TSTP Solution File: ITP125^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP125^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:23:09 EDT 2024

% Result   : Theorem 22.25s 6.27s
% Output   : Refutation 23.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  315
% Syntax   : Number of formulae    :  601 ( 168 unt;  31 typ;   0 def)
%            Number of atoms       : 1650 ( 366 equ;  12 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 4919 ( 176   ~;  50   |;  80   &;3789   @)
%                                         (   0 <=>; 824  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   8 avg)
%            Number of types       :    7 (   6 usr)
%            Number of type conns  :  147 ( 147   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   29 (  26 usr;  17 con; 0-4 aty)
%            Number of variables   : 1704 ( 108   ^1528   !;  68   ?;1704   :)

% Comments : 
%------------------------------------------------------------------------------
thf(prefix1027212443list_a_type,type,
    prefix1027212443list_a: $tType ).

thf(trace_1367752404list_a_type,type,
    trace_1367752404list_a: $tType ).

thf(i_type,type,
    i: $tType ).

thf(formula_a_type,type,
    formula_a: $tType ).

thf(list_a_type,type,
    list_a: $tType ).

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

thf(one_one_nat_type,type,
    one_one_nat: nat ).

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

thf(until_a_type,type,
    until_a: formula_a > i > formula_a > formula_a ).

thf(sat_a_type,type,
    sat_a: trace_1367752404list_a > list_a > nat > formula_a > $o ).

thf(monito1457594016ress_a_type,type,
    monito1457594016ress_a: trace_1367752404list_a > formula_a > nat > nat ).

thf(ord_less_nat_type,type,
    ord_less_nat: nat > nat > $o ).

thf(ord_le887097159list_a_type,type,
    ord_le887097159list_a: prefix1027212443list_a > prefix1027212443list_a > $o ).

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

thf(ord_le699472955list_a_type,type,
    ord_le699472955list_a: prefix1027212443list_a > prefix1027212443list_a > $o ).

thf(tau_Pr257024512list_a_type,type,
    tau_Pr257024512list_a: trace_1367752404list_a > nat > nat ).

thf(plen_P694648887list_a_type,type,
    plen_P694648887list_a: prefix1027212443list_a > nat ).

thf(prefix1041802747list_a_type,type,
    prefix1041802747list_a: prefix1027212443list_a > trace_1367752404list_a > $o ).

thf(i2_type,type,
    i2: i ).

thf(phi_type,type,
    phi: formula_a ).

thf(phi_1_type,type,
    phi_1: formula_a ).

thf(phi_2_type,type,
    phi_2: formula_a ).

thf(pi_type,type,
    pi: prefix1027212443list_a ).

thf(sigma_type,type,
    sigma: trace_1367752404list_a ).

thf(sigma2_type,type,
    sigma2: trace_1367752404list_a ).

thf(b_type,type,
    b: nat ).

thf(i3_type,type,
    i3: nat ).

thf(ia_type,type,
    ia: nat ).

thf(j_type,type,
    j: nat ).

thf(ja_type,type,
    ja: nat ).

thf(k_type,type,
    k: nat ).

thf(159,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_dual__order_Ostrict__implies__not__eq) ).

thf(809,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(215,axiom,
    ~ ! [A: nat] :
        ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma2 @ A ) )
       => ( ( ord_less_eq_nat @ A @ ( monito1457594016ress_a @ sigma2 @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
         => ~ ( ord_less_eq_nat @ A @ ( monito1457594016ress_a @ sigma2 @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(1024,plain,
    ~ ! [A: nat] :
        ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma2 @ A ) )
       => ( ( ord_less_eq_nat @ A @ ( monito1457594016ress_a @ sigma2 @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
         => ~ ( ord_less_eq_nat @ A @ ( monito1457594016ress_a @ sigma2 @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(144,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
      = ( ( ord_less_nat @ A @ B )
        | ( ord_less_nat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_neq__iff) ).

thf(760,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
      = ( ( ord_less_nat @ A @ B )
        | ( ord_less_nat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(25,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le699472955list_a @ B @ C )
       => ( ord_le699472955list_a @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_order_Otrans) ).

thf(347,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le699472955list_a @ B @ C )
       => ( ord_le699472955list_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(232,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ C @ D )
       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_add__strict__mono) ).

thf(1083,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ C @ D )
       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(191,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ A @ B )
        = ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_antisym__conv1) ).

thf(941,plain,
    ! [A: nat,B: nat] :
      ( ~ ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ A @ B )
        = ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(266,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( ord_less_nat @ A @ B )
       => ( ord_less_nat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_neqE) ).

thf(1179,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( ord_less_nat @ A @ B )
       => ( ord_less_nat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(150,axiom,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_less__irrefl) ).

thf(777,plain,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(115,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le699472955list_a @ B @ C )
       => ( ord_le699472955list_a @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_order__trans) ).

thf(666,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le699472955list_a @ B @ C )
       => ( ord_le699472955list_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(243,axiom,
    ! [A: nat > nat,B: nat,C: nat] :
      ( ! [D: nat,E: nat] :
          ( ( ord_less_nat @ D @ E )
         => ( ord_less_nat @ ( A @ D ) @ ( A @ E ) ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ ( A @ B ) @ C ) @ ( A @ ( plus_plus_nat @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_mono__nat__linear__lb) ).

thf(1110,plain,
    ! [A: nat > nat,B: nat,C: nat] :
      ( ! [D: nat,E: nat] :
          ( ( ord_less_nat @ D @ E )
         => ( ord_less_nat @ ( A @ D ) @ ( A @ E ) ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ ( A @ B ) @ C ) @ ( A @ ( plus_plus_nat @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(61,axiom,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_ord__le__eq__subst) ).

thf(481,plain,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(20,axiom,
    ( ord_less_eq_nat
    = ( ^ [A: nat,B: nat] :
        ? [C: nat] :
          ( B
          = ( plus_plus_nat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_le__iff__add) ).

thf(333,plain,
    ( ord_less_eq_nat
    = ( ^ [A: nat,B: nat] :
        ? [C: nat] :
          ( B
          = ( plus_plus_nat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(217,axiom,
    ! [A: nat,B: nat] :
      ( ( ~ ( ord_less_nat @ A @ B ) )
      = ( ( ord_less_nat @ B @ A )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_not__less__iff__gr__or__eq) ).

thf(1031,plain,
    ! [A: nat,B: nat] :
      ( ( ~ ( ord_less_nat @ A @ B ) )
      = ( ( ord_less_nat @ B @ A )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(93,axiom,
    ! [A: nat,B: nat,C: trace_1367752404list_a] :
    ? [D: nat] :
      ( ( ord_less_eq_nat @ A @ D )
      & ( ord_less_eq_nat @ B @ ( tau_Pr257024512list_a @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_ex__le___092_060tau_062) ).

thf(582,plain,
    ! [A: nat,B: nat,C: trace_1367752404list_a] :
    ? [D: nat] :
      ( ( ord_less_eq_nat @ A @ D )
      & ( ord_less_eq_nat @ B @ ( tau_Pr257024512list_a @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(209,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_order_Oasym) ).

thf(994,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(138,axiom,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_verit__comp__simplify1_I1_J) ).

thf(741,plain,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(276,axiom,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ B @ C )
     => ~ ( ord_less_nat @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_pinf_I5_J) ).

thf(1205,plain,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ B @ C )
     => ~ ( ord_less_nat @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(254,axiom,
    ! [A: nat,B: list_a] :
      ( ( ord_less_nat @ A @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) )
     => ( ( sat_a @ sigma @ B @ A @ phi_2 )
        = ( sat_a @ sigma2 @ B @ A @ phi_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_Until_OIH_I2_J) ).

thf(1142,plain,
    ! [A: nat,B: list_a] :
      ( ( ord_less_nat @ A @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) )
     => ( ( sat_a @ sigma @ B @ A @ phi_2 )
        = ( sat_a @ sigma2 @ B @ A @ phi_2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(119,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ~ ! [C: nat] :
            ( B
           != ( plus_plus_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_less__eqE) ).

thf(677,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ~ ! [C: nat] :
            ( B
           != ( plus_plus_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(175,axiom,
    ord_less_nat @ ia @ ( monito1457594016ress_a @ sigma2 @ ( until_a @ phi_1 @ i2 @ phi_2 ) @ ( plen_P694648887list_a @ pi ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198__092_060open_062i_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_Iformula_OUntil_A_092_060phi_0621_AI_A_092_060phi_0622_J_A_Iplen_A_092_060pi_062_J_092_060close_062) ).

thf(861,plain,
    ord_less_nat @ ia @ ( monito1457594016ress_a @ sigma2 @ ( until_a @ phi_1 @ i2 @ phi_2 ) @ ( plen_P694648887list_a @ pi ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(36,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ C @ B ) )
      = ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_add__right__cancel) ).

thf(384,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ C @ B ) )
      = ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(252,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( ord_less_nat @ A @ B )
     => ( ord_less_eq_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_leI) ).

thf(1137,plain,
    ! [A: nat,B: nat] :
      ( ~ ( ord_less_nat @ A @ B )
     => ( ord_less_eq_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(66,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ~ ( ord_le887097159list_a @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_leD) ).

thf(500,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ~ ( ord_le887097159list_a @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(130,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_trans__le__add1) ).

thf(715,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(161,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_less__le__trans) ).

thf(814,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(126,axiom,
    ! [A: nat,B: nat,C: nat > prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_le887097159list_a @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_le699472955list_a @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_le887097159list_a @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_order__le__less__subst2) ).

thf(698,plain,
    ! [A: nat,B: nat,C: nat > prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_le887097159list_a @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_le699472955list_a @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_le887097159list_a @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(140,axiom,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_less__not__refl) ).

thf(747,plain,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(23,axiom,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_order__subst2) ).

thf(340,plain,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(79,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_le__cases) ).

thf(538,plain,
    ! [A: nat,B: nat] :
      ( ~ ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(237,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_add__strict__left__mono) ).

thf(1095,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(212,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_add__strict__right__mono) ).

thf(1001,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(248,axiom,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ C @ B )
     => ~ ( ord_less_nat @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_minf_I7_J) ).

thf(1127,plain,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ C @ B )
     => ~ ( ord_less_nat @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(43,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le699472955list_a @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_antisym) ).

thf(417,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le699472955list_a @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(184,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( A = B )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_ord__eq__less__trans) ).

thf(885,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( A = B )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(90,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le887097159list_a @ B @ C )
       => ( ord_le887097159list_a @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_le__less__trans) ).

thf(570,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le887097159list_a @ B @ C )
       => ( ord_le887097159list_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(34,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( A = B )
        & ( ord_less_eq_nat @ C @ D ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_add__mono__thms__linordered__semiring_I2_J) ).

thf(372,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( A = B )
        & ( ord_less_eq_nat @ C @ D ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(95,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le887097159list_a @ A @ B )
     => ( ord_le699472955list_a @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_order_Ostrict__implies__order) ).

