4_J) ).

thf(350,plain,
    ! [A: real] :
      ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(102,axiom,
    ! [A: a] :
      ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
        = top_top_set_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_rev_Oclosed__orbit__global__existence) ).

thf(540,plain,
    ! [A: a] :
      ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
        = top_top_set_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(142,axiom,
    ! [A: real,B: real,C: a,D: real] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( ( member_real @ D @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) ) )
       => ( member_real @ ( minus_minus_real @ ( plus_plus_real @ A @ D ) @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_rev_Ogeneral_Oexistence__ivl__trans) ).

thf(672,plain,
    ! [A: real,B: real,C: a,D: real] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( ( member_real @ D @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) ) )
       => ( member_real @ ( minus_minus_real @ ( plus_plus_real @ A @ D ) @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(70,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ zero_zero_real )
     => ( ( ord_less_real @ B @ zero_zero_real )
       => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_add__neg__neg) ).

thf(445,plain,
    ! [A: real,B: real] :
      ( ( ord_less_real @ A @ zero_zero_real )
     => ( ( ord_less_real @ B @ zero_zero_real )
       => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(230,axiom,
    ! [A: a,B: real] :
      ( ( auto_ll_on_flow0_a @ f @ x @ A @ B )
      = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ ( uminus_uminus_real @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_rev_Orev__eq__flow) ).

thf(936,plain,
    ! [A: a,B: real] :
      ( ( auto_ll_on_flow0_a @ f @ x @ A @ B )
      = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ ( uminus_uminus_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(170,axiom,
    ! [A: a] :
      ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
      = ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
        & ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_rev_Operiodic__orbit__def) ).

thf(764,plain,
    ! [A: a] :
      ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
      = ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
        & ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(57,axiom,
    ! [A: real,B: real] :
      ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
      = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_add_Oinverse__distrib__swap) ).

thf(406,plain,
    ! [A: real,B: real] :
      ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
      = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(145,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( member_real @ A @ top_top_set_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_local_Orev_Omem__existence__ivl__subset) ).

thf(681,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( member_real @ A @ top_top_set_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(121,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/sandbox2/benchmark/theBenchmark.p',fact_206_add__diff__cancel__left) ).

thf(599,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)],[121]) ).

thf(206,axiom,
    ! [A: real,B: a] :
      ( ~ ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A )
        = zero_zero_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_local_Orev_Oflow__undefined0) ).

thf(863,plain,
    ! [A: real,B: a] :
      ( ~ ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A )
        = zero_zero_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(43,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ C @ B ) )
      = ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_add__right__cancel) ).

thf(362,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)],[43]) ).

thf(72,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ A @ zero_zero_real )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_add_Ocomm__neutral) ).

thf(451,plain,
    ! [A: real] :
      ( ( plus_plus_real @ A @ zero_zero_real )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(111,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ top_top_set_real )
     => ( ( member_a @ B @ x )
       => ( member_real @ ( minus_minus_real @ A @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_rev_Ogeneral_Oexistence__ivl__initial__time) ).

thf(567,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ top_top_set_real )
     => ( ( member_a @ B @ x )
       => ( member_real @ ( minus_minus_real @ A @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(161,axiom,
    ! [A: a] :
      ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ( ( ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
          = zero_zero_real )
       => ( ( uminus_uminus_a_a @ f @ A )
          = zero_zero_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_rev_Oclosed__orbit__period__zero__fixed__point) ).

thf(737,plain,
    ! [A: a] :
      ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ( ( ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
          = zero_zero_real )
       => ( ( uminus_uminus_a_a @ f @ A )
          = zero_zero_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(28,axiom,
    ! [A: real] :
      ( ( A
        = ( uminus_uminus_real @ A ) )
      = ( A = zero_zero_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_equal__neg__zero) ).

thf(318,plain,
    ! [A: real] :
      ( ( A
        = ( uminus_uminus_real @ A ) )
      = ( A = zero_zero_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(127,axiom,
    ! [A: a] :
      ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
     => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
        = bot_bot_set_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_local_Orev_Oexistence__ivl__empty1) ).

thf(616,plain,
    ! [A: a] :
      ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
     => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
        = bot_bot_set_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(23,axiom,
    ! [A: real] :
      ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
      = ( ord_less_real @ zero_zero_real @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_neg__less__0__iff__less) ).

thf(303,plain,
    ! [A: real] :
      ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
      = ( ord_less_real @ zero_zero_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(51,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/sandbox2/benchmark/theBenchmark.p',fact_287_add__mono__thms__linordered__semiring_I4_J) ).

thf(387,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)],[51]) ).

thf(168,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ ( minus_minus_real @ A @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
      = ( ( member_real @ A @ top_top_set_real )
        & ( member_a @ B @ x ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_rev_Ogeneral_Oexistence__ivl__initial__time__iff) ).

thf(758,plain,
    ! [A: real,B: a] :
      ( ( member_real @ ( minus_minus_real @ A @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
      = ( ( member_real @ A @ top_top_set_real )
        & ( member_a @ B @ x ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(106,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) @ ( minus_minus_real @ B @ A ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_general_Oflows__reverse) ).

thf(552,plain,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) @ ( minus_minus_real @ B @ A ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(100,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( member_a @ C @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_rev_Ogeneral_Omem__existence__ivl__iv__defined_I2_J) ).

thf(535,plain,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( member_a @ C @ x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(191,axiom,
    ! [A: a] :
      ( ( member_a @ A @ x )
     => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_existence__ivl__zero) ).

thf(816,plain,
    ! [A: a] :
      ( ( member_a @ A @ x )
     => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(95,axiom,
    ! [A: a] :
      ( ( period138238489rbit_a @ f @ x @ A )
      = ( ( period720806154rbit_a @ f @ x @ A )
        & ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_periodic__orbit__def) ).

thf(520,plain,
    ! [A: a] :
      ( ( period138238489rbit_a @ f @ x @ A )
      = ( ( period720806154rbit_a @ f @ x @ A )
        & ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(75,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ A @ zero_zero_real )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_verit__sum__simplify) ).

thf(462,plain,
    ! [A: real] :
      ( ( plus_plus_real @ A @ zero_zero_real )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(238,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) @ ( minus_minus_real @ zero_zero_real @ A ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_local_Oflows__reverse) ).

