TSTP Solution File: TOP047+1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : TOP047+1 : TPTP v8.2.0. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.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 : Tue May 21 09:17:35 EDT 2024

% Result   : Theorem 83.15s 14.16s
% Output   : Refutation 83.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  143
% Syntax   : Number of formulae    :  236 (  25 unt;  52 typ;   0 def)
%            Number of atoms       :  722 (  49 equ;   0 cnn)
%            Maximal formula atoms :   25 (   3 avg)
%            Number of connectives : 1890 (  97   ~;   2   |; 333   &;1255   @)
%                                         (   6 <=>; 197  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   73 (  73   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   54 (  52 usr;   2 con; 0-3 aty)
%            Number of variables   :  330 (   0   ^ 267   !;  63   ?; 330   :)

% Comments : 
%------------------------------------------------------------------------------
thf(v2_orders_2_type,type,
    v2_orders_2: $i > $o ).

thf(v3_orders_2_type,type,
    v3_orders_2: $i > $o ).

thf(v4_orders_2_type,type,
    v4_orders_2: $i > $o ).

thf(v24_waybel_0_type,type,
    v24_waybel_0: $i > $o ).

thf(v25_waybel_0_type,type,
    v25_waybel_0: $i > $o ).

thf(v2_lattice3_type,type,
    v2_lattice3: $i > $o ).

thf(l1_orders_2_type,type,
    l1_orders_2: $i > $o ).

thf(g1_orders_2_type,type,
    g1_orders_2: $i > $i > $i ).

thf(u1_struct_0_type,type,
    u1_struct_0: $i > $i ).

thf(u1_orders_2_type,type,
    u1_orders_2: $i > $i ).

thf(k14_yellow_6_type,type,
    k14_yellow_6: $i > $i > $i ).

thf(k3_waybel28_type,type,
    k3_waybel28: $i > $i ).

thf(v1_relat_1_type,type,
    v1_relat_1: $i > $o ).

thf(v3_relat_1_type,type,
    v3_relat_1: $i > $o ).

thf(v1_funct_1_type,type,
    v1_funct_1: $i > $o ).

thf(v1_xboole_0_type,type,
    v1_xboole_0: $i > $o ).

thf(k2_tarski_type,type,
    k2_tarski: $i > $i > $i ).

thf(v2_funct_1_type,type,
    v2_funct_1: $i > $o ).

thf(k1_xboole_0_type,type,
    k1_xboole_0: $i ).

thf(v3_struct_0_type,type,
    v3_struct_0: $i > $o ).

thf(l1_struct_0_type,type,
    l1_struct_0: $i > $o ).

thf(m4_yellow_6_type,type,
    m4_yellow_6: $i > $i > $o ).

thf(m2_relset_1_type,type,
    m2_relset_1: $i > $i > $i > $o ).

thf(m1_relset_1_type,type,
    m1_relset_1: $i > $i > $i > $o ).

thf(k2_zfmisc_1_type,type,
    k2_zfmisc_1: $i > $i > $i ).

thf(m1_subset_1_type,type,
    m1_subset_1: $i > $i > $o ).

thf(k1_zfmisc_1_type,type,
    k1_zfmisc_1: $i > $i ).

thf(v1_finset_1_type,type,
    v1_finset_1: $i > $o ).

thf(r1_tarski_type,type,
    r1_tarski: $i > $i > $o ).

thf(r2_hidden_type,type,
    r2_hidden: $i > $i > $o ).

thf(k4_tarski_type,type,
    k4_tarski: $i > $i > $i ).

thf(k1_tarski_type,type,
    k1_tarski: $i > $i ).

thf(l1_pre_topc_type,type,
    l1_pre_topc: $i > $o ).

thf(l1_waybel_0_type,type,
    l1_waybel_0: $i > $i > $o ).

thf(g1_pre_topc_type,type,
    g1_pre_topc: $i > $i > $i ).

thf(v1_pre_topc_type,type,
    v1_pre_topc: $i > $o ).