thf(587,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le887097159list_a @ A @ B )
     => ( ord_le699472955list_a @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(127,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( A != B )
       => ( ord_le887097159list_a @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_le__neq__trans) ).

thf(702,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( A != B )
       => ( ord_le887097159list_a @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(24,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_dual__order_Oantisym) ).

thf(344,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(29,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le699472955list_a @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_order__class_Oorder_Oantisym) ).

thf(357,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le699472955list_a @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(225,axiom,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_less__irrefl__nat) ).

thf(1059,plain,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(250,axiom,
    ! [A: trace_1367752404list_a,B: nat,C: nat] :
      ( ( ord_less_nat @ ( tau_Pr257024512list_a @ A @ B ) @ ( tau_Pr257024512list_a @ A @ C ) )
     => ( ord_less_nat @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_less___092_060tau_062D) ).

thf(1132,plain,
    ! [A: trace_1367752404list_a,B: nat,C: nat] :
      ( ( ord_less_nat @ ( tau_Pr257024512list_a @ A @ B ) @ ( tau_Pr257024512list_a @ A @ C ) )
     => ( ord_less_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(108,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_add__mono) ).

thf(638,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(178,axiom,
    ord_less_eq_nat @ ja @ ( monito1457594016ress_a @ sigma2 @ phi_2 @ ( plen_P694648887list_a @ pi ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062) ).

thf(870,plain,
    ord_less_eq_nat @ ja @ ( monito1457594016ress_a @ sigma2 @ phi_2 @ ( plen_P694648887list_a @ pi ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(147,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_eq_nat @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_order_Ostrict__implies__order) ).

thf(770,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_eq_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(183,axiom,
    ! [A: nat,B: prefix1027212443list_a > nat,C: prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_less_nat @ A @ ( B @ C ) )
     => ( ( ord_le699472955list_a @ C @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_order__less__le__subst1) ).

thf(881,plain,
    ! [A: nat,B: prefix1027212443list_a > nat,C: prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_less_nat @ A @ ( B @ C ) )
     => ( ( ord_le699472955list_a @ C @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(17,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
     => ( ord_less_eq_nat @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_add__leD1) ).

thf(325,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
     => ( ord_less_eq_nat @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(4,axiom,
    ! [A: prefix1027212443list_a,B: nat > prefix1027212443list_a,C: nat,D: nat] :
      ( ( ord_le887097159list_a @ A @ ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_le699472955list_a @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_le887097159list_a @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_order__less__le__subst1) ).

thf(289,plain,
    ! [A: prefix1027212443list_a,B: nat > prefix1027212443list_a,C: nat,D: nat] :
      ( ( ord_le887097159list_a @ A @ ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_le699472955list_a @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_le887097159list_a @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(50,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
     => ( ord_less_eq_nat @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_add__le__imp__le__right) ).

thf(448,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
     => ( ord_less_eq_nat @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(14,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_antisym) ).

thf(316,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(239,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ( plus_plus_nat @ C @ B )
          = ( plus_plus_nat @ A @ D ) )
       => ( ord_less_nat @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_less__add__eq__less) ).

thf(1100,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ( plus_plus_nat @ C @ B )
          = ( plus_plus_nat @ A @ D ) )
       => ( ord_less_nat @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(162,axiom,
    ( ord_less_eq_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_nat @ A @ B )
          | ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_order_Oorder__iff__strict) ).

thf(817,plain,
    ( ord_less_eq_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_nat @ A @ B )
          | ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(187,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ord_less_nat @ A @ B )
        & ( ord_less_eq_nat @ C @ D ) )
     => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_add__mono__thms__linordered__field_I3_J) ).

thf(902,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ord_less_nat @ A @ B )
        & ( ord_less_eq_nat @ C @ D ) )
     => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(220,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_leD) ).

thf(1040,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(35,axiom,
    ! [A: nat,B: prefix1027212443list_a > nat,C: prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_le699472955list_a @ C @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_ord__eq__le__subst) ).

thf(376,plain,
    ! [A: nat,B: prefix1027212443list_a > nat,C: prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_le699472955list_a @ C @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(164,axiom,
    ! [A: nat > nat,B: nat,C: nat] :
      ( ! [D: nat,E: nat] :
          ( ( ord_less_nat @ D @ E )
         => ( ord_less_nat @ ( A @ D ) @ ( A @ E ) ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_less__mono__imp__le__mono) ).

thf(821,plain,
    ! [A: nat > nat,B: nat,C: nat] :
      ( ! [D: nat,E: nat] :
          ( ( ord_less_nat @ D @ E )
         => ( ord_less_nat @ ( A @ D ) @ ( A @ E ) ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(27,axiom,
    ( ( (=) @ prefix1027212443list_a )
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le699472955list_a @ A @ B )
          & ( ord_le699472955list_a @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_eq__iff) ).

thf(353,plain,
    ( ( (=) @ prefix1027212443list_a )
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le699472955list_a @ A @ B )
          & ( ord_le699472955list_a @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(199,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_less__imp__not__less) ).

thf(966,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(99,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ A @ ( plus_plus_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_trans__le__add2) ).

thf(602,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ A @ ( plus_plus_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(5,axiom,
    ! [A: prefix1027212443list_a] :
    ? [B: trace_1367752404list_a] : ( prefix1041802747list_a @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_ex__prefix__of) ).

thf(293,plain,
    ! [A: prefix1027212443list_a] :
    ? [B: trace_1367752404list_a] : ( prefix1041802747list_a @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(177,axiom,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_nat @ E @ F )
             => ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_order__less__subst2) ).

thf(866,plain,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_nat @ E @ F )
             => ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(229,axiom,
    ! [A: nat,B: nat] :
      ( ( ( ord_less_nat @ A @ B )
        | ( A = B ) )
     => ( ord_less_eq_nat @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_less__or__eq__imp__le) ).

thf(1072,plain,
    ! [A: nat,B: nat] :
      ( ( ( ord_less_nat @ A @ B )
        | ( A = B ) )
     => ( ord_less_eq_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(149,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ~ ( ord_less_nat @ A @ B ) )
        = ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_antisym__conv2) ).

thf(774,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ~ ( ord_less_nat @ A @ B ) )
        = ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(40,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ord_less_eq_nat @ A @ B )
       => ~ ( ord_less_eq_nat @ B @ C ) )
     => ( ( ( ord_less_eq_nat @ B @ A )
         => ~ ( ord_less_eq_nat @ A @ C ) )
       => ( ( ( ord_less_eq_nat @ A @ C )
           => ~ ( ord_less_eq_nat @ C @ B ) )
         => ( ( ( ord_less_eq_nat @ C @ B )
             => ~ ( ord_less_eq_nat @ B @ A ) )
           => ( ( ( ord_less_eq_nat @ B @ C )
               => ~ ( ord_less_eq_nat @ C @ A ) )
             => ~ ( ( ord_less_eq_nat @ C @ A )
                 => ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_le__cases3) ).

thf(396,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ord_less_eq_nat @ A @ B )
       => ~ ( ord_less_eq_nat @ B @ C ) )
     => ( ( ( ord_less_eq_nat @ B @ A )
         => ~ ( ord_less_eq_nat @ A @ C ) )
       => ( ( ( ord_less_eq_nat @ A @ C )
           => ~ ( ord_less_eq_nat @ C @ B ) )
         => ( ( ( ord_less_eq_nat @ C @ B )
             => ~ ( ord_less_eq_nat @ B @ A ) )
           => ( ( ( ord_less_eq_nat @ B @ C )
               => ~ ( ord_less_eq_nat @ C @ A ) )
             => ~ ( ( ord_less_eq_nat @ C @ A )
                 => ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(211,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
      = ( ord_less_nat @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_nat__add__left__cancel__less) ).

thf(998,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
      = ( ord_less_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(274,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma2 @ A ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) )
     => ( ord_less_nat @ A @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207__C11_C) ).

thf(1201,plain,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma2 @ A ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) )
     => ( ord_less_nat @ A @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(68,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_add__left__mono) ).

thf(507,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(75,axiom,
    ! [A: nat,B: nat,C: trace_1367752404list_a] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ C @ A ) @ ( tau_Pr257024512list_a @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218__092_060tau_062__mono) ).

thf(527,plain,
    ! [A: nat,B: nat,C: trace_1367752404list_a] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ C @ A ) @ ( tau_Pr257024512list_a @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(263,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( ord_less_eq_nat @ A @ B )
     => ( ord_less_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_not__le__imp__less) ).

thf(1169,plain,
    ! [A: nat,B: nat] :
      ( ~ ( ord_less_eq_nat @ A @ B )
     => ( ord_less_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(122,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
     => ( ord_less_eq_nat @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_add__leD2) ).

thf(687,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
     => ( ord_less_eq_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(278,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma @ A ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) )
     => ( ord_less_nat @ A @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212__C1_C) ).

thf(1215,plain,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma @ A ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) )
     => ( ord_less_nat @ A @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(107,axiom,
    ! [A: nat,B: nat,C: nat > prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_le699472955list_a @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_le699472955list_a @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_le699472955list_a @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_order__subst2) ).

thf(634,plain,
    ! [A: nat,B: nat,C: nat > prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_le699472955list_a @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_le699472955list_a @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_le699472955list_a @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(240,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( ord_less_nat @ A @ B )
     => ( ( ~ ( ord_less_nat @ B @ A ) )
        = ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_antisym__conv3) ).

thf(1104,plain,
    ! [A: nat,B: nat] :
      ( ~ ( ord_less_nat @ A @ B )
     => ( ( ~ ( ord_less_nat @ B @ A ) )
        = ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(283,axiom,
    ! [A: nat,B: nat] :
      ~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_not__add__less1) ).

thf(1242,plain,
    ! [A: nat,B: nat] :
      ~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(70,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a > prefix1027212443list_a,C: prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ ( B @ C ) )
     => ( ( ord_le699472955list_a @ C @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_le699472955list_a @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_le699472955list_a @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_order__subst1) ).

thf(512,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a > prefix1027212443list_a,C: prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ ( B @ C ) )
     => ( ( ord_le699472955list_a @ C @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_le699472955list_a @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_le699472955list_a @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(113,axiom,
    ( ( (=) @ prefix1027212443list_a )
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le699472955list_a @ B @ A )
          & ( ord_le699472955list_a @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_dual__order_Oeq__iff) ).

thf(661,plain,
    ( ( (=) @ prefix1027212443list_a )
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le699472955list_a @ B @ A )
          & ( ord_le699472955list_a @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(273,axiom,
    ( ord_less_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( A != B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_nat__less__le) ).

thf(1199,plain,
    ( ord_less_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( A != B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(258,axiom,
    ! [A: prefix1027212443list_a,B: trace_1367752404list_a,C: trace_1367752404list_a,D: nat] :
      ( ( prefix1041802747list_a @ A @ B )
     => ( ( prefix1041802747list_a @ A @ C )
       => ( ( ord_less_nat @ D @ ( plen_P694648887list_a @ A ) )
         => ( ( tau_Pr257024512list_a @ B @ D )
            = ( tau_Pr257024512list_a @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241__092_060tau_062__prefix__conv) ).