thf(959,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) @ ( minus_minus_real @ zero_zero_real @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(195,axiom,
    ! [A: real,B: real,C: real,D: a] :
      ( ( member_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ D ) )
     => ( ( member_real @ ( minus_minus_real @ A @ C ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ D ) )
       => ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ D @ ( minus_minus_real @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_rev_Ogeneral_Oexistence__ivl__trans_H) ).

thf(827,plain,
    ! [A: real,B: real,C: real,D: a] :
      ( ( member_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ D ) )
     => ( ( member_real @ ( minus_minus_real @ A @ C ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ D ) )
       => ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ D @ ( minus_minus_real @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(14,axiom,
    ! [A: real] :
      ( ( ( uminus_uminus_real @ A )
        = zero_zero_real )
      = ( A = zero_zero_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_neg__equal__0__iff__equal) ).

thf(278,plain,
    ! [A: real] :
      ( ( ( uminus_uminus_real @ A )
        = zero_zero_real )
      = ( A = zero_zero_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(124,axiom,
    ! [A: a] :
      ( ( member_real @ zero_zero_real @ top_top_set_real )
     => ( ( member_a @ A @ x )
       => ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_local_Oflow__initial__time) ).

thf(608,plain,
    ! [A: a] :
      ( ( member_real @ zero_zero_real @ top_top_set_real )
     => ( ( member_a @ A @ x )
       => ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(24,axiom,
    ! [A: real,B: real] :
      ( ( ( plus_plus_real @ A @ B )
        = B )
      = ( A = zero_zero_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_add__cancel__left__left) ).

thf(306,plain,
    ! [A: real,B: real] :
      ( ( ( plus_plus_real @ A @ B )
        = B )
      = ( A = zero_zero_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(22,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ A @ C ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_add__left__imp__eq) ).

thf(299,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)],[22]) ).

thf(225,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A )
          = B )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( uminus_uminus_real @ A ) )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_rev_Orecurrence__time__flip__sign_I2_J) ).

thf(922,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A )
          = B )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( uminus_uminus_real @ A ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(9,axiom,
    initia826609931terval @ top_top_set_real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_interval__axioms) ).

thf(267,plain,
    initia826609931terval @ top_top_set_real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(202,axiom,
    ! [A: a] :
      ( ~ ( member_a @ A @ x )
     => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
        = bot_bot_set_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_local_Orev_Oexistence__ivl__undefined) ).

thf(851,plain,
    ! [A: a] :
      ( ~ ( member_a @ A @ x )
     => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
        = bot_bot_set_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(79,axiom,
    ! [A: real,B: real] :
      ( ( ( uminus_uminus_real @ A )
        = B )
      = ( ( uminus_uminus_real @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_minus__equation__iff) ).

thf(473,plain,
    ! [A: real,B: real] :
      ( ( ( uminus_uminus_real @ A )
        = B )
      = ( ( uminus_uminus_real @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(118,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/sandbox2/benchmark/theBenchmark.p',fact_329_diff__add__eq__diff__diff__swap) ).

thf(589,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)],[118]) ).

thf(182,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( ( member_a @ C @ x )
       => ( ! [D: real,E: real,F: a] :
              ( ( member_a @ F @ x )
             => ( ( uminus_uminus_a_a @ f @ F )
                = ( uminus_uminus_a_a @ f @ F ) ) )
         => ( ( top_top_set_real = top_top_set_real )
           => ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_rev_Omem__existence__ivl__shift__autonomous2) ).

thf(795,plain,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( ( member_a @ C @ x )
       => ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(138,axiom,
    ! [A: real] :
      ( ( minus_minus_real @ zero_zero_real @ A )
      = ( uminus_uminus_real @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_verit__minus__simplify_I3_J) ).

thf(663,plain,
    ! [A: real] :
      ( ( minus_minus_real @ zero_zero_real @ A )
      = ( uminus_uminus_real @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(227,axiom,
    ! [A: a,B: real] :
      ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_rev_Oclosed__orbit__flow0) ).

thf(927,plain,
    ! [A: a,B: real] :
      ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(5,axiom,
    ! [A: real] :
      ( ( zero_zero_real = A )
      = ( A = zero_zero_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_zero__reorient) ).

thf(255,plain,
    ! [A: real] :
      ( ( zero_zero_real = A )
      = ( A = zero_zero_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(189,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( member_real @ zero_zero_real @ top_top_set_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_local_Omem__existence__ivl__iv__defined_I1_J) ).

thf(812,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( member_real @ zero_zero_real @ top_top_set_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(165,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( minus_minus_real @ A @ B )
        = ( minus_minus_real @ C @ D ) )
     => ( ( ord_less_real @ A @ B )
        = ( ord_less_real @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_diff__eq__diff__less) ).

thf(749,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( minus_minus_real @ A @ B )
        = ( minus_minus_real @ C @ D ) )
     => ( ( ord_less_real @ A @ B )
        = ( ord_less_real @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(231,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_general_Oflow__in__domain) ).

thf(939,plain,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) @ x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(198,axiom,
    ! [A: a,B: real] :
      ( ( period720806154rbit_a @ f @ x @ A )
     => ( period720806154rbit_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_closed__orbit__flow0) ).

thf(836,plain,
    ! [A: a,B: real] :
      ( ( period720806154rbit_a @ f @ x @ A )
     => ( period720806154rbit_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(84,axiom,
    ! [A: real] :
      ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
      = zero_zero_real ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_add_Oleft__inverse) ).

thf(490,plain,
    ! [A: real] :
      ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
      = zero_zero_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(143,axiom,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_add__diff__cancel__right_H) ).

thf(675,plain,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(135,axiom,
    ! [A: a] :
      ( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ A ) )
      = ( ( member_real @ zero_zero_real @ top_top_set_real )
        & ( member_a @ A @ x ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_local_Oexistence__ivl__initial__time__iff) ).

thf(648,plain,
    ! [A: a] :
      ( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ A ) )
      = ( ( member_real @ zero_zero_real @ top_top_set_real )
        & ( member_a @ A @ x ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(83,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ zero_zero_real @ A )
     => ( ( ord_less_real @ zero_zero_real @ B )
       => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_add__pos__pos) ).

thf(487,plain,
    ! [A: real,B: real] :
      ( ( ord_less_real @ zero_zero_real @ A )
     => ( ( ord_less_real @ zero_zero_real @ B )
       => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(241,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ord_less_real @ A @ B )
     => ( ( ord_less_real @ C @ D )
       => ( ord_less_real @ ( minus_minus_real @ A @ D ) @ ( minus_minus_real @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_diff__strict__mono) ).