thf(v1_membered_type,type,
    v1_membered: $i > $o ).

thf(v2_membered_type,type,
    v2_membered: $i > $o ).

thf(v3_membered_type,type,
    v3_membered: $i > $o ).

thf(v4_membered_type,type,
    v4_membered: $i > $o ).

thf(v5_membered_type,type,
    v5_membered: $i > $o ).

thf(v2_tops_1_type,type,
    v2_tops_1: $i > $i > $o ).

thf(v2_pre_topc_type,type,
    v2_pre_topc: $i > $o ).

thf(v3_pre_topc_type,type,
    v3_pre_topc: $i > $i > $o ).

thf(v4_pre_topc_type,type,
    v4_pre_topc: $i > $i > $o ).

thf(u1_pre_topc_type,type,
    u1_pre_topc: $i > $i ).

thf(a_2_1_yellow_6_type,type,
    a_2_1_yellow_6: $i > $i > $i ).

thf(v3_tops_1_type,type,
    v3_tops_1: $i > $i > $o ).

thf(v1_yellow_0_type,type,
    v1_yellow_0: $i > $o ).

thf(v1_orders_2_type,type,
    v1_orders_2: $i > $o ).

thf(v7_waybel_0_type,type,
    v7_waybel_0: $i > $o ).

thf(r1_waybel_0_type,type,
    r1_waybel_0: $i > $i > $i > $o ).

thf(12,axiom,
    ( ( v1_xboole_0 @ k1_xboole_0 )
    & ( v1_relat_1 @ k1_xboole_0 )
    & ( v3_relat_1 @ k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).

thf(142,plain,
    ( ( v1_xboole_0 @ k1_xboole_0 )
    & ( v1_relat_1 @ k1_xboole_0 )
    & ( v3_relat_1 @ k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(84,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A )
        & ( m4_yellow_6 @ B @ A ) )
     => ( ( v1_pre_topc @ ( k14_yellow_6 @ A @ B ) )
        & ( l1_pre_topc @ ( k14_yellow_6 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k14_yellow_6) ).

thf(411,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A )
        & ( m4_yellow_6 @ B @ A ) )
     => ( ( v1_pre_topc @ ( k14_yellow_6 @ A @ B ) )
        & ( l1_pre_topc @ ( k14_yellow_6 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_relat_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).

thf(129,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_relat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(49,axiom,
    ? [A: $i] :
      ( ( l1_struct_0 @ A )
      & ~ ( v3_struct_0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).

thf(259,plain,
    ? [A: $i] :
      ( ( l1_struct_0 @ A )
      & ~ ( v3_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(92,axiom,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v1_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v7_waybel_0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_yellow_6) ).

thf(445,plain,
    ? [A: $i] :
      ( ( l1_orders_2 @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v1_orders_2 @ A )
      & ( v3_orders_2 @ A )
      & ( v7_waybel_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

thf(154,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(71,axiom,
    ! [A: $i] :
      ( ( l1_struct_0 @ A )
     => ! [B: $i] :
          ( ( l1_waybel_0 @ B @ A )
         => ( l1_orders_2 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_waybel_0) ).

thf(347,plain,
    ! [A: $i] :
      ( ( l1_struct_0 @ A )
     => ! [B: $i] :
          ( ( l1_waybel_0 @ B @ A )
         => ( l1_orders_2 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(78,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v3_pre_topc @ B @ A )
          & ( v4_pre_topc @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_tops_1) ).

thf(365,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v3_pre_topc @ B @ A )
          & ( v4_pre_topc @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v2_funct_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).

thf(138,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v2_funct_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
         => ( ( ( v3_pre_topc @ B @ A )
              & ( v3_tops_1 @ B @ A ) )
           => ( ( v1_xboole_0 @ B )
              & ( v3_pre_topc @ B @ A )
              & ( v4_pre_topc @ B @ A )
              & ( v1_membered @ B )
              & ( v2_membered @ B )
              & ( v3_membered @ B )
              & ( v4_membered @ B )
              & ( v5_membered @ B )
              & ( v2_tops_1 @ B @ A )
              & ( v3_tops_1 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_tops_1) ).