thf(1153,plain,
    ! [A: prefix1027212443list_a,B: trace_1367752404list_a,C: trace_1367752404list_a,D: nat] :
      ( ( prefix1041802747list_a @ A @ B )
     => ( ( prefix1041802747list_a @ A @ C )
       => ( ( ord_less_nat @ D @ ( plen_P694648887list_a @ A ) )
         => ( ( tau_Pr257024512list_a @ B @ D )
            = ( tau_Pr257024512list_a @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(77,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ? [C: nat] :
          ( B
          = ( plus_plus_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_le__Suc__ex) ).

thf(534,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ? [C: nat] :
          ( B
          = ( plus_plus_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(224,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_eq_nat @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_less__imp__le__nat) ).

thf(1057,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_eq_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(261,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ C )
     => ( ord_less_nat @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_add__lessD1) ).

thf(1163,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ C )
     => ( ord_less_nat @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(189,axiom,
    ! [A: nat,B: nat,C: nat > $o] :
      ( ( ord_less_nat @ A @ B )
     => ( ( C @ A )
       => ( ~ ( C @ B )
         => ? [D: nat] :
              ( ( ord_less_eq_nat @ A @ D )
              & ( ord_less_eq_nat @ D @ B )
              & ! [E: nat] :
                  ( ( ( ord_less_eq_nat @ A @ E )
                    & ( ord_less_nat @ E @ D ) )
                 => ( C @ E ) )
              & ! [E: nat] :
                  ( ! [F: nat] :
                      ( ( ( ord_less_eq_nat @ A @ F )
                        & ( ord_less_nat @ F @ E ) )
                     => ( C @ F ) )
                 => ( ord_less_eq_nat @ E @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_complete__interval) ).

thf(910,plain,
    ! [A: nat,B: nat,C: nat > $o] :
      ( ( ord_less_nat @ A @ B )
     => ( ( C @ A )
       => ( ~ ( C @ B )
         => ? [D: nat] :
              ( ( ord_less_eq_nat @ A @ D )
              & ( ord_less_eq_nat @ D @ B )
              & ! [E: nat] :
                  ( ( ( ord_less_eq_nat @ A @ E )
                    & ( ord_less_nat @ E @ D ) )
                 => ( C @ E ) )
              & ! [E: nat] :
                  ( ! [F: nat] :
                      ( ( ( ord_less_eq_nat @ A @ F )
                        & ( ord_less_nat @ F @ E ) )
                     => ( C @ F ) )
                 => ( ord_less_eq_nat @ E @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(186,axiom,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_nat @ E @ F )
             => ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_ord__less__eq__subst) ).

thf(894,plain,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_nat @ E @ F )
             => ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(235,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
     => ( ord_less_nat @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_add__less__imp__less__left) ).

thf(1091,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
     => ( ord_less_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(165,axiom,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ C @ B )
     => ( ord_less_eq_nat @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_minf_I6_J) ).

thf(825,plain,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ C @ B )
     => ( ord_less_eq_nat @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(221,axiom,
    ( ord_less_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( A != B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_less__le) ).

thf(1042,plain,
    ( ord_less_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( A != B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(9,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
     => ~ ( ( ord_less_eq_nat @ A @ C )
         => ~ ( ord_less_eq_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_add__leE) ).

thf(302,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
     => ~ ( ( ord_less_eq_nat @ A @ C )
         => ~ ( ord_less_eq_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(176,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ord_less_nat @ A @ B )
        & ( C = D ) )
     => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_add__mono__thms__linordered__field_I1_J) ).

thf(862,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ord_less_nat @ A @ B )
        & ( C = D ) )
     => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(279,axiom,
    ! [A: nat > nat > $o,B: nat,C: nat] :
      ( ! [D: nat,E: nat] :
          ( ( ord_less_nat @ D @ E )
         => ( A @ D @ E ) )
     => ( ! [D: nat] : ( A @ D @ D )
       => ( ! [D: nat,E: nat] :
              ( ( A @ E @ D )
             => ( A @ D @ E ) )
         => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_linorder__less__wlog) ).

thf(1217,plain,
    ! [A: nat > nat > $o,B: nat,C: nat] :
      ( ! [D: nat,E: nat] :
          ( ( ord_less_nat @ D @ E )
         => ( A @ D @ E ) )
     => ( ! [D: nat] : ( A @ D @ D )
       => ( ! [D: nat,E: nat] :
              ( ( A @ E @ D )
             => ( A @ D @ E ) )
         => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(87,axiom,
    ( ord_le887097159list_a
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le699472955list_a @ A @ B )
          & ( A != B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_order_Ostrict__iff__order) ).

thf(561,plain,
    ( ord_le887097159list_a
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le699472955list_a @ A @ B )
          & ( A != B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(7,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_le__trans) ).

thf(297,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(106,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ A @ C ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_add__left__imp__eq) ).

thf(630,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ A @ C ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(154,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
      = ( ord_less_nat @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_add__less__cancel__left) ).

thf(788,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
      = ( ord_less_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(134,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_trans__less__add1) ).

thf(729,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(281,axiom,
    ord_less_nat @ i3 @ ( monito1457594016ress_a @ sigma @ phi @ ( plen_P694648887list_a @ pi ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I3_J) ).

thf(1238,plain,
    ord_less_nat @ i3 @ ( monito1457594016ress_a @ sigma @ phi @ ( plen_P694648887list_a @ pi ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(56,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le887097159list_a @ A @ B )
     => ( ( ord_le699472955list_a @ C @ A )
       => ( ord_le887097159list_a @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_dual__order_Ostrict__trans2) ).

thf(467,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le887097159list_a @ A @ B )
     => ( ( ord_le699472955list_a @ C @ A )
       => ( ord_le887097159list_a @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(171,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_le__less__trans) ).

thf(847,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(182,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_less__asym_H) ).

thf(879,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(168,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ C @ D )
       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_add__less__mono) ).

thf(830,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ C @ D )
       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(54,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ~ ( ord_le887097159list_a @ A @ B ) )
        = ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_antisym__conv2) ).

thf(461,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ~ ( ord_le887097159list_a @ A @ B ) )
        = ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(272,axiom,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ B @ C )
     => ( C != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_pinf_I4_J) ).

thf(1195,plain,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ B @ C )
     => ( C != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(82,axiom,
    ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma @ j ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214__092_060open_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_____092_060close_062) ).

thf(551,plain,
    ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma @ j ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(52,axiom,
    ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_le__add1) ).

thf(456,plain,
    ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(72,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ord_less_eq_nat @ A @ B )
        & ( ord_less_eq_nat @ C @ D ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_add__mono__thms__linordered__semiring_I1_J) ).

thf(519,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ord_less_eq_nat @ A @ B )
        & ( ord_less_eq_nat @ C @ D ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(180,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_less__not__sym) ).

thf(874,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(133,axiom,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_nat @ E @ F )
             => ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_order__less__le__subst2) ).

thf(725,plain,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_nat @ E @ F )
             => ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(205,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( A = B )
        & ( ord_less_nat @ C @ D ) )
     => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_add__mono__thms__linordered__field_I2_J) ).

thf(980,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( A = B )
        & ( ord_less_nat @ C @ D ) )
     => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(152,axiom,
    ord_less_nat @ k @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062) ).

thf(783,plain,
    ord_less_nat @ k @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(44,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_le__antisym) ).

thf(420,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(84,axiom,
    ! [A: prefix1027212443list_a] : ( ord_le699472955list_a @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_order__refl) ).

thf(554,plain,
    ! [A: prefix1027212443list_a] : ( ord_le699472955list_a @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(267,axiom,
    ( ( '?' @ nat )
    = ( ^ [A: nat > $o] :
        ? [B: nat] :
          ( ( A @ B )
          & ! [C: nat] :
              ( ( ord_less_nat @ C @ B )
             => ~ ( A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_exists__least__iff) ).

thf(1182,plain,
    ( ( '?' @ nat )
    = ( ^ [A: nat > $o] :
        ? [B: nat] :
          ( ( A @ B )
          & ! [C: nat] :
              ( ( ord_less_nat @ C @ B )
             => ~ ( A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(78,axiom,
    ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma2 @ ja ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215__092_060open_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_092_060close_062) ).

thf(537,plain,
    ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma2 @ ja ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(116,axiom,
    ! [A: nat] :
      ( ( one_one_nat = A )
      = ( A = one_one_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_one__reorient) ).

thf(669,plain,
    ! [A: nat] :
      ( ( one_one_nat = A )
      = ( A = one_one_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(59,axiom,
    ( ( (=) @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ B @ A )
          & ( ord_less_eq_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_dual__order_Oeq__iff) ).

thf(476,plain,
    ( ( (=) @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ B @ A )
          & ( ord_less_eq_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(62,axiom,
    ( ord_le699472955list_a
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le887097159list_a @ A @ B )
          | ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_dual__order_Oorder__iff__strict) ).

thf(489,plain,
    ( ord_le699472955list_a
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le887097159list_a @ A @ B )
          | ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(277,axiom,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_nat @ E @ F )
             => ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_ord__eq__less__subst) ).

thf(1207,plain,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_nat @ E @ F )
             => ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(201,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_eq_nat @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_dual__order_Ostrict__implies__order) ).

thf(970,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_eq_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(244,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ( ord_less_eq_nat @ A @ B )
       => ( ord_less_nat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_order_Onot__eq__order__implies__strict) ).

thf(1114,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ( ord_less_eq_nat @ A @ B )
       => ( ord_less_nat @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(257,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_order_Ostrict__trans1) ).

thf(1150,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(271,axiom,
    ! [A: trace_1367752404list_a,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ A @ B ) @ ( tau_Pr257024512list_a @ A @ C ) )
     => ( ( ord_less_nat @ C @ B )
       => ( ( tau_Pr257024512list_a @ A @ B )
          = ( tau_Pr257024512list_a @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_le___092_060tau_062__less) ).

thf(1192,plain,
    ! [A: trace_1367752404list_a,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ A @ B ) @ ( tau_Pr257024512list_a @ A @ C ) )
     => ( ( ord_less_nat @ C @ B )
       => ( ( tau_Pr257024512list_a @ A @ B )
          = ( tau_Pr257024512list_a @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(206,axiom,
    ! [A: nat,B: nat] :
      ~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_not__add__less2) ).

thf(984,plain,
    ! [A: nat,B: nat] :
      ~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(285,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ C @ D )
       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_add__le__less__mono) ).

thf(1246,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ C @ D )
       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(100,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_add__right__mono) ).

thf(605,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(233,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
     => ( ord_less_nat @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_add__less__imp__less__right) ).

thf(1086,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
     => ( ord_less_nat @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(30,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
      = ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_add_Oleft__commute) ).

thf(360,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
      = ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(158,axiom,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ ( B @ C ) )
     => ( ( ord_less_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_nat @ E @ F )
             => ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_order__le__less__subst1) ).