thf(968,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ord_less_real @ A @ B )
     => ( ( ord_less_real @ C @ D )
       => ( ord_less_real @ ( minus_minus_real @ A @ D ) @ ( minus_minus_real @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(74,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = ( plus_plus_real @ C @ B ) )
     => ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_add__right__imp__eq) ).

thf(458,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)],[74]) ).

thf(194,axiom,
    ! [A: a] :
      ( ( member_real @ zero_zero_real @ top_top_set_real )
     => ( ( member_a @ A @ x )
       => ( ( auto_l612940ivl0_a @ f @ x @ A )
         != bot_bot_set_real ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_local_Oexistence__ivl__notempty) ).

thf(823,plain,
    ! [A: a] :
      ( ( member_real @ zero_zero_real @ top_top_set_real )
     => ( ( member_a @ A @ x )
       => ( ( auto_l612940ivl0_a @ f @ x @ A )
         != bot_bot_set_real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(174,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( ( member_a @ C @ x )
       => ( ! [D: real,E: real,F: a] :
              ( ( member_a @ F @ x )
             => ( ( f @ F )
                = ( f @ F ) ) )
         => ( ( top_top_set_real = top_top_set_real )
           => ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_mem__existence__ivl__shift__autonomous2) ).

thf(776,plain,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( ( member_a @ C @ x )
       => ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(97,axiom,
    ! [A: a] :
      ( ( ( auto_l612940ivl0_a @ f @ x @ A )
        = bot_bot_set_real )
      = ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
        | ~ ( member_a @ A @ x ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_local_Oexistence__ivl__empty__iff) ).

thf(525,plain,
    ! [A: a] :
      ( ( ( auto_l612940ivl0_a @ f @ x @ A )
        = bot_bot_set_real )
      = ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
        | ~ ( member_a @ A @ x ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(209,axiom,
    ! [A: a] :
      ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ( member_a @ A @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_rev_Oclosed__orbit__in__domain) ).

thf(872,plain,
    ! [A: a] :
      ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ( member_a @ A @ x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(242,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( ( member_a @ C @ x )
       => ( ! [D: real,E: real,F: a] :
              ( ( member_a @ F @ x )
             => ( ( uminus_uminus_a_a @ f @ F )
                = ( uminus_uminus_a_a @ f @ F ) ) )
         => ( ( top_top_set_real = top_top_set_real )
           => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) )
              = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_rev_Oflow__shift__autonomous2) ).

thf(971,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(31,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
     => ( ord_less_real @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_add__less__imp__less__left) ).

thf(327,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
     => ( ord_less_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(58,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_add__strict__left__mono) ).

thf(409,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(117,axiom,
    ! [A: real,B: real,C: a,D: real] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( ( member_real @ D @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) ) )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ ( plus_plus_real @ A @ D ) @ B ) )
          = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_rev_Ogeneral_Oflow__trans) ).

thf(585,plain,
    ! [A: real,B: real,C: a,D: real] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( ( member_real @ D @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) ) )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ ( plus_plus_real @ A @ D ) @ B ) )
          = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(155,axiom,
    ! [A: real] :
      ( ( minus_minus_real @ A @ A )
      = zero_zero_real ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_diff__self) ).

thf(717,plain,
    ! [A: real] :
      ( ( minus_minus_real @ A @ A )
      = zero_zero_real ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(35,axiom,
    ! [A: a] :
      ( ( zero_zero_a = A )
      = ( A = zero_zero_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_zero__reorient) ).

thf(338,plain,
    ! [A: a] :
      ( ( zero_zero_a = A )
      = ( A = zero_zero_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(114,axiom,
    ! [A: real,B: real,C: a] :
      ( ~ ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) )
        = zero_zero_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_general_Oflow__undefined0) ).

thf(576,plain,
    ! [A: real,B: real,C: a] :
      ( ~ ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) )
        = zero_zero_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(187,axiom,
    member_a @ xx @ x,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062xx_A_092_060in_062_AX_092_060close_062) ).

thf(808,plain,
    member_a @ xx @ x,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(42,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/sandbox2/benchmark/theBenchmark.p',fact_273_add_Oleft__commute) ).

thf(359,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)],[42]) ).

thf(126,axiom,
    ! [A: a] :
      ( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) )
      = ( ( member_real @ zero_zero_real @ top_top_set_real )
        & ( member_a @ A @ x ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_local_Orev_Oexistence__ivl__initial__time__iff) ).

thf(613,plain,
    ! [A: a] :
      ( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) )
      = ( ( member_real @ zero_zero_real @ top_top_set_real )
        & ( member_a @ A @ x ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(120,axiom,
    ! [A: real,B: real,C: a] :
      ( ( A != B )
     => ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ C ) )
       => ( ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ C ) )
         => ( ( ( auto_ll_on_flow0_a @ f @ x @ C @ A )
              = ( auto_ll_on_flow0_a @ f @ x @ C @ B ) )
           => ( ( ( f @ C )
               != zero_zero_a )
             => ( period138238489rbit_a @ f @ x @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_periodic__orbitI) ).

thf(595,plain,
    ! [A: real,B: real,C: a] :
      ( ( A != B )
     => ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ C ) )
       => ( ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ C ) )
         => ( ( ( auto_ll_on_flow0_a @ f @ x @ C @ A )
              = ( auto_ll_on_flow0_a @ f @ x @ C @ B ) )
           => ( ( ( f @ C )
               != zero_zero_a )
             => ( period138238489rbit_a @ f @ x @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(125,axiom,
    member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_ss__ex) ).

thf(612,plain,
    member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(76,axiom,
    ! [A: real,B: real > $o] :
      ( ( member_real @ A @ ( collect_real @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_mem__Collect__eq) ).

thf(465,plain,
    ! [A: real,B: real > $o] :
      ( ( member_real @ A @ ( collect_real @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(130,axiom,
    ! [A: real,B: a] :
      ( ( ( ( member_real @ A @ top_top_set_real )
          & ( member_a @ B @ x ) )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( minus_minus_real @ A @ A ) )
          = B ) )
      & ( ~ ( ( member_real @ A @ top_top_set_real )
            & ( member_a @ B @ x ) )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( minus_minus_real @ A @ A ) )
          = zero_zero_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_rev_Ogeneral_Oflow__initial__time__if) ).