thf(333,plain,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
         => ( ( ( v3_pre_topc @ B @ A )
              & ( v3_tops_1 @ B @ A ) )
           => ( ( v1_xboole_0 @ B )
              & ( v3_pre_topc @ B @ A )
              & ( v4_pre_topc @ B @ A )
              & ( v1_membered @ B )
              & ( v2_membered @ B )
              & ( v3_membered @ B )
              & ( v4_membered @ B )
              & ( v5_membered @ B )
              & ( v2_tops_1 @ B @ A )
              & ( v3_tops_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).

thf(249,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(83,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
          & ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).

thf(408,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
          & ~ ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(4,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v3_relat_1 @ A )
      & ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).

thf(115,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v3_relat_1 @ A )
      & ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(54,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( v1_pre_topc @ ( g1_pre_topc @ A @ B ) )
        & ( l1_pre_topc @ ( g1_pre_topc @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_pre_topc) ).

thf(276,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( v1_pre_topc @ ( g1_pre_topc @ A @ B ) )
        & ( l1_pre_topc @ ( g1_pre_topc @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(44,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_finset_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).

thf(247,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_finset_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(91,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v25_waybel_0 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v2_lattice3 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_waybel_0) ).

thf(440,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v25_waybel_0 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v2_lattice3 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(52,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).

thf(269,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(86,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_relset_1 @ B @ A @ A )
     => ! [C: $i,D: $i] :
          ( ( ( g1_orders_2 @ A @ B )
            = ( g1_orders_2 @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).

thf(417,plain,
    ! [A: $i,B: $i] :
      ( ( m1_relset_1 @ B @ A @ A )
     => ! [C: $i,D: $i] :
          ( ( ( g1_orders_2 @ A @ B )
            = ( g1_orders_2 @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(60,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A ) )
     => ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).

thf(301,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A ) )
     => ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(23,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).

thf(184,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(70,axiom,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
         => ( ( ( v4_pre_topc @ B @ A )
              & ( v2_tops_1 @ B @ A ) )
           => ( ( v2_tops_1 @ B @ A )
              & ( v3_tops_1 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_tops_1) ).

thf(344,plain,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
         => ( ( ( v4_pre_topc @ B @ A )
              & ( v2_tops_1 @ B @ A ) )
           => ( ( v2_tops_1 @ B @ A )
              & ( v3_tops_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(28,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(196,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(17,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
    <=> ( m1_relset_1 @ C @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