thf(805,plain,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ ( B @ C ) )
     => ( ( ord_less_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_nat @ E @ F )
             => ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(12,axiom,
    ( ( (=) @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( ord_less_eq_nat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_eq__iff) ).

thf(311,plain,
    ( ( (=) @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( ord_less_eq_nat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(86,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le887097159list_a @ A @ B )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_le__imp__less__or__eq) ).

thf(558,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le887097159list_a @ A @ B )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(269,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma @ A ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) )
     => ( ord_less_nat @ A @ ( plen_P694648887list_a @ pi ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211__C3_C) ).

thf(1187,plain,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma @ A ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) )
     => ( ord_less_nat @ A @ ( plen_P694648887list_a @ pi ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(76,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( ord_less_eq_nat @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_eq__refl) ).

thf(530,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( ord_less_eq_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(195,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ord_less_eq_nat @ A @ B )
        & ( ord_less_nat @ C @ D ) )
     => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_add__mono__thms__linordered__field_I4_J) ).

thf(953,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ord_less_eq_nat @ A @ B )
        & ( ord_less_nat @ C @ D ) )
     => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(156,axiom,
    prefix1041802747list_a @ pi @ sigma,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_assms_I1_J) ).

thf(794,plain,
    prefix1041802747list_a @ pi @ sigma,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(131,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a > nat,D: nat] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_less_eq_nat @ ( C @ B ) @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_order__subst2) ).

thf(718,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a > nat,D: nat] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_less_eq_nat @ ( C @ B ) @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(141,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_less__imp__not__eq2) ).

thf(750,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(255,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ord_less_nat @ A @ B )
        & ( ord_less_nat @ C @ D ) )
     => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_add__mono__thms__linordered__field_I5_J) ).

thf(1146,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ord_less_nat @ A @ B )
        & ( ord_less_nat @ C @ D ) )
     => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(174,axiom,
    ! [A: nat > $o,B: nat] :
      ( ! [C: nat] :
          ( ~ ( A @ C )
         => ? [D: nat] :
              ( ( ord_less_nat @ D @ C )
              & ~ ( A @ D ) ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_infinite__descent) ).

thf(856,plain,
    ! [A: nat > $o,B: nat] :
      ( ! [C: nat] :
          ( ~ ( A @ C )
         => ? [D: nat] :
              ( ( ord_less_nat @ D @ C )
              & ~ ( A @ D ) ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(91,axiom,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_order__subst1) ).

thf(573,plain,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(123,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_le__refl) ).

thf(689,plain,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(163,axiom,
    ( ord_less_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ~ ( ord_less_eq_nat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_less__le__not__le) ).

thf(819,plain,
    ( ord_less_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ~ ( ord_less_eq_nat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(188,axiom,
    ! [A: nat,B: trace_1367752404list_a,C: trace_1367752404list_a,D: formula_a] :
      ( ! [E: nat] :
          ( ( ord_less_nat @ E @ A )
         => ( ( tau_Pr257024512list_a @ B @ E )
            = ( tau_Pr257024512list_a @ C @ E ) ) )
     => ( ( monito1457594016ress_a @ B @ D @ A )
        = ( monito1457594016ress_a @ C @ D @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_progress__time__conv) ).

thf(904,plain,
    ! [A: nat,B: trace_1367752404list_a,C: trace_1367752404list_a,D: formula_a] :
      ( ! [E: nat] :
          ( ( ord_less_nat @ E @ A )
         => ( ( tau_Pr257024512list_a @ B @ E )
            = ( tau_Pr257024512list_a @ C @ E ) ) )
     => ( ( monito1457594016ress_a @ B @ D @ A )
        = ( monito1457594016ress_a @ C @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(45,axiom,
    ! [A: nat,B: nat,C: nat > prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_le699472955list_a @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_le699472955list_a @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_ord__le__eq__subst) ).

thf(423,plain,
    ! [A: nat,B: nat,C: nat > prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_le699472955list_a @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_le699472955list_a @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(135,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_add__less__mono1) ).

thf(732,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(148,axiom,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ B @ C )
     => ~ ( ord_less_eq_nat @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_pinf_I6_J) ).

thf(772,plain,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ B @ C )
     => ~ ( ord_less_eq_nat @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(1,conjecture,
    ord_less_nat @ k @ ( plen_P694648887list_a @ pi ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(286,plain,
    ~ ( ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(92,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( A = B )
     => ( ( ord_le699472955list_a @ B @ C )
       => ( ord_le699472955list_a @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_ord__eq__le__trans) ).

thf(577,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( A = B )
     => ( ( ord_le699472955list_a @ B @ C )
       => ( ord_le699472955list_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(197,axiom,
    ! [A: nat > $o,B: nat] :
      ( ! [C: nat] :
          ( ! [D: nat] :
              ( ( ord_less_nat @ D @ C )
             => ( A @ D ) )
         => ( A @ C ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_nat__less__induct) ).

thf(958,plain,
    ! [A: nat > $o,B: nat] :
      ( ! [C: nat] :
          ( ! [D: nat] :
              ( ( ord_less_nat @ D @ C )
             => ( A @ D ) )
         => ( A @ C ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(170,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_less__not__refl2) ).

thf(843,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(247,axiom,
    ( ord_less_eq_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_nat @ A @ B )
          | ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_dual__order_Oorder__iff__strict) ).

thf(1125,plain,
    ( ord_less_eq_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_nat @ A @ B )
          | ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(109,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_order__trans) ).

thf(641,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(253,axiom,
    ! [A: nat,B: nat] :
      ( ( ~ ( ord_less_eq_nat @ A @ B ) )
      = ( ord_less_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_not__le) ).

thf(1139,plain,
    ! [A: nat,B: nat] :
      ( ( ~ ( ord_less_eq_nat @ A @ B ) )
      = ( ord_less_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(49,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le887097159list_a @ B @ C )
       => ( ord_le887097159list_a @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_order_Ostrict__trans1) ).

thf(445,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le887097159list_a @ B @ C )
       => ( ord_le887097159list_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(13,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_order_Otrans) ).

thf(313,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(241,axiom,
    ord_less_nat @ ia @ ( monito1457594016ress_a @ sigma @ ( until_a @ phi_1 @ i2 @ phi_2 ) @ ( plen_P694648887list_a @ pi ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_Until_Oprems) ).

thf(1107,plain,
    ord_less_nat @ ia @ ( monito1457594016ress_a @ sigma @ ( until_a @ phi_1 @ i2 @ phi_2 ) @ ( plen_P694648887list_a @ pi ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(282,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( A != B )
       => ( ord_less_nat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_le__neq__implies__less) ).

thf(1239,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( A != B )
       => ( ord_less_nat @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(21,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le887097159list_a @ A @ B )
     => ( ord_le699472955list_a @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_dual__order_Ostrict__implies__order) ).

thf(335,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le887097159list_a @ A @ B )
     => ( ord_le699472955list_a @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(193,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_order_Ostrict__implies__not__eq) ).

thf(947,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(26,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le699472955list_a @ B @ A )
        = ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_antisym__conv) ).

thf(350,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le699472955list_a @ B @ A )
        = ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(80,axiom,
    ! [A: prefix1027212443list_a,B: trace_1367752404list_a,C: prefix1027212443list_a] :
      ( ( prefix1041802747list_a @ A @ B )
     => ( ( prefix1041802747list_a @ C @ B )
       => ( ( ord_le699472955list_a @ A @ C )
          | ( ord_le699472955list_a @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_prefix__of__imp__linear) ).

thf(540,plain,
    ! [A: prefix1027212443list_a,B: trace_1367752404list_a,C: prefix1027212443list_a] :
      ( ( prefix1041802747list_a @ A @ B )
     => ( ( prefix1041802747list_a @ C @ B )
       => ( ( ord_le699472955list_a @ A @ C )
          | ( ord_le699472955list_a @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(117,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
      | ~ ( ord_less_eq_nat @ A @ B )
      | ~ ( ord_less_eq_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_verit__la__disequality) ).

thf(672,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
      | ~ ( ord_less_eq_nat @ A @ B )
      | ~ ( ord_less_eq_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(204,axiom,
    ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma2 @ k ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_that) ).

thf(979,plain,
    ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma2 @ k ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(120,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ord_less_eq_nat @ A @ B )
        & ( C = D ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_add__mono__thms__linordered__semiring_I3_J) ).

thf(681,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ord_less_eq_nat @ A @ B )
        & ( C = D ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(223,axiom,
    ! [A: nat,B: nat > $o,C: nat] :
      ( ! [D: nat] :
          ( ( ord_less_nat @ A @ D )
         => ( B @ D ) )
     => ( ! [D: nat] :
            ( ( ord_less_eq_nat @ D @ A )
           => ( ! [E: nat] :
                  ( ( ord_less_nat @ D @ E )
                 => ( B @ E ) )
             => ( B @ D ) ) )
       => ( B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_nat__descend__induct) ).

thf(1048,plain,
    ! [A: nat,B: nat > $o,C: nat] :
      ( ! [D: nat] :
          ( ( ord_less_nat @ A @ D )
         => ( B @ D ) )
     => ( ! [D: nat] :
            ( ( ord_less_eq_nat @ D @ A )
           => ( ! [E: nat] :
                  ( ( ord_less_nat @ D @ E )
                 => ( B @ E ) )
             => ( B @ D ) ) )
       => ( B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(210,axiom,
    ( ord_less_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( A != B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_order_Ostrict__iff__order) ).

thf(996,plain,
    ( ord_less_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( A != B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(137,axiom,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ B @ C )
     => ( C != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_pinf_I3_J) ).

thf(737,plain,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ B @ C )
     => ( C != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(47,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a > prefix1027212443list_a,C: prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_le699472955list_a @ C @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_le699472955list_a @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_le699472955list_a @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_ord__eq__le__subst) ).

thf(434,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a > prefix1027212443list_a,C: prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_le699472955list_a @ C @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_le699472955list_a @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_le699472955list_a @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(265,axiom,
    ! [A: prefix1027212443list_a,B: nat > prefix1027212443list_a,C: nat,D: nat] :
      ( ( ord_le699472955list_a @ A @ ( B @ C ) )
     => ( ( ord_less_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_nat @ E @ F )
             => ( ord_le887097159list_a @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_le887097159list_a @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_order__le__less__subst1) ).

thf(1175,plain,
    ! [A: prefix1027212443list_a,B: nat > prefix1027212443list_a,C: nat,D: nat] :
      ( ( ord_le699472955list_a @ A @ ( B @ C ) )
     => ( ( ord_less_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_nat @ E @ F )
             => ( ord_le887097159list_a @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_le887097159list_a @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(153,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_less__not__refl3) ).

thf(784,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(245,axiom,
    ! [A: nat,B: nat,C: $o] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ B @ A )
       => C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_less__imp__triv) ).

thf(1117,plain,
    ! [A: nat,B: nat,C: $o] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ B @ A )
       => C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(185,axiom,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ C @ B )
     => ( C != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_minf_I4_J) ).