thf(627,plain,
    ! [A: real,B: a] :
      ( ( ( ( member_real @ A @ top_top_set_real )
          & ( member_a @ B @ x ) )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( minus_minus_real @ A @ A ) )
          = B ) )
      & ( ~ ( ( member_real @ A @ top_top_set_real )
            & ( member_a @ B @ x ) )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( minus_minus_real @ A @ A ) )
          = zero_zero_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(147,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( member_real @ zero_zero_real @ top_top_set_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_local_Orev_Omem__existence__ivl__iv__defined_I1_J) ).

thf(688,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( member_real @ zero_zero_real @ top_top_set_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(116,axiom,
    ! [A: real,B: a,C: real] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) ) )
       => ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( plus_plus_real @ A @ C ) )
          = ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_local_Oflow__trans) ).

thf(581,plain,
    ! [A: real,B: a,C: real] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) ) )
       => ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( plus_plus_real @ A @ C ) )
          = ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(86,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( ( ( auto_ll_on_flow0_a @ f @ x @ B @ A )
          = B )
       => ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( uminus_uminus_real @ A ) )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_recurrence__time__flip__sign_I2_J) ).

thf(495,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( ( ( auto_ll_on_flow0_a @ f @ x @ B @ A )
          = B )
       => ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( uminus_uminus_real @ A ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(45,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( A = B )
        & ( ord_less_real @ C @ D ) )
     => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_add__mono__thms__linordered__field_I2_J) ).

thf(368,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( A = B )
        & ( ord_less_real @ C @ D ) )
     => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(151,axiom,
    ! [A: a] :
      ( ( ( ( member_real @ zero_zero_real @ top_top_set_real )
          & ( member_a @ A @ x ) )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
          = A ) )
      & ( ~ ( ( member_real @ zero_zero_real @ top_top_set_real )
            & ( member_a @ A @ x ) )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
          = zero_zero_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_local_Orev_Oflow__initial__time__if) ).

thf(699,plain,
    ! [A: a] :
      ( ( ( ( member_real @ zero_zero_real @ top_top_set_real )
          & ( member_a @ A @ x ) )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
          = A ) )
      & ( ~ ( ( member_real @ zero_zero_real @ top_top_set_real )
            & ( member_a @ A @ x ) )
       => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
          = zero_zero_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(94,axiom,
    ! [A: a] :
      ( ( member_a @ A @ x )
     => ( ( ( uminus_uminus_a_a @ f @ A )
          = zero_zero_a )
       => ( ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
          = zero_zero_real ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_rev_Ofixed__point__imp__closed__orbit__period__zero_I2_J) ).

thf(517,plain,
    ! [A: a] :
      ( ( member_a @ A @ x )
     => ( ( ( uminus_uminus_a_a @ f @ A )
          = zero_zero_a )
       => ( ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
          = zero_zero_real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(6,axiom,
    ! [A: real,B: real] :
      ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
      = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_minus__add__distrib) ).

thf(258,plain,
    ! [A: real,B: real] :
      ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
      = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(176,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( member_a @ B @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_local_Omem__existence__ivl__iv__defined_I2_J) ).

thf(781,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( member_a @ B @ x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(159,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_diff__strict__right__mono) ).

thf(731,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ A @ B )
     => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(61,axiom,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( ord_less_real @ A @ B )
        & ( C = D ) )
     => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_add__mono__thms__linordered__field_I1_J) ).

thf(418,plain,
    ! [A: real,B: real,C: real,D: real] :
      ( ( ( ord_less_real @ A @ B )
        & ( C = D ) )
     => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(178,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_flow0__defined) ).

thf(786,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
     => ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) @ x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(140,axiom,
    ! [A: real,B: a,C: real] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( ( member_real @ C @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) )
       => ( member_real @ ( plus_plus_real @ A @ C ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_local_Orev_Oexistence__ivl__trans) ).

thf(667,plain,
    ! [A: real,B: a,C: real] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( ( member_real @ C @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) )
       => ( member_real @ ( plus_plus_real @ A @ C ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(105,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ top_top_set_real )
     => ( ( member_a @ B @ x )
       => ( member_real @ ( minus_minus_real @ A @ A ) @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_general_Oexistence__ivl__initial__time) ).

thf(549,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ top_top_set_real )
     => ( ( member_a @ B @ x )
       => ( member_real @ ( minus_minus_real @ A @ A ) @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(184,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( plus_plus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ C ) )
       => ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_local_Oexistence__ivl__trans_H) ).

thf(800,plain,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( plus_plus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ C ) )
       => ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(222,axiom,
    ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ xx @ tt ) @ ( uminus_uminus_real @ tt ) )
    = ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) @ ( uminus_uminus_real @ tt ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062flow0_A_Iflow0_Axx_Att_J_A_I_N_Att_J_A_061_Aflow0_A_Iflow0_Ax_Ass_J_A_I_N_Att_J_092_060close_062) ).

thf(914,plain,
    ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ xx @ tt ) @ ( uminus_uminus_real @ tt ) )
    = ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) @ ( uminus_uminus_real @ tt ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(48,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
      = ( ord_less_real @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_add__less__cancel__left) ).

thf(378,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
      = ( ord_less_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(66,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
      = ( ord_less_real @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_neg__less__iff__less) ).

thf(433,plain,
    ! [A: real,B: real] :
      ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
      = ( ord_less_real @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(91,axiom,
    ! [A: a] :
      ( ( member_a @ A @ x )
     => ( ( ( f @ A )
          = zero_zero_a )
       => ( ( period1305449585riod_a @ f @ x @ A )
          = zero_zero_real ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_fixed__point__imp__closed__orbit__period__zero_I2_J) ).

thf(510,plain,
    ! [A: a] :
      ( ( member_a @ A @ x )
     => ( ( ( f @ A )
          = zero_zero_a )
       => ( ( period1305449585riod_a @ f @ x @ A )
          = zero_zero_real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(197,axiom,
    ! [A: a] :
      ( ( member_real @ zero_zero_real @ top_top_set_real )
     => ( ( member_a @ A @ x )
       => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
         != bot_bot_set_real ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_local_Orev_Oexistence__ivl__notempty) ).