thf(157,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m2_relset_1 @ C @ A @ B )
       => ( m1_relset_1 @ C @ A @ B ) )
      & ( ( m1_relset_1 @ C @ A @ B )
       => ( m2_relset_1 @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v24_waybel_0 @ A )
        & ( v25_waybel_0 @ A )
        & ( v2_lattice3 @ A )
        & ( l1_orders_2 @ A ) )
     => ! [B: $i] :
          ( ( ( v2_orders_2 @ B )
            & ( v3_orders_2 @ B )
            & ( v4_orders_2 @ B )
            & ( v24_waybel_0 @ B )
            & ( v25_waybel_0 @ B )
            & ( v2_lattice3 @ B )
            & ( l1_orders_2 @ B ) )
         => ( ( ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) )
              = ( g1_orders_2 @ ( u1_struct_0 @ B ) @ ( u1_orders_2 @ B ) ) )
           => ( ( k14_yellow_6 @ A @ ( k3_waybel28 @ A ) )
              = ( k14_yellow_6 @ B @ ( k3_waybel28 @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_waybel33) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v24_waybel_0 @ A )
          & ( v25_waybel_0 @ A )
          & ( v2_lattice3 @ A )
          & ( l1_orders_2 @ A ) )
       => ! [B: $i] :
            ( ( ( v2_orders_2 @ B )
              & ( v3_orders_2 @ B )
              & ( v4_orders_2 @ B )
              & ( v24_waybel_0 @ B )
              & ( v25_waybel_0 @ B )
              & ( v2_lattice3 @ B )
              & ( l1_orders_2 @ B ) )
           => ( ( ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) )
                = ( g1_orders_2 @ ( u1_struct_0 @ B ) @ ( u1_orders_2 @ B ) ) )
             => ( ( k14_yellow_6 @ A @ ( k3_waybel28 @ A ) )
                = ( k14_yellow_6 @ B @ ( k3_waybel28 @ B ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(93,plain,
    ~ ! [A: $i] :
        ( ( ( v2_orders_2 @ A )
          & ( v3_orders_2 @ A )
          & ( v4_orders_2 @ A )
          & ( v24_waybel_0 @ A )
          & ( v25_waybel_0 @ A )
          & ( v2_lattice3 @ A )
          & ( l1_orders_2 @ A ) )
       => ! [B: $i] :
            ( ( ( v2_orders_2 @ B )
              & ( v3_orders_2 @ B )
              & ( v4_orders_2 @ B )
              & ( v24_waybel_0 @ B )
              & ( v25_waybel_0 @ B )
              & ( v2_lattice3 @ B )
              & ( l1_orders_2 @ B ) )
           => ( ( ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) )
                = ( g1_orders_2 @ ( u1_struct_0 @ B ) @ ( u1_orders_2 @ B ) ) )
             => ( ( k14_yellow_6 @ A @ ( k3_waybel28 @ A ) )
                = ( k14_yellow_6 @ B @ ( k3_waybel28 @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(57,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
      & ( v1_finset_1 @ ( k2_tarski @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finset_1) ).

thf(284,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
      & ( v1_finset_1 @ ( k2_tarski @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A ) )
     => ! [B: $i] :
          ( ( m4_yellow_6 @ B @ A )
         => ( v1_relat_1 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_yellow_6) ).

thf(152,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A ) )
     => ! [B: $i] :
          ( ( m4_yellow_6 @ B @ A )
         => ( v1_relat_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(58,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

thf(289,plain,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_finset_1 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).

thf(164,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_finset_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(21,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
      & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).

thf(179,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
      & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(59,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
          & ( v1_xboole_0 @ B )
          & ( v1_membered @ B )
          & ( v2_membered @ B )
          & ( v3_membered @ B )
          & ( v4_membered @ B )
          & ( v5_membered @ B )
          & ( v2_tops_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_tops_1) ).

thf(292,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
          & ( v1_xboole_0 @ B )
          & ( v1_membered @ B )
          & ( v2_membered @ B )
          & ( v3_membered @ B )
          & ( v4_membered @ B )
          & ( v5_membered @ B )
          & ( v2_tops_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(39,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(233,plain,
    ! [A: $i] : ( r1_tarski @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(34,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

thf(220,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(72,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( v2_lattice3 @ A )
       => ~ ( v3_struct_0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice3) ).

thf(349,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( v2_lattice3 @ A )
       => ~ ( v3_struct_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(88,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_orders_2 @ A ) )
     => ( m4_yellow_6 @ ( k3_waybel28 @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_waybel28) ).

thf(424,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_orders_2 @ A ) )
     => ( m4_yellow_6 @ ( k3_waybel28 @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).

thf(192,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(46,axiom,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(252,plain,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(36,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).

thf(224,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(81,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( v1_pre_topc @ A )
       => ( A
          = ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_pre_topc) ).

thf(403,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( v1_pre_topc @ A )
       => ( A
          = ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(25,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).