thf(890,plain,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ C @ B )
     => ( C != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(37,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ~ ( ord_le887097159list_a @ A @ B )
     => ( ( ord_le699472955list_a @ A @ B )
        = ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_antisym__conv1) ).

thf(387,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ~ ( ord_le887097159list_a @ A @ B )
     => ( ( ord_le699472955list_a @ A @ B )
        = ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(64,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le887097159list_a @ A @ B )
     => ( ( ord_le699472955list_a @ B @ C )
       => ( ord_le887097159list_a @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_order_Ostrict__trans2) ).

thf(494,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le887097159list_a @ A @ B )
     => ( ( ord_le699472955list_a @ B @ C )
       => ( ord_le887097159list_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(104,axiom,
    ! [A: nat > nat > $o,B: nat,C: nat] :
      ( ! [D: nat,E: nat] :
          ( ( ord_less_eq_nat @ D @ E )
         => ( A @ D @ E ) )
     => ( ! [D: nat,E: nat] :
            ( ( A @ E @ D )
           => ( A @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_linorder__wlog) ).

thf(621,plain,
    ! [A: nat > nat > $o,B: nat,C: nat] :
      ( ! [D: nat,E: nat] :
          ( ( ord_less_eq_nat @ D @ E )
         => ( A @ D @ E ) )
     => ( ! [D: nat,E: nat] :
            ( ( A @ E @ D )
           => ( A @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(216,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma2 @ A ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) )
     => ( ord_less_nat @ A @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206__C21_C) ).

thf(1029,plain,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma2 @ A ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) )
     => ( ord_less_nat @ A @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(19,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
      = ( ord_less_eq_nat @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_add__le__cancel__left) ).

thf(330,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
      = ( ord_less_eq_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(32,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_ab__semigroup__add__class_Oadd__ac_I1_J) ).

thf(367,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(83,axiom,
    ( ( (=) @ prefix1027212443list_a )
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le699472955list_a @ A @ B )
          & ( ord_le699472955list_a @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_order__class_Oorder_Oeq__iff) ).

thf(552,plain,
    ( ( (=) @ prefix1027212443list_a )
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le699472955list_a @ A @ B )
          & ( ord_le699472955list_a @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(227,axiom,
    ! [A: nat,B: nat,C: nat > prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_le699472955list_a @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_nat @ E @ F )
             => ( ord_le887097159list_a @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_le887097159list_a @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_order__less__le__subst2) ).

thf(1066,plain,
    ! [A: nat,B: nat,C: nat > prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_le699472955list_a @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_nat @ E @ F )
             => ( ord_le887097159list_a @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_le887097159list_a @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(151,axiom,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_dual__order_Oirrefl) ).

thf(780,plain,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(101,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a > prefix1027212443list_a,C: prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_le887097159list_a @ A @ ( B @ C ) )
     => ( ( ord_le699472955list_a @ C @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_le699472955list_a @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_le887097159list_a @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_order__less__le__subst1) ).

thf(608,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a > prefix1027212443list_a,C: prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_le887097159list_a @ A @ ( B @ C ) )
     => ( ( ord_le699472955list_a @ C @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_le699472955list_a @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_le887097159list_a @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(39,axiom,
    ( ( (=) @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( ord_less_eq_nat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_order__class_Oorder_Oeq__iff) ).

thf(394,plain,
    ( ( (=) @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( ord_less_eq_nat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(88,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( A
        = ( plus_plus_nat @ B @ C ) )
     => ( ( plus_plus_nat @ A @ D )
        = ( plus_plus_nat @ B @ ( plus_plus_nat @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_group__cancel_Oadd1) ).

thf(563,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( A
        = ( plus_plus_nat @ B @ C ) )
     => ( ( plus_plus_nat @ A @ D )
        = ( plus_plus_nat @ B @ ( plus_plus_nat @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(46,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
        = ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_antisym__conv) ).

thf(431,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
        = ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(121,axiom,
    ( ord_le887097159list_a
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le699472955list_a @ A @ B )
          & ~ ( ord_le699472955list_a @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_less__prefix__def) ).

thf(685,plain,
    ( ord_le887097159list_a
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le699472955list_a @ A @ B )
          & ~ ( ord_le699472955list_a @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(73,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( A = B )
     => ( ord_le699472955list_a @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_eq__refl) ).

thf(521,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( A = B )
     => ( ord_le699472955list_a @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(264,axiom,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ C @ B )
     => ( C != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_minf_I3_J) ).

thf(1171,plain,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ C @ B )
     => ( C != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(146,axiom,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ B @ C )
     => ( ord_less_nat @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_pinf_I7_J) ).

thf(768,plain,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ B @ C )
     => ( ord_less_nat @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(166,axiom,
    ord_less_eq_nat @ j @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062) ).

thf(827,plain,
    ord_less_eq_nat @ j @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(222,axiom,
    ! [A: prefix1027212443list_a,B: trace_1367752404list_a,C: trace_1367752404list_a,D: formula_a] :
      ( ( prefix1041802747list_a @ A @ B )
     => ( ( prefix1041802747list_a @ A @ C )
       => ( ( monito1457594016ress_a @ B @ D @ ( plen_P694648887list_a @ A ) )
          = ( monito1457594016ress_a @ C @ D @ ( plen_P694648887list_a @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_progress__prefix__conv) ).

thf(1044,plain,
    ! [A: prefix1027212443list_a,B: trace_1367752404list_a,C: trace_1367752404list_a,D: formula_a] :
      ( ( prefix1041802747list_a @ A @ B )
     => ( ( prefix1041802747list_a @ A @ C )
       => ( ( monito1457594016ress_a @ B @ D @ ( plen_P694648887list_a @ A ) )
          = ( monito1457594016ress_a @ C @ D @ ( plen_P694648887list_a @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(125,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_add__le__mono) ).

thf(695,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(284,axiom,
    ord_less_eq_nat @ ja @ ( monito1457594016ress_a @ sigma2 @ phi_1 @ ( plen_P694648887list_a @ pi ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062) ).

thf(1245,plain,
    ord_less_eq_nat @ ja @ ( monito1457594016ress_a @ sigma2 @ phi_1 @ ( plen_P694648887list_a @ pi ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(132,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le699472955list_a @ C @ A )
       => ( ord_le699472955list_a @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_dual__order_Otrans) ).

thf(722,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le699472955list_a @ C @ A )
       => ( ord_le699472955list_a @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(218,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
      | ( A = B )
      | ( ord_less_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_less__linear) ).

thf(1034,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
      | ( A = B )
      | ( ord_less_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(118,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
      | ( ord_less_eq_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_nat__le__linear) ).

thf(675,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
      | ( ord_less_eq_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(192,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_less__trans) ).

thf(944,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(157,axiom,
    ! [A: nat > $o,B: nat > $o,C: nat > $o,D: nat > $o] :
      ( ? [E: nat] :
        ! [F: nat] :
          ( ( ord_less_nat @ F @ E )
         => ( ( A @ F )
            = ( B @ F ) ) )
     => ( ? [E: nat] :
          ! [F: nat] :
            ( ( ord_less_nat @ F @ E )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ? [E: nat] :
          ! [F: nat] :
            ( ( ord_less_nat @ F @ E )
           => ( ( ( A @ F )
                | ( C @ F ) )
              = ( ( B @ F )
                | ( D @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_minf_I2_J) ).

thf(795,plain,
    ! [A: nat > $o,B: nat > $o,C: nat > $o,D: nat > $o] :
      ( ? [E: nat] :
        ! [F: nat] :
          ( ( ord_less_nat @ F @ E )
         => ( ( A @ F )
            = ( B @ F ) ) )
     => ( ? [E: nat] :
          ! [F: nat] :
            ( ( ord_less_nat @ F @ E )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ? [E: nat] :
          ! [F: nat] :
            ( ( ord_less_nat @ F @ E )
           => ( ( ( A @ F )
                | ( C @ F ) )
              = ( ( B @ F )
                | ( D @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(114,axiom,
    ! [A: formula_a,B: i,C: formula_a,D: formula_a,E: i,F: formula_a] :
      ( ( ( until_a @ A @ B @ C )
        = ( until_a @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_formula_Oinject_I9_J) ).

thf(663,plain,
    ! [A: formula_a,B: i,C: formula_a,D: formula_a,E: i,F: formula_a] :
      ( ( ( until_a @ A @ B @ C )
        = ( until_a @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(251,axiom,
    ! [A: nat,B: nat] :
      ( ( ~ ( ord_less_nat @ A @ B ) )
      = ( ord_less_eq_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_not__less) ).

thf(1134,plain,
    ! [A: nat,B: nat] :
      ( ( ~ ( ord_less_nat @ A @ B ) )
      = ( ord_less_eq_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(231,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma @ A ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) )
     => ( ord_less_nat @ A @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213__C2_C) ).

thf(1081,plain,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma @ A ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) )
     => ( ord_less_nat @ A @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(190,axiom,
    ( ord_less_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( B != A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_dual__order_Ostrict__iff__order) ).

thf(939,plain,
    ( ord_less_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
          & ( B != A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(28,axiom,
    ( plus_plus_nat
    = ( ^ [A: nat,B: nat] : ( plus_plus_nat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_add_Ocommute) ).

thf(355,plain,
    ( plus_plus_nat
    = ( ^ [A: nat,B: nat] : ( plus_plus_nat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(142,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( B = C )
       => ( ord_less_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_ord__less__eq__trans) ).

thf(754,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( B = C )
       => ( ord_less_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(275,axiom,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ B @ C )
     => ( ord_less_eq_nat @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_pinf_I8_J) ).

thf(1203,plain,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ B @ C )
     => ( ord_less_eq_nat @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(96,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ A )
       => ( ord_less_eq_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_dual__order_Otrans) ).

thf(589,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ A )
       => ( ord_less_eq_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(103,axiom,
    ! [A: prefix1027212443list_a,B: nat > prefix1027212443list_a,C: nat,D: nat] :
      ( ( ord_le699472955list_a @ A @ ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_le699472955list_a @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_le699472955list_a @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_order__subst1) ).

thf(617,plain,
    ! [A: prefix1027212443list_a,B: nat > prefix1027212443list_a,C: nat,D: nat] :
      ( ( ord_le699472955list_a @ A @ ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_le699472955list_a @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_le699472955list_a @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(71,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
      = ( ord_less_eq_nat @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_nat__add__left__cancel__le) ).

thf(516,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
      = ( ord_less_eq_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(200,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_less__asym) ).

thf(968,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(53,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le887097159list_a @ A @ B )
     => ( ( ord_le699472955list_a @ B @ C )
       => ( ord_le887097159list_a @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_less__le__trans) ).

thf(458,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le887097159list_a @ A @ B )
     => ( ( ord_le699472955list_a @ B @ C )
       => ( ord_le887097159list_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(74,axiom,
    ( ord_le699472955list_a
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le887097159list_a @ A @ B )
          | ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_order_Oorder__iff__strict) ).

thf(525,plain,
    ( ord_le699472955list_a
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le887097159list_a @ A @ B )
          | ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(6,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
      | ( ord_less_eq_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_linear) ).