thf(832,plain,
    ! [A: a] :
      ( ( member_real @ zero_zero_real @ top_top_set_real )
     => ( ( member_a @ A @ x )
       => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
         != bot_bot_set_real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(146,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ top_top_set_real )
     => ( ( member_a @ B @ x )
       => ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( minus_minus_real @ A @ A ) )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_general_Oflow__initial__time) ).

thf(684,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ top_top_set_real )
     => ( ( member_a @ B @ x )
       => ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( minus_minus_real @ A @ A ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(128,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ( plus_plus_real @ A @ B )
        = C )
     => ( A
        = ( minus_minus_real @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_add__implies__diff) ).

thf(620,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)],[128]) ).

thf(166,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/sandbox2/benchmark/theBenchmark.p',fact_327_diff__diff__add) ).

thf(752,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)],[166]) ).

thf(27,axiom,
    ! [A: real,B: real] :
      ( ( ( uminus_uminus_real @ A )
        = ( uminus_uminus_real @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_neg__equal__iff__equal) ).

thf(315,plain,
    ! [A: real,B: real] :
      ( ( ( uminus_uminus_real @ A )
        = ( uminus_uminus_real @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(235,axiom,
    ! [A: real,B: real,C: real,D: a] :
      ( ( member_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) @ ( auto_l612940ivl0_a @ f @ x @ D ) )
     => ( ( member_real @ ( minus_minus_real @ A @ C ) @ ( auto_l612940ivl0_a @ f @ x @ D ) )
       => ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ D @ ( minus_minus_real @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_general_Oexistence__ivl__trans_H) ).

thf(950,plain,
    ! [A: real,B: real,C: real,D: a] :
      ( ( member_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) @ ( auto_l612940ivl0_a @ f @ x @ D ) )
     => ( ( member_real @ ( minus_minus_real @ A @ C ) @ ( auto_l612940ivl0_a @ f @ x @ D ) )
       => ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ D @ ( minus_minus_real @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(192,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( member_real @ ( minus_minus_real @ B @ A ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_general_Oexistence__ivl__reverse) ).

thf(818,plain,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( member_real @ ( minus_minus_real @ B @ A ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(203,axiom,
    ! [A: a] :
      ( ( member_a @ A @ x )
     => ( ( ( uminus_uminus_a_a @ f @ A )
          = zero_zero_a )
       => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
          = top_top_set_real ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_rev_Ofixpoint__sol_I1_J) ).

thf(854,plain,
    ! [A: a] :
      ( ( member_a @ A @ x )
     => ( ( ( uminus_uminus_a_a @ f @ A )
          = zero_zero_a )
       => ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
          = top_top_set_real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(12,axiom,
    ! [A: real] :
      ( ( zero_zero_real
        = ( plus_plus_real @ A @ A ) )
      = ( A = zero_zero_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_double__zero__sym) ).

thf(273,plain,
    ! [A: real] :
      ( ( zero_zero_real
        = ( plus_plus_real @ A @ A ) )
      = ( A = zero_zero_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(62,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/sandbox2/benchmark/theBenchmark.p',fact_281_add_Oassoc) ).

thf(422,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)],[62]) ).

thf(180,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( member_real @ ( minus_minus_real @ B @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_rev_Ogeneral_Oexistence__ivl__reverse) ).

thf(790,plain,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( member_real @ ( minus_minus_real @ B @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(36,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
      = ( ord_less_real @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_add__less__cancel__right) ).

thf(341,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
      = ( ord_less_real @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(10,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
     => ( ord_less_real @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_add__less__imp__less__right) ).

thf(268,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
     => ( ord_less_real @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(99,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( member_real @ B @ top_top_set_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_general_Omem__existence__ivl__iv__defined_I1_J) ).

thf(532,plain,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
     => ( member_real @ B @ top_top_set_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(150,axiom,
    ! [A: a] :
      ( ( member_real @ zero_zero_real @ top_top_set_real )
     => ( ( member_a @ A @ x )
       => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_local_Oexistence__ivl__initial__time) ).

thf(696,plain,
    ! [A: a] :
      ( ( member_real @ zero_zero_real @ top_top_set_real )
     => ( ( member_a @ A @ x )
       => ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(156,axiom,
    ! [A: real,B: real,C: a] :
      ( ( A != B )
     => ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
       => ( ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
         => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ A )
              = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ B ) )
           => ( ( ( uminus_uminus_a_a @ f @ C )
               != zero_zero_a )
             => ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_rev_Operiodic__orbitI) ).

thf(720,plain,
    ! [A: real,B: real,C: a] :
      ( ( A != B )
     => ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
       => ( ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
         => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ A )
              = ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ B ) )
           => ( ( ( uminus_uminus_a_a @ f @ C )
               != zero_zero_a )
             => ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(237,axiom,
    ! [A: a] :
      ( ( period720806154rbit_a @ f @ x @ A )
     => ~ ! [B: real] :
            ( ( ord_less_real @ zero_zero_real @ B )
           => ~ ! [C: real] :
                  ( ( auto_ll_on_flow0_a @ f @ x @ A @ ( plus_plus_real @ C @ B ) )
                  = ( auto_ll_on_flow0_a @ f @ x @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_closed__orbitE) ).

thf(955,plain,
    ! [A: a] :
      ( ( period720806154rbit_a @ f @ x @ A )
     => ~ ! [B: real] :
            ( ( ord_less_real @ zero_zero_real @ B )
           => ~ ! [C: real] :
                  ( ( auto_ll_on_flow0_a @ f @ x @ A @ ( plus_plus_real @ C @ B ) )
                  = ( auto_ll_on_flow0_a @ f @ x @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(60,axiom,
    ! [A: real] :
      ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
      = ( ord_less_real @ A @ zero_zero_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_less__neg__neg) ).

thf(415,plain,
    ! [A: real] :
      ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
      = ( ord_less_real @ A @ zero_zero_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(216,axiom,
    ord_less_real @ tt @ d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_tt_I2_J) ).

thf(897,plain,
    ord_less_real @ tt @ d,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(171,axiom,
    ! [A: a] :
      ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
      = ( period720806154rbit_a @ f @ x @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_rev_Oclosed__orbit__eq__rev) ).

thf(767,plain,
    ! [A: a] :
      ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
      = ( period720806154rbit_a @ f @ x @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(33,axiom,
    ! [A: set_real] :
      ( ( collect_real
        @ ^ [B: real] : ( member_real @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Collect__mem__eq) ).