thf(188,plain,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(67,axiom,
    ! [A: $i] :
      ( ( ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v24_waybel_0 @ A )
        & ( v25_waybel_0 @ A )
        & ( v2_lattice3 @ A )
        & ( l1_orders_2 @ A ) )
     => ! [B: $i] :
          ( ( ( v2_orders_2 @ B )
            & ( v3_orders_2 @ B )
            & ( v4_orders_2 @ B )
            & ( v24_waybel_0 @ B )
            & ( v25_waybel_0 @ B )
            & ( v2_lattice3 @ B )
            & ( l1_orders_2 @ B ) )
         => ( ( ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) )
              = ( g1_orders_2 @ ( u1_struct_0 @ B ) @ ( u1_orders_2 @ B ) ) )
           => ( r1_tarski @ ( u1_pre_topc @ ( k14_yellow_6 @ A @ ( k3_waybel28 @ A ) ) ) @ ( u1_pre_topc @ ( k14_yellow_6 @ B @ ( k3_waybel28 @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12_waybel33) ).

thf(328,plain,
    ! [A: $i] :
      ( ( ( v2_orders_2 @ A )
        & ( v3_orders_2 @ A )
        & ( v4_orders_2 @ A )
        & ( v24_waybel_0 @ A )
        & ( v25_waybel_0 @ A )
        & ( v2_lattice3 @ A )
        & ( l1_orders_2 @ A ) )
     => ! [B: $i] :
          ( ( ( v2_orders_2 @ B )
            & ( v3_orders_2 @ B )
            & ( v4_orders_2 @ B )
            & ( v24_waybel_0 @ B )
            & ( v25_waybel_0 @ B )
            & ( v2_lattice3 @ B )
            & ( l1_orders_2 @ B ) )
         => ( ( ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) )
              = ( g1_orders_2 @ ( u1_struct_0 @ B ) @ ( u1_orders_2 @ B ) ) )
           => ( r1_tarski @ ( u1_pre_topc @ ( k14_yellow_6 @ A @ ( k3_waybel28 @ A ) ) ) @ ( u1_pre_topc @ ( k14_yellow_6 @ B @ ( k3_waybel28 @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(48,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(256,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(41,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
      & ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).

thf(237,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
      & ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(51,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_finset_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).

thf(266,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_finset_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(76,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( v1_orders_2 @ A )
       => ( A
          = ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).

thf(360,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( v1_orders_2 @ A )
       => ( A
          = ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(64,axiom,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
          & ( v3_pre_topc @ B @ A )
          & ( v4_pre_topc @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tops_1) ).

thf(311,plain,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
          & ( v3_pre_topc @ B @ A )
          & ( v4_pre_topc @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(55,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
        & ( v1_xboole_0 @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

thf(279,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
        & ( v1_xboole_0 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(14,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).

thf(149,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(82,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( l1_struct_0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).

thf(406,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( l1_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(38,axiom,
    ! [A: $i,B: $i] :
      ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).

thf(230,plain,
    ! [A: $i,B: $i] :
      ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( l1_struct_0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).

thf(245,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( l1_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(61,axiom,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
          & ( v3_pre_topc @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tops_1) ).

thf(303,plain,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
          & ( v3_pre_topc @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(53,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i,D: $i] :
          ( ( ( g1_pre_topc @ A @ B )
            = ( g1_pre_topc @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_pre_topc) ).

thf(271,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i,D: $i] :
          ( ( ( g1_pre_topc @ A @ B )
            = ( g1_pre_topc @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(32,axiom,
    ? [A: $i] : ( l1_struct_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).

thf(213,plain,
    ? [A: $i] : ( l1_struct_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(29,axiom,
    ! [A: $i] :
      ( ( v1_finset_1 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( v1_finset_1 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).

thf(198,plain,
    ! [A: $i] :
      ( ( v1_finset_1 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( v1_finset_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(62,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A )
        & ( m4_yellow_6 @ B @ A ) )
     => ( ~ ( v3_struct_0 @ ( k14_yellow_6 @ A @ B ) )
        & ( v1_pre_topc @ ( k14_yellow_6 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc24_yellow_6) ).

thf(306,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A )
        & ( m4_yellow_6 @ B @ A ) )
     => ( ~ ( v3_struct_0 @ ( k14_yellow_6 @ A @ B ) )
        & ( v1_pre_topc @ ( k14_yellow_6 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(10,axiom,
    ? [A: $i] :
      ( ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).