thf(295,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
      | ( ord_less_eq_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(228,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_dual__order_Oasym) ).

thf(1070,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(128,axiom,
    ! [A: trace_1367752404list_a,B: formula_a,C: nat] : ( ord_less_eq_nat @ ( monito1457594016ress_a @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_progress__le) ).

thf(705,plain,
    ! [A: trace_1367752404list_a,B: formula_a,C: nat] : ( ord_less_eq_nat @ ( monito1457594016ress_a @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(129,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a > prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_le699472955list_a @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_le699472955list_a @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_ord__le__eq__subst) ).

thf(707,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a > prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_le699472955list_a @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_le699472955list_a @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(18,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: trace_1367752404list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( prefix1041802747list_a @ B @ C )
       => ( prefix1041802747list_a @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_prefix__of__antimono) ).

thf(327,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: trace_1367752404list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( prefix1041802747list_a @ B @ C )
       => ( prefix1041802747list_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(238,axiom,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ C @ B )
     => ( ord_less_nat @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_minf_I5_J) ).

thf(1098,plain,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ C @ B )
     => ( ord_less_nat @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(155,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
      = ( ord_less_nat @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_add__less__cancel__right) ).

thf(791,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
      = ( ord_less_nat @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(67,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_ord__le__eq__trans) ).

thf(502,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(280,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_nat @ A @ ( plus_plus_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_trans__less__add2) ).

thf(1235,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_nat @ A @ ( plus_plus_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(57,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a > prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le887097159list_a @ ( C @ B ) @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_le699472955list_a @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_le887097159list_a @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_order__le__less__subst2) ).

thf(470,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a > prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le887097159list_a @ ( C @ B ) @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_le699472955list_a @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_le887097159list_a @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(194,axiom,
    ( ord_less_eq_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_nat @ A @ B )
          | ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_le__less) ).

thf(951,plain,
    ( ord_less_eq_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_nat @ A @ B )
          | ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(94,axiom,
    ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_le__add2) ).

thf(585,plain,
    ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(33,axiom,
    ( ord_le887097159list_a
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le699472955list_a @ A @ B )
          & ( B != A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_dual__order_Ostrict__iff__order) ).

thf(370,plain,
    ( ord_le887097159list_a
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le699472955list_a @ A @ B )
          & ( B != A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(139,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( ord_less_nat @ A @ B )
     => ( ( A != B )
       => ( ord_less_nat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_linorder__cases) ).

thf(744,plain,
    ! [A: nat,B: nat] :
      ( ~ ( ord_less_nat @ A @ B )
     => ( ( A != B )
       => ( ord_less_nat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(112,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( B = C )
       => ( ord_le699472955list_a @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_ord__le__eq__trans) ).

thf(656,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( B = C )
       => ( ord_le699472955list_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(98,axiom,
    ( ord_le699472955list_a
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le887097159list_a @ A @ B )
          | ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_le__less) ).

thf(600,plain,
    ( ord_le699472955list_a
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le887097159list_a @ A @ B )
          | ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(102,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( A = B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_ord__eq__le__trans) ).

thf(612,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( A = B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(208,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_order_Ostrict__trans) ).

thf(991,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(65,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( A != B )
     => ( ( ord_le699472955list_a @ A @ B )
       => ( ord_le887097159list_a @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_order_Onot__eq__order__implies__strict) ).

thf(497,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( A != B )
     => ( ( ord_le699472955list_a @ A @ B )
       => ( ord_le887097159list_a @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(181,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( A != B )
       => ( ord_less_nat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_le__neq__trans) ).

thf(876,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( A != B )
       => ( ord_less_nat @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(105,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le887097159list_a @ C @ A )
       => ( ord_le887097159list_a @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_dual__order_Ostrict__trans1) ).

thf(627,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le887097159list_a @ C @ A )
       => ( ord_le887097159list_a @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(51,axiom,
    ! [A: nat > $o,B: nat,C: nat] :
      ( ( A @ B )
     => ( ! [D: nat] :
            ( ( A @ D )
           => ( ord_less_eq_nat @ D @ C ) )
       => ? [D: nat] :
            ( ( A @ D )
            & ! [E: nat] :
                ( ( A @ E )
               => ( ord_less_eq_nat @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Nat_Oex__has__greatest__nat) ).

thf(450,plain,
    ! [A: nat > $o,B: nat,C: nat] :
      ( ( A @ B )
     => ( ! [D: nat] :
            ( ( A @ D )
           => ( ord_less_eq_nat @ D @ C ) )
       => ? [D: nat] :
            ( ( A @ D )
            & ! [E: nat] :
                ( ( A @ E )
               => ( ord_less_eq_nat @ E @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(259,axiom,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_order__le__less__subst2) ).

thf(1157,plain,
    ! [A: nat,B: nat,C: nat > nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ ( C @ B ) @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(203,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ A )
       => ( ord_less_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_dual__order_Ostrict__trans2) ).

thf(976,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ A )
       => ( ord_less_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(143,axiom,
    ord_less_eq_nat @ j @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062) ).

thf(759,plain,
    ord_less_eq_nat @ j @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(270,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ C @ A )
       => ( ord_less_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_dual__order_Ostrict__trans) ).

thf(1189,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ C @ A )
       => ( ord_less_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(242,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ord_less_eq_nat @ ( plen_P694648887list_a @ A ) @ ( plen_P694648887list_a @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_plen__mono) ).

thf(1108,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ord_less_eq_nat @ ( plen_P694648887list_a @ A ) @ ( plen_P694648887list_a @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(31,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( ord_less_eq_nat @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_eq__imp__le) ).

thf(363,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( ord_less_eq_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(85,axiom,
    ( ord_le887097159list_a
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le699472955list_a @ A @ B )
          & ~ ( ord_le699472955list_a @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_less__le__not__le) ).

thf(556,plain,
    ( ord_le887097159list_a
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le699472955list_a @ A @ B )
          & ~ ( ord_le699472955list_a @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(160,axiom,
    prefix1041802747list_a @ pi @ sigma2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_assms_I2_J) ).

thf(813,plain,
    prefix1041802747list_a @ pi @ sigma2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(198,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_order_Ostrict__trans2) ).

thf(963,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(15,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_add_Oassoc) ).

thf(319,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(226,axiom,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( ord_less_nat @ A @ ( B @ C ) )
     => ( ( ord_less_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_nat @ E @ F )
             => ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_order__less__subst1) ).

thf(1062,plain,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( ord_less_nat @ A @ ( B @ C ) )
     => ( ( ord_less_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_nat @ E @ F )
             => ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(111,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( A = B )
        & ( C = D ) )
     => ( ( plus_plus_nat @ A @ C )
        = ( plus_plus_nat @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_add__mono__thms__linordered__semiring_I4_J) ).

thf(652,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( A = B )
        & ( C = D ) )
     => ( ( plus_plus_nat @ A @ C )
        = ( plus_plus_nat @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(38,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ C @ B ) )
     => ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_add__right__imp__eq) ).

thf(390,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ C @ B ) )
     => ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(89,axiom,
    ( ord_less_eq_nat
    = ( ^ [A: nat,B: nat] :
        ? [C: nat] :
          ( B
          = ( plus_plus_nat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_nat__le__iff__add) ).

thf(568,plain,
    ( ord_less_eq_nat
    = ( ^ [A: nat,B: nat] :
        ? [C: nat] :
          ( B
          = ( plus_plus_nat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(69,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_dual__order_Orefl) ).

thf(510,plain,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(145,axiom,
    ! [A: nat > $o,B: nat] :
      ( ! [C: nat] :
          ( ! [D: nat] :
              ( ( ord_less_nat @ D @ C )
             => ( A @ D ) )
         => ( A @ C ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_less__induct) ).

thf(763,plain,
    ! [A: nat > $o,B: nat] :
      ( ! [C: nat] :
          ( ! [D: nat] :
              ( ( ord_less_nat @ D @ C )
             => ( A @ D ) )
         => ( A @ C ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(230,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a > nat,D: nat] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_less_nat @ ( C @ B ) @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_order__le__less__subst2) ).

thf(1077,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a > nat,D: nat] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_less_nat @ ( C @ B ) @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(60,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
      = ( ord_less_eq_nat @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_add__le__cancel__right) ).

thf(478,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
      = ( ord_less_eq_nat @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(260,axiom,
    ! [A: nat] :
    ? [B: nat] : ( ord_less_nat @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_gt__ex) ).

thf(1161,plain,
    ! [A: nat] :
    ? [B: nat] : ( ord_less_nat @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(3,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_order__refl) ).

thf(287,plain,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(8,axiom,
    ( ord_le887097159list_a
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le699472955list_a @ A @ B )
          & ( A != B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_less__le) ).

thf(300,plain,
    ( ord_le887097159list_a
    = ( ^ [A: prefix1027212443list_a,B: prefix1027212443list_a] :
          ( ( ord_le699472955list_a @ A @ B )
          & ( A != B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(173,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_eq_nat @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_less__imp__le) ).

thf(854,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_eq_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(256,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
      | ( ord_less_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_le__less__linear) ).

thf(1148,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
      | ( ord_less_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(136,axiom,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ C @ B )
     => ~ ( ord_less_eq_nat @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_minf_I8_J) ).

thf(735,plain,
    ! [A: nat] :
    ? [B: nat] :
    ! [C: nat] :
      ( ( ord_less_nat @ C @ B )
     => ~ ( ord_less_eq_nat @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(169,axiom,
    ! [A: nat > $o,B: nat > $o,C: nat > $o,D: nat > $o] :
      ( ? [E: nat] :
        ! [F: nat] :
          ( ( ord_less_nat @ E @ F )
         => ( ( A @ F )
            = ( B @ F ) ) )
     => ( ? [E: nat] :
          ! [F: nat] :
            ( ( ord_less_nat @ E @ F )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ? [E: nat] :
          ! [F: nat] :
            ( ( ord_less_nat @ E @ F )
           => ( ( ( A @ F )
                | ( C @ F ) )
              = ( ( B @ F )
                | ( D @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_pinf_I2_J) ).

thf(833,plain,
    ! [A: nat > $o,B: nat > $o,C: nat > $o,D: nat > $o] :
      ( ? [E: nat] :
        ! [F: nat] :
          ( ( ord_less_nat @ E @ F )
         => ( ( A @ F )
            = ( B @ F ) ) )
     => ( ? [E: nat] :
          ! [F: nat] :
            ( ( ord_less_nat @ E @ F )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ? [E: nat] :
          ! [F: nat] :
            ( ( ord_less_nat @ E @ F )
           => ( ( ( A @ F )
                | ( C @ F ) )
              = ( ( B @ F )
                | ( D @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(41,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( A
        = ( plus_plus_nat @ B @ C ) )
     => ( ( plus_plus_nat @ D @ A )
        = ( plus_plus_nat @ B @ ( plus_plus_nat @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_group__cancel_Oadd2) ).