thf(332,plain,
    ! [A: set_real] :
      ( ( collect_real
        @ ^ [B: real] : ( member_real @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(205,axiom,
    ! [A: a] :
      ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_rev_Operiodic__orbit__period_I2_J) ).

thf(860,plain,
    ! [A: a] :
      ( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
     => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(98,axiom,
    ! [A: a,B: real] :
      ( ( member_a @ A @ x )
     => ( ( ( f @ A )
          = zero_zero_a )
       => ( ( auto_ll_on_flow0_a @ f @ x @ A @ B )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_fixpoint__sol_I2_J) ).

thf(528,plain,
    ! [A: a,B: real] :
      ( ( member_a @ A @ x )
     => ( ( ( f @ A )
          = zero_zero_a )
       => ( ( auto_ll_on_flow0_a @ f @ x @ A @ B )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(220,axiom,
    ! [A: a] :
      ( ( period720806154rbit_a @ f @ x @ A )
     => ( ( ( period1305449585riod_a @ f @ x @ A )
          = zero_zero_real )
       => ( ( f @ A )
          = zero_zero_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_closed__orbit__period__zero__fixed__point) ).

thf(908,plain,
    ! [A: a] :
      ( ( period720806154rbit_a @ f @ x @ A )
     => ( ( ( period1305449585riod_a @ f @ x @ A )
          = zero_zero_real )
       => ( ( f @ A )
          = zero_zero_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(148,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( member_a @ B @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_local_Orev_Omem__existence__ivl__iv__defined_I2_J) ).

thf(691,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( member_a @ B @ x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(69,axiom,
    ! [A: real,B: real] :
      ( ( A
        = ( uminus_uminus_real @ B ) )
      = ( B
        = ( uminus_uminus_real @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_equation__minus__iff) ).

thf(442,plain,
    ! [A: real,B: real] :
      ( ( A
        = ( uminus_uminus_real @ B ) )
      = ( B
        = ( uminus_uminus_real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(88,axiom,
    ! [A: real,B: real] :
      ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_diff__add__cancel) ).

thf(501,plain,
    ! [A: real,B: real] :
      ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(54,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
      = ( ord_less_real @ A @ zero_zero_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_add__less__same__cancel2) ).

thf(395,plain,
    ! [A: real,B: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
      = ( ord_less_real @ A @ zero_zero_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(129,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( member_real @ B @ top_top_set_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_rev_Ogeneral_Omem__existence__ivl__iv__defined_I1_J) ).

thf(624,plain,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( member_real @ B @ top_top_set_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(199,axiom,
    ! [A: real,B: real,C: real] :
      ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_cancel__ab__semigroup__add__class_Odiff__right__commute) ).

thf(839,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)],[199]) ).

thf(158,axiom,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_add__diff__cancel__left_H) ).

thf(728,plain,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(162,axiom,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A )
          = B )
       => ( member_real @ ( uminus_uminus_real @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_rev_Orecurrence__time__flip__sign_I1_J) ).

thf(740,plain,
    ! [A: real,B: a] :
      ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
     => ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A )
          = B )
       => ( member_real @ ( uminus_uminus_real @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(25,axiom,
    ! [A: real,B: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ A )
      = ( ord_less_real @ B @ zero_zero_real ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_add__less__same__cancel1) ).

thf(309,plain,
    ! [A: real,B: real] :
      ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ A )
      = ( ord_less_real @ B @ zero_zero_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(103,axiom,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
      = ( plus_plus_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_diff__minus__eq__add) ).

thf(543,plain,
    ! [A: real,B: real] :
      ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
      = ( plus_plus_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(167,axiom,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) @ ( minus_minus_real @ B @ A ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_rev_Ogeneral_Oflows__reverse) ).

thf(755,plain,
    ! [A: real,B: real,C: a] :
      ( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
     => ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) @ ( minus_minus_real @ B @ A ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(119,axiom,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_diff__less__eq) ).

thf(592,plain,
    ! [A: real,B: real,C: real] :
      ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
      = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(73,axiom,
    ! [A: real,B: real] :
      ( ( A = B )
     => ( ( uminus_uminus_real @ A )
        = ( uminus_uminus_real @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_verit__negate__coefficient_I3_J) ).

thf(454,plain,
    ! [A: real,B: real] :
      ( ( A = B )
     => ( ( uminus_uminus_real @ A )
        = ( uminus_uminus_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(243,axiom,
    ! [A: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_rev_Omvar_Ointerval__axioms) ).

thf(972,plain,
    ! [A: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(1124,plain,
    $false,
    inference(cvc4,[status(thm)],[645,809,365,479,347,846,249,941,555,666,962,468,977,523,276,247,384,797,945,930,670,829,898,709,288,436,651,724,570,372,504,934,802,344,559,881,448,261,284,770,321,353,602,877,734,293,866,774,428,312,292,439,678,270,661,546,925,761,381,714,894,746,778,952,820,392,693,788,815,916,252,879,329,493,710,842,566,484,324,974,874,356,869,783,857,980,403,471,884,537,642,637,901,476,515,911,605,792,805,508,398,412,965,425,264,573,296,375,513,430,743,281,562,904,579,291,641,391,498,335,919,947,350,540,672,445,936,764,406,681,599,863,362,451,567,737,318,616,303,387,758,552,535,816,520,462,959,827,278,608,306,299,922,267,851,473,589,795,663,927,255,812,749,939,836,490,675,648,487,968,458,823,776,525,872,971,327,409,585,717,338,576,808,359,613,595,612,465,627,688,581,495,368,699,517,258,781,731,418,786,667,549,800,914,378,433,510,832,684,620,752,315,950,818,854,273,422,790,341,268,532,696,720,955,415,897,767,332,860,528,908,691,442,501,395,624,839,728,740,309,543,755,592,454,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : ITP146^1 : TPTP v8.2.0. Released v7.5.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n027.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sat May 18 17:21:09 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.96/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.67/1.10  % [INFO] 	 Parsing done (237ms). 
% 1.67/1.11  % [INFO] 	 Running in sequential loop mode. 
% 2.43/1.33  % [INFO] 	 eprover registered as external prover. 
% 2.73/1.34  % [INFO] 	 cvc4 registered as external prover. 
% 2.73/1.34  % [INFO] 	 Scanning for conjecture ... 
% 2.84/1.43  % [INFO] 	 Found a conjecture (or negated_conjecture) and 342 axioms. Running axiom selection ... 
% 3.34/1.52  % [INFO] 	 Axiom selection finished. Selected 244 axioms (removed 98 axioms). 
% 3.71/1.67  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.71/1.68  % [INFO] 	 Type checking passed. 
% 3.89/1.68  % [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 ... 
% 12.45/3.68  % External prover 'cvc4' found a proof!
% 12.45/3.68  % [INFO] 	 Killing All external provers ... 
% 12.45/3.68  % Time passed: 3154ms (effective reasoning time: 2563ms)
% 12.45/3.68  % 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)>
% 12.45/3.68  % Axioms used in derivation (244): fact_307_verit__negate__coefficient_I2_J, fact_263_add__strict__mono, fact_76_rev_Orecurrence__time__flip__sign_I2_J, fact_185_add__cancel__right__right, fact_81_rev_Oclosed__orbit__global__existence, fact_200_add__diff__cancel__right_H, fact_48_Collect__mem__eq, fact_175_add_Oright__neutral, fact_78_rev_Ofixpoint__sol_I1_J, fact_196_minus__add__cancel, fact_77_rev_Orecurrence__time__flip__sign_I1_J, fact_335_add__diff__eq, fact_157_add__left__cancel, fact_187_neg__less__iff__less, fact_73_rev_Ogeneral_Oexistence__ivl__reverse, fact_249_add__neg__neg, fact_303_add_Ocomm__neutral, fact_273_add_Oleft__commute, fact_57_rev__eq__flow, fact_71_general_Omem__existence__ivl__subset, fact_251_add__pos__pos, fact_213_tt_I2_J, fact_67_rev_Ogeneral_Omem__existence__ivl__subset, fact_119_local_Orev_Oexistence__ivl__initial__time__iff, fact_113_minus__diff__eq, fact_283_group__cancel_Oadd2, fact_313_diff__strict__right__mono, fact_22_local_Oflow__in__domain, fact_122_local_Orev_Oflow__initial__time, fact_10_general_Oflow__in__domain, fact_237_add_Oright__inverse, fact_120_local_Omem__existence__ivl__iv__defined_I1_J, fact_34_local_Oexistence__ivl__reverse, fact_291_add__mono__thms__linordered__field_I2_J, fact_147_periodic__orbit__period_I2_J, fact_8_diff__existence__ivl__trans, fact_225_add__less__same__cancel2, fact_325_add__implies__diff, fact_54_local_Orev_Omem__existence__ivl__subset, fact_7_neg__tt__ex, fact_192_add__less__cancel__left, fact_230_double__add__less__zero__iff__single__add__less__zero, fact_107_diff__0__right, fact_223_add__less__same__cancel1, fact_1__092_060open_062flow0_A_Iflow0_Axx_Att_J_A_I_N_Att_J_A_061_Aflow0_A_Iflow0_Ax_Ass_J_A_I_N_Att_J_092_060close_062, fact_53_rev_Ogeneral_Omem__existence__ivl__iv__defined_I2_J, fact_75_rev_Ogeneral_Oflows__reverse, fact_194_add__minus__cancel, fact_89_flow__shift__autonomous2, fact_115_local_Orev_Omem__existence__ivl__iv__defined_I2_J, fact_241_diff__minus__eq__add, fact_244_local_Oexistence__ivl__empty__iff, fact_70_mem__existence__ivl__shift__autonomous2, fact_58_rev_Ofixpoint__sol_I2_J, fact_148_rev_Ofixed__point__imp__closed__orbit__period__zero_I2_J, fact_214_rev_Oclosed__orbitE, fact_231_linordered__ab__group__add__class_Ozero__less__double__add__iff__zero__less__single__add, fact_26_closed__orbit__periodic, fact_33_local_Oflows__reverse, fact_257_add__less__imp__less__left, fact_15_fixed__point__imp__closed__orbit__period__zero_I1_J, fact_66_rev_Omem__existence__ivl__shift__autonomous2, fact_160_local_Oexistence__ivl__trans_H, fact_72_rev_Odiff__existence__ivl__trans, fact_135_verit__negate__coefficient_I3_J, fact_91_local_Oflow__initial__time__if, fact_0__092_060open_062xx_A_092_060in_062_AX_092_060close_062, fact_3_assms_I8_J, fact_50_Collect__cong, fact_285_group__cancel_Oadd1, fact_183_add__cancel__right__left, fact_211_rev_Operiodic__orbit__period_I1_J, fact_287_add__mono__thms__linordered__semiring_I4_J, fact_227_less__add__same__cancel1, fact_20_general_Oflow__undefined0, fact_275_add_Ocommute, fact_329_diff__add__eq__diff__diff__swap, fact_161_local_Oexistence__ivl__trans, fact_188_closed__orbitE, fact_212_periodic__orbit__def, fact_327_diff__diff__add, fact_94_rev_Ogeneral_Oflow__initial__time__if, fact_149_fixed__point__imp__closed__orbit__period__zero_I2_J, fact_317_diff__eq__diff__less, fact_60_rev_Omvar_Ointerval__axioms, fact_166_general_Oflow__trans, fact_242_local_Oexistence__ivl__undefined, fact_96_neg