thf(410,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( A
        = ( plus_plus_nat @ B @ C ) )
     => ( ( plus_plus_nat @ D @ A )
        = ( plus_plus_nat @ B @ ( plus_plus_nat @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(10,axiom,
    ! [A: nat,B: prefix1027212443list_a > nat,C: prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_less_eq_nat @ A @ ( B @ C ) )
     => ( ( ord_le699472955list_a @ C @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_order__subst1) ).

thf(305,plain,
    ! [A: nat,B: prefix1027212443list_a > nat,C: prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_less_eq_nat @ A @ ( B @ C ) )
     => ( ( ord_le699472955list_a @ C @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(58,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le887097159list_a @ A @ B )
     => ( ord_le699472955list_a @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_less__imp__le) ).

thf(474,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le887097159list_a @ A @ B )
     => ( ord_le699472955list_a @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(167,axiom,
    ( ord_less_nat
    = ( ^ [A: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A @ one_one_nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_discrete) ).

thf(828,plain,
    ( ord_less_nat
    = ( ^ [A: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A @ one_one_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(262,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_less__imp__neq) ).

thf(1165,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(196,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ A @ B )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_le__imp__less__or__eq) ).

thf(955,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ A @ B )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(42,axiom,
    ! [A: prefix1027212443list_a] : ( ord_le699472955list_a @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_dual__order_Orefl) ).

thf(415,plain,
    ! [A: prefix1027212443list_a] : ( ord_le699472955list_a @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(236,axiom,
    ( ord_less_eq_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_nat @ A @ B )
          | ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_le__eq__less__or__eq) ).

thf(1093,plain,
    ( ord_less_eq_nat
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_nat @ A @ B )
          | ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(207,axiom,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( ord_less_nat @ A @ ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_order__less__le__subst1) ).

thf(987,plain,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( ord_less_nat @ A @ ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(55,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_add__le__mono1) ).

thf(464,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(249,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_add__less__le__mono) ).

thf(1129,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(110,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a > nat,D: nat] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_ord__le__eq__subst) ).

thf(644,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a > nat,D: nat] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ( C @ B )
          = D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(172,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_less__imp__not__eq) ).

thf(850,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(213,axiom,
    ! [A: nat > $o,B: nat > $o,C: nat > $o,D: nat > $o] :
      ( ? [E: nat] :
        ! [F: nat] :
          ( ( ord_less_nat @ E @ F )
         => ( ( A @ F )
            = ( B @ F ) ) )
     => ( ? [E: nat] :
          ! [F: nat] :
            ( ( ord_less_nat @ E @ F )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ? [E: nat] :
          ! [F: nat] :
            ( ( ord_less_nat @ E @ F )
           => ( ( ( A @ F )
                & ( C @ F ) )
              = ( ( B @ F )
                & ( D @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_pinf_I1_J) ).

thf(1004,plain,
    ! [A: nat > $o,B: nat > $o,C: nat > $o,D: nat > $o] :
      ( ? [E: nat] :
        ! [F: nat] :
          ( ( ord_less_nat @ E @ F )
         => ( ( A @ F )
            = ( B @ F ) ) )
     => ( ? [E: nat] :
          ! [F: nat] :
            ( ( ord_less_nat @ E @ F )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ? [E: nat] :
          ! [F: nat] :
            ( ( ord_less_nat @ E @ F )
           => ( ( ( A @ F )
                & ( C @ F ) )
              = ( ( B @ F )
                & ( D @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(124,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a > prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le699472955list_a @ ( C @ B ) @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_le699472955list_a @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_le699472955list_a @ ( C @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_order__subst2) ).

thf(691,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C: prefix1027212443list_a > prefix1027212443list_a,D: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le699472955list_a @ ( C @ B ) @ D )
       => ( ! [E: prefix1027212443list_a,F: prefix1027212443list_a] :
              ( ( ord_le699472955list_a @ E @ F )
             => ( ord_le699472955list_a @ ( C @ E ) @ ( C @ F ) ) )
         => ( ord_le699472955list_a @ ( C @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(48,axiom,
    ! [A: nat,B: nat,C: trace_1367752404list_a,D: formula_a] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( monito1457594016ress_a @ C @ D @ A ) @ ( monito1457594016ress_a @ C @ D @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_progress__mono) ).

thf(442,plain,
    ! [A: nat,B: nat,C: trace_1367752404list_a,D: formula_a] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( monito1457594016ress_a @ C @ D @ A ) @ ( monito1457594016ress_a @ C @ D @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(179,axiom,
    ! [A: nat,B: nat] :
      ( ( ~ ( ord_less_eq_nat @ A @ B ) )
      = ( ord_less_nat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_verit__comp__simplify1_I3_J) ).

thf(871,plain,
    ! [A: nat,B: nat] :
      ( ( ~ ( ord_less_eq_nat @ A @ B ) )
      = ( ord_less_nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(246,axiom,
    ~ ! [A: nat] :
        ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma @ A ) )
       => ( ( ord_less_eq_nat @ A @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
         => ~ ( ord_less_eq_nat @ A @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(1120,plain,
    ~ ! [A: nat] :
        ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma @ A ) )
       => ( ( ord_less_eq_nat @ A @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
         => ~ ( ord_less_eq_nat @ A @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(16,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_add__left__cancel) ).

thf(322,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(22,axiom,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le699472955list_a @ B @ A )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_dual__order_Oantisym) ).

thf(337,plain,
    ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
      ( ( ord_le699472955list_a @ A @ B )
     => ( ( ord_le699472955list_a @ B @ A )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(268,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ C @ A )
       => ( ord_less_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_dual__order_Ostrict__trans1) ).

thf(1184,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ C @ A )
       => ( ord_less_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(11,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
     => ( ord_less_eq_nat @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_add__le__imp__le__left) ).

thf(309,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
     => ( ord_less_eq_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(81,axiom,
    ! [A: prefix1027212443list_a,B: nat > prefix1027212443list_a,C: nat,D: nat] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_le699472955list_a @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_le699472955list_a @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_ord__eq__le__subst) ).

thf(543,plain,
    ! [A: prefix1027212443list_a,B: nat > prefix1027212443list_a,C: nat,D: nat] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_le699472955list_a @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_le699472955list_a @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(219,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
      = ( ( ord_less_nat @ A @ B )
        | ( ord_less_nat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_nat__neq__iff) ).

thf(1037,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
      = ( ( ord_less_nat @ A @ B )
        | ( ord_less_nat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(97,axiom,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_ord__eq__le__subst) ).

thf(592,plain,
    ! [A: nat,B: nat > nat,C: nat,D: nat] :
      ( ( A
        = ( B @ C ) )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ! [E: nat,F: nat] :
              ( ( ord_less_eq_nat @ E @ F )
             => ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
         => ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(63,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_order__class_Oorder_Oantisym) ).

thf(491,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(234,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( ord_less_nat @ A @ B )
       => ( ord_less_nat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_linorder__neqE__nat) ).

thf(1088,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( ord_less_nat @ A @ B )
       => ( ord_less_nat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(214,axiom,
    ! [A: nat > $o,B: nat > $o,C: nat > $o,D: nat > $o] :
      ( ? [E: nat] :
        ! [F: nat] :
          ( ( ord_less_nat @ F @ E )
         => ( ( A @ F )
            = ( B @ F ) ) )
     => ( ? [E: nat] :
          ! [F: nat] :
            ( ( ord_less_nat @ F @ E )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ? [E: nat] :
          ! [F: nat] :
            ( ( ord_less_nat @ F @ E )
           => ( ( ( A @ F )
                & ( C @ F ) )
              = ( ( B @ F )
                & ( D @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_minf_I1_J) ).

thf(1014,plain,
    ! [A: nat > $o,B: nat > $o,C: nat > $o,D: nat > $o] :
      ( ? [E: nat] :
        ! [F: nat] :
          ( ( ord_less_nat @ F @ E )
         => ( ( A @ F )
            = ( B @ F ) ) )
     => ( ? [E: nat] :
          ! [F: nat] :
            ( ( ord_less_nat @ F @ E )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ? [E: nat] :
          ! [F: nat] :
            ( ( ord_less_nat @ F @ E )
           => ( ( ( A @ F )
                & ( C @ F ) )
              = ( ( B @ F )
                & ( D @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(202,axiom,
    ! [A: nat,B: list_a] :
      ( ( ord_less_nat @ A @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
     => ( ( sat_a @ sigma @ B @ A @ phi_1 )
        = ( sat_a @ sigma2 @ B @ A @ phi_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Until_OIH_I1_J) ).

thf(972,plain,
    ! [A: nat,B: list_a] :
      ( ( ord_less_nat @ A @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
     => ( ( sat_a @ sigma @ B @ A @ phi_1 )
        = ( sat_a @ sigma2 @ B @ A @ phi_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(1529,plain,
    $false,
    inference(e,[status(thm)],[809,1024,760,347,1083,941,1179,777,666,1110,481,333,1031,582,994,741,1205,1142,677,861,384,1137,500,715,814,698,747,340,538,1095,1001,1127,417,885,570,372,587,702,344,357,1059,1132,638,870,770,881,325,289,448,316,1100,817,902,1040,376,821,353,966,602,293,866,1072,774,396,998,1201,507,527,1169,687,1215,634,1104,1242,512,661,1199,1153,534,1057,1163,910,894,1091,825,1042,302,862,1217,561,297,630,788,729,1238,467,847,879,830,461,1195,551,456,519,874,725,980,783,420,554,1182,537,669,476,489,1207,970,1114,1150,1192,984,1246,605,1086,360,805,311,558,1187,530,953,794,718,750,1146,856,573,689,819,904,423,732,772,286,577,958,843,1125,641,1139,445,313,1107,1239,335,947,350,540,672,979,681,1048,996,737,434,1175,784,1117,890,387,494,621,1029,330,367,552,1066,780,608,394,563,431,685,521,1171,768,827,1044,695,1245,722,1034,675,944,795,663,1134,1081,939,355,754,1203,589,617,516,968,458,525,295,1070,705,707,327,1098,791,502,1235,470,951,585,370,744,656,600,612,991,497,876,627,450,1157,976,759,1189,1108,363,556,813,963,319,1062,652,390,568,510,763,1077,478,1161,287,300,854,1148,735,833,410,305,474,828,1165,955,415,1093,987,464,1129,644,850,1004,691,442,871,1120,322,337,1184,309,543,1037,592,491,1088,1014,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : ITP125^1 : TPTP v8.2.0. Released v7.5.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.13/0.36  % Computer : n006.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Sat May 18 18:38:39 EDT 2024
% 0.13/0.36  % CPUTime  : 
% 0.83/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.80/1.13  % [INFO] 	 Parsing done (291ms). 
% 1.80/1.15  % [INFO] 	 Running in sequential loop mode. 
% 2.49/1.45  % [INFO] 	 eprover registered as external prover. 
% 2.49/1.45  % [INFO] 	 cvc4 registered as external prover. 
% 2.49/1.46  % [INFO] 	 Scanning for conjecture ... 
% 2.69/1.54  % [INFO] 	 Found a conjecture (or negated_conjecture) and 283 axioms. Running axiom selection ... 
% 3.01/1.67  % [INFO] 	 Axiom selection finished. Selected 283 axioms (removed 0 axioms). 
% 3.62/1.94  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.88/1.97  % [INFO] 	 Type checking passed. 
% 3.88/1.97  % [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 ... 
% 22.25/6.26  % External prover 'e' found a proof!
% 22.25/6.26  % [INFO] 	 Killing All external provers ... 
% 22.25/6.27  % Time passed: 5773ms (effective reasoning time: 5117ms)
% 22.25/6.27  % 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)>
% 22.25/6.27  % Axioms used in derivation (283): fact_106_order__subst2, fact_192_dual__order_Ostrict__trans1, fact_80_order__class_Oorder_Oeq__iff, fact_232_le__Suc__ex, fact_281_add__mono__thms__linordered__field_I4_J, fact_27_le__neq__implies__less, fact_66_dual__order_Oeq__iff, fact_280_add__mono__thms__linordered__field_I3_J, fact_26_less__mono__imp__le__mono, fact_48_Until_OIH_I1_J, fact_3_nat__neq__iff, fact_229_le__add2, fact_278_add__less__le__mono, fact_279_add__le__less__mono, fact_81_order__class_Oorder_Oeq__iff, fact_246_add__right__cancel, fact_263_add__mono, fact_144_leD, fact_137_less__imp__not__less, fact_276_add__less__imp__less__left, fact_59_order_Ostrict__implies__order, fact_225_add__less__mono, fact_5_less__not__refl2, fact_8_nat__less__induct, fact_21_progress__mono, fact_239_progress__time__conv, fact_145_leD, fact_271_add__mono__thms__linordered__field_I2_J, fact_37_pinf_I5_J, fact_30_less__imp__le__nat, fact_194_dual__order_Ostrict__trans2, fact_142_order_Ostrict__implies__not__eq, fact_126_ord__less__eq__trans, fact_228_le__add1, fact_160_order__less__le__subst1, fact_174_le__less__trans, fact_244_add__less__cancel__right, fact_147_le__less, fact_197_verit__comp__simplify1_I3_J, fact_249_add__less__cancel__left, fact_97_ord__le__eq__subst, fact_102_ord__eq__le__subst, fact_107_order__subst1, fact_65_dual__order_Oeq__iff, fact_154_order__le__less__subst2, fact_219_less__add__eq__less, fact_215__092_060open_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_092_060close_062, fact_39_minf_I1_J, fact_34_pinf_I2_J, fact_12_assms_I2_J, fact_140_dual__order_Ostrict__trans, fact_114_order__less__subst2, fact_15_le__trans, fact_270_add__mono__thms__linordered__field_I5_J, fact_259_add__right__imp__eq, fact_128_less__imp__not__eq, fact_236_trans__le__add2, fact_255_add_Oassoc, fact_267_le__iff__add, fact_200_verit__la__disequality, fact_157_order__less__le__subst1, fact_223_not__add__less2, fact_119_less__imp__neq, fact_211__C3_C, fact_141_not__less__iff__gr__or__eq, fact_28_less__or__eq__imp__le, fact_29_le__eq__less__or__eq, fact_156_order__le__less__subst2, fact_274_add__strict__left__mono, fact_265_less__eqE, fact_172_less__imp__le, fact_162_order__less__le__subst2, fact_190_order_Ostrict__iff__order, fact_129_less__not__sym, fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062, fact_68_dual__order_Otrans, fact_251_ab__semigroup__add__class_Oadd__ac_I1_J, fact_74_order__class_Oorder_Oantisym, fact_109_order__subst1, fact_245_add__left__cancel, fact_70_dual__order_Orefl, fact_50_complete__interval, fact_136_order_Ostrict__trans, fact_138_exists__least__iff, fact_63_dual__order_Oantisym, fact_159_order__less__le__subst1, fact_151_order__le__less__subst1, fact_155_order__le__less__subst2, fact_139_linorder__less__wlog, fact_84_le__cases3, fact_199_less__prefix__def, fact_205_formula_Oinject_I9_J, fact_36_pinf_I4_J, fact_240_le___092_060tau_062__less, fact_158_order__less__le__subst1, fact_231_add__leD2, fact_111_ord__eq__less__subst, fact_146_leI, fact_216_less___092_060tau_062D, fact_93_eq__iff, fact_72_order__trans, fact_53_dual__order_Ostrict__implies__order, fact_121_less__asym_H, fact_177_le__less__linear, fact_104_order__subst2, fact_18_nat__le__linear, fact_52_order_Onot__eq__order__implies__strict, fact_168_antisym__conv1, fact_167_antisym__conv1, fact_153_order__le__less__subst2, fact_178_le__imp__less__or__eq, fact_95_ord__le__eq__subst, fact_181_less__le__not__le, fact_266_add__right__mono, fact_152_order__le__less__subst1, fact_195_Until_Oprems, fact_47_order__refl, fact_260_add__mono__thms__linordered__semiring_I3_J, fact_187_order_Oorder__iff__strict, fact_234_add__le__mono1, fact_122_less__trans, fact_277_add__less__imp__less__right, fact_165_le__neq__trans, fact_149_less__le, fact_85_order_Otrans, fact_143_dual__order_Ostrict__implies__not__eq, fact_176_less__le__trans, fact_44_minf_I7_J, fact_113_order__less__subst1, fact_227_add__leE, fact_241__092_060tau_062__prefix__conv, fact_100_ord__eq__le__subst, fact_40_minf_I2_J, fact_127_dual__order_Oasym, fact_183_order_Ostrict__trans1, fact_91_antisym, fact_250_one__reorient, fact_170_antisym__conv2, fact_209_nat__add__left__cancel__less, fact_105_order__subst2, fact_220_trans__less__add2, fact_182_not__le__imp__less, fact_208_that, fact_179_le__imp__less__or__eq, fact_115_gt__ex, fact_248_add__le__cancel__right, fact_32_progress__prefix__conv, fact_92_antisym, fact_185_order_Ostrict__trans2, fact_22_pinf_I6_J, fact_124_less__irrefl, fact_191_dual__order_Ostrict__trans1, fact_87_le__cases, fact_161_order__less__le__subst2, fact_261_add__mono__thms__linordered__semiring_I2_J, fact_256_add_Ocommute, fact_150_less__le, fact_25_minf_I8_J, fact_171_less__imp__le, fact_130_less__induct, fact_123_less__linear, fact_45__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062, fact_213__C2_C, fact_269_add__le__imp__le__right, fact_273_add__strict__mono, fact_254_group__cancel_Oadd2, fact_11__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062, fact_282_discrete, fact_60_order_Ostrict__implies__order, fact_78_ord__eq__le__trans, fact_230_add__leD1, fact_49_nat__descend__induct, fact_62_Until_OIH_I2_J, fact_9_infinite__descent, fact_212__C1_C, fact_24_minf_I6_J, fact_242__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_243__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_166_le__neq__trans, fact_7_less__irrefl__nat, fact_35_pinf_I3_J, fact_46_order__refl, fact_210_nat__add__left__cancel__le, fact_217_ex__le___092_060tau_062, fact_77_ord__le__eq__trans, fact_207__C11_C, fact_103_order__subst2, fact_118_order_Oasym, fact_98_ord__le__eq__subst, fact_20_progress__le, fact_13__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062, fact_43_minf_I5_J, fact_83_antisym__conv, fact_86_order_Otrans, fact_1_assms_I3_J, fact_112_ord__less__eq__subst, fact_38_pinf_I7_J, fact_61__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062, fact_16_eq__imp__le, fact_134_linorder__cases, fact_224_not__add__less1, fact_233_add__le__mono, fact_253_group__cancel_Oadd1, fact_189_order_Ostrict__iff__order, fact_71_dual__order_Orefl, fact_67_dual__order_Otrans, fact_79_ord__eq__le__trans, fact_75_order__class_Oorder_Oantisym, fact_19_Nat_Oex__has__greatest__nat, fact_135_dual__order_Oirrefl, fact_222_add__less__mono1, fact_206__C21_C, fact_90_linear, fact_201_verit__comp__simplify1_I1_J, fact_221_trans__less__add1, fact_235_trans__le__add1, fact_33_pinf_I1_J, fact_184_order_Ostrict__trans1, fact_69_linorder__wlog, fact_51_order_Onot__eq__order__implies__strict, fact_101_ord__eq__le__subst, fact_203_prefix__of__antimono, fact_193_dual__order_Ostrict__trans2, fact_196_plen__mono, fact_14_le__refl, fact_117_neq__iff, fact_99_ord__eq__le__subst, fact_247_add__le__cancel__left, fact_164_not__less, fact_108_order__subst1, fact_54_dual__order_Ostrict__implies__order, fact_169_antisym__conv2, fact_96_ord__le__eq__subst, fact_89_eq__refl, fact_94_eq__iff, fact_56_dual__order_Ostrict__iff__order, fact_88_eq__refl, fact_264_add__left__mono, fact_57_dual__order_Oorder__iff__strict, fact_6_less__not__refl3, fact_268_add__le__imp__le__left, fact_180_less__le__not__le, fact_198__092_060open_062i_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_Iformula_OUntil_A_092_060phi_0621_AI_A_092_060phi_0622_J_A_Iplen_A_092_060pi_062_J_092_060close_062, fact_82_antisym__conv, fact_31_nat__less__le, fact_133_less__imp__triv, fact_132_less__imp__not__eq2, fact_58_dual__order_Oorder__iff__strict, fact_41_minf_I3_J, fact_258_add__left__imp__eq, fact_257_add_Oleft__commute, fact_275_add__strict__right__mono, fact_226_add__lessD1, fact_2_assms_I1_J, fact_76_ord__le__eq__trans, fact_272_add__mono__thms__linordered__field_I1_J, fact_4_less__not__refl, fact_252_add__mono__thms__linordered__semiring_I4_J, fact_148_le__less, fact_188_order_Oorder__iff__strict, fact_131_antisym__conv3, fact_218__092_060tau_062__mono, fact_204_prefix__of__imp__linear, fact_120_less__asym, fact_175_less__le__trans, fact_262_add__mono__thms__linordered__semiring_I1_J, fact_64_dual__order_Oantisym, fact_186_order_Ostrict__trans2, fact_55_dual__order_Ostrict__iff__order, fact_238_mono__nat__linear__lb, fact_214__092_060open_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_____092_060close_062, fact_73_order__trans, fact_17_le__antisym, fact_23_pinf_I8_J, fact_110_order__subst1, fact_237_nat__le__iff__add, fact_125_ord__eq__less__trans, fact_10_linorder__neqE__nat, fact_163_not__le, fact_116_neqE, fact_173_le__less__trans, fact_42_minf_I4_J, fact_202_ex__prefix__of
% 22.25/6.27  % No. of inferences in proof: 570
% 22.25/6.27  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5773 ms resp. 5117 ms w/o parsing
% 23.10/6.50  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 23.10/6.51  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------