__equal__zero, fact_337_eq__diff__eq, fact_277_add_Oright__cancel, fact_105_diff__self, fact_17_recurrence__time__flip__sign_I2_J, fact_297_verit__comp__simplify1_I1_J, fact_144_rev_Oclosed__orbit__period__zero__fixed__point, fact_56_rev_Orev__eq__flow, fact_92_rev_Oclosed__orbit__def, fact_19_closed__orbitI, fact_295_ab__semigroup__add__class_Oadd__ac_I1_J, fact_126_rev_Ogeneral_Oflow__initial__time, fact_16_recurrence__time__flip__sign_I1_J, fact_176_linordered__ab__group__add__class_Odouble__zero, fact_158_d, fact_24_mvar_Ointerval__axioms, fact_155_add__right__cancel, fact_341_group__cancel_Osub1, fact_281_add_Oassoc, fact_255_add__less__imp__less__right, fact_167_general_Oexistence__ivl__trans_H, fact_85_rev_Oclosed__orbit__periodic, fact_37_rev_Oclosed__orbit__eq__rev, fact_101_neg__0__equal__iff__equal, fact_46_mem__Collect__eq, fact_32_closed__orbit__def, fact_177_double__zero__sym, fact_141_eq__iff__diff__eq__0, fact_9_general_Oexistence__ivl__reverse, fact_29_diff__0, fact_145_closed__orbit__period__zero__fixed__point, fact_173_add_Oleft__neutral, fact_31_verit__minus__simplify_I3_J, fact_62_local_Orev_Oexistence__ivl__initial__time, fact_25_periodic__orbitI, fact_168_general_Oexistence__ivl__trans, fact_179_add__cancel__left__left, fact_139_cancel__ab__semigroup__add__class_Odiff__right__commute, fact_18_local_Oflow__undefined0, fact_114_tt_I1_J, fact_27_periodic__orbit__imp__flow0__regular, fact_4_tt__ex, fact_90_local_Orev_Oflow__initial__time__if, fact_279_add_Oleft__cancel, fact_5_ss__ex, fact_259_add__strict__right__mono, fact_215_rev_Operiodic__orbit__def, fact_153_i2_I2_J, fact_125_general_Oexistence__ivl__initial__time__iff, fact_165_local_Orev_Oexistence__ivl__trans, fact_309_less__minus__iff, fact_82_closed__orbit__global__existence, fact_79_fixpoint__sol_I1_J, fact_63_local_Oexistence__ivl__initial__time, fact_261_add__strict__left__mono, fact_11_general_Oflows__reverse, fact_221_neg__less__0__iff__less, fact_339_diff__eq__eq, fact_65_rev_Ogeneral_Oexistence__ivl__initial__time, fact_116_rev_Oflow0__defined, fact_80_local_Orev_Oflow__undefined0, fact_323_add_Oinverse__distrib__swap, fact_206_add__diff__cancel__left, fact_127_general_Oflow__initial__time, fact_235_add_Oleft__inverse, fact_204_add__diff__cancel__left_H, fact_333_diff__diff__eq2, fact_88_rev_Oflow__shift__autonomous2, fact_305_add_Ogroup__left__neutral, fact_124_rev_Ogeneral_Oexistence__ivl__initial__time__iff, fact_143_minus__diff__commute, fact_45_rev_Oexistence__ivl__zero, fact_121_local_Oexistence__ivl__initial__time__iff, fact_61_rev_Ofixed__point__imp__closed__orbit__period__zero_I1_J, fact_129_zero__reorient, fact_21_local_Omem__existence__ivl__iv__defined_I2_J, fact_51_Collect__cong, fact_202_add__diff__cancel__right, fact_163_local_Orev_Oflow__trans, fact_271_diff__less__eq, fact_111_cancel__comm__monoid__add__class_Odiff__cancel, fact_216_less__neg__neg, fact_181_add__cancel__left__right, fact_84_rev_Operiodic__orbit__imp__flow0__regular, fact_162_i2_I3_J, fact_169_periodic__orbit__period_I1_J, fact_59_rev_Oclosed__orbit__flow0, fact_118_local_Orev_Omem__existence__ivl__iv__defined_I1_J, fact_265_add__right__imp__eq, fact_42_add_Oinverse__inverse, fact_269_less__diff__eq, fact_74_rev_Ogeneral_Oflow__in__domain, fact_49_Collect__mem__eq, fact_164_local_Orev_Oexistence__ivl__trans_H, fact_64_rev_Ogeneral_Omem__existence__ivl__iv__defined_I1_J, fact_2_eq, fact_99_neg__equal__0__iff__equal, fact_117_local_Orev_Oflow__in__domain, fact_152_rev_Ogeneral_Oexistence__ivl__trans, fact_86_local_Orev_Oexistence__ivl__reverse, fact_6_fixpoint__sol_I2_J, fact_243_local_Orev_Oexistence__ivl__undefined, fact_55_local_Omem__existence__ivl__subset, fact_87_local_Orev_Oflows__reverse, fact_52_existence__ivl__zero, fact_245_local_Oexistence__ivl__empty1, fact_150_local_Orev_Oexistence__ivl__notempty, fact_35_general_Oflow__initial__time__if, fact_315_diff__strict__left__mono, fact_253_pos__add__strict, fact_36_interval__axioms, fact_109_diff__zero, fact_13_closed__orbit__flow0, fact_171_rev_Ogeneral_Oexistence__ivl__trans_H, fact_128_zero__reorient, fact_311_minus__less__iff, fact_198_minus__add__distrib, fact_299_verit__sum__simplify, fact_151_local_Oexistence__ivl__notempty, fact_83_rev_Oclosed__orbitI, fact_319_diff__strict__mono, fact_133_equation__minus__iff, fact_69_general_Oexistence__ivl__initial__time, fact_14_closed__orbit__in__domain, fact_23_flow0__defined, fact_38_rev_Oclosed__orbit__in__domain, fact_47_mem__Collect__eq, fact_219_neg__0__less__iff__less, fact_137_diff__eq__diff__eq, fact_95_rev_Operiodic__orbitI, fact_97_equal__neg__zero, fact_246_local_Orev_Oexistence__ivl__empty__iff, fact_12_general_Omem__existence__ivl__iv__defined_I2_J, fact_293_add__mono__thms__linordered__field_I5_J, fact_170_rev_Ogeneral_Oflow__trans, fact_229_less__add__same__cancel2, fact_93_rev_Ogeneral_Oflow__undefined0, fact_68_general_Omem__existence__ivl__iv__defined_I1_J, fact_301_comm__monoid__add__class_Oadd__0, fact_267_add__left__imp__eq, fact_103_add_Oinverse__neutral, fact_239_uminus__add__conv__diff, fact_146_rev_Operiodic__orbit__period_I2_J, fact_217_neg__less__pos, fact_233_diff__gt__0__iff__gt, fact_159_local_Oflow__trans, fact_44_verit__minus__simplify_I4_J, fact_40_neg__equal__iff__equal, fact_289_add__mono__thms__linordered__field_I1_J, fact_208_diff__add__cancel, fact_247_local_Orev_Oexistence__ivl__empty1, fact_190_add__less__cancel__right, fact_210_add__diff__cancel, fact_123_local_Oflow__initial__time, fact_321_group__cancel_Oneg1, fact_331_diff__add__eq, fact_131_minus__equation__iff
% 12.45/3.68  % No. of inferences in proof: 492
% 12.45/3.68  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3154 ms resp. 2563 ms w/o parsing
% 13.24/3.82  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.24/3.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------