thf(135,plain,
    ? [A: $i] :
      ( ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(37,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_finset_1 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).

thf(226,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_finset_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(90,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( m2_relset_1 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).

thf(438,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( m2_relset_1 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(89,axiom,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
          & ( v1_xboole_0 @ B )
          & ( v3_pre_topc @ B @ A )
          & ( v4_pre_topc @ B @ A )
          & ( v1_membered @ B )
          & ( v2_membered @ B )
          & ( v3_membered @ B )
          & ( v4_membered @ B )
          & ( v5_membered @ B )
          & ( v2_tops_1 @ B @ A )
          & ( v3_tops_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_tops_1) ).

thf(426,plain,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
          & ( v1_xboole_0 @ B )
          & ( v3_pre_topc @ B @ A )
          & ( v4_pre_topc @ B @ A )
          & ( v1_membered @ B )
          & ( v2_membered @ B )
          & ( v3_membered @ B )
          & ( v4_membered @ B )
          & ( v5_membered @ B )
          & ( v2_tops_1 @ B @ A )
          & ( v3_tops_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).

thf(162,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(80,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v3_struct_0 @ B )
        & ( l1_struct_0 @ B )
        & ( m4_yellow_6 @ C @ B ) )
     => ( ( r2_hidden @ A @ ( a_2_1_yellow_6 @ B @ C ) )
      <=> ? [D: $i] :
            ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
            & ( A = D )
            & ! [E: $i] :
                ( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
               => ( ( r2_hidden @ E @ D )
                 => ! [F: $i] :
                      ( ( ~ ( v3_struct_0 @ F )
                        & ( v3_orders_2 @ F )
                        & ( v7_waybel_0 @ F )
                        & ( l1_waybel_0 @ F @ B ) )
                     => ( ( r2_hidden @ ( k4_tarski @ F @ E ) @ C )
                       => ( r1_waybel_0 @ B @ F @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_yellow_6) ).

thf(374,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v3_struct_0 @ B )
        & ( l1_struct_0 @ B )
        & ( m4_yellow_6 @ C @ B ) )
     => ( ( ( r2_hidden @ A @ ( a_2_1_yellow_6 @ B @ C ) )
         => ? [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
              & ( A = D )
              & ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
                 => ( ( r2_hidden @ E @ D )
                   => ! [F: $i] :
                        ( ( ~ ( v3_struct_0 @ F )
                          & ( v3_orders_2 @ F )
                          & ( v7_waybel_0 @ F )
                          & ( l1_waybel_0 @ F @ B ) )
                       => ( ( r2_hidden @ ( k4_tarski @ F @ E ) @ C )
                         => ( r1_waybel_0 @ B @ F @ D ) ) ) ) ) ) )
        & ( ? [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
              & ( A = D )
              & ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
                 => ( ( r2_hidden @ E @ D )
                   => ! [F: $i] :
                        ( ( ~ ( v3_struct_0 @ F )
                          & ( v3_orders_2 @ F )
                          & ( v7_waybel_0 @ F )
                          & ( l1_waybel_0 @ F @ B ) )
                       => ( ( r2_hidden @ ( k4_tarski @ F @ E ) @ C )
                         => ( r1_waybel_0 @ B @ F @ D ) ) ) ) ) )
         => ( r2_hidden @ A @ ( a_2_1_yellow_6 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(3,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v3_relat_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).

thf(112,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v3_relat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(6,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).

thf(123,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(27,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).

thf(194,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(56,axiom,
    ? [A: $i] : ( l1_pre_topc @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).

thf(282,plain,
    ? [A: $i] : ( l1_pre_topc @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(85,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_relset_1 @ B @ A @ A )
     => ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) )
        & ( l1_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_orders_2) ).

thf(414,plain,
    ! [A: $i,B: $i] :
      ( ( m1_relset_1 @ B @ A @ A )
     => ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) )
        & ( l1_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(22,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ( v1_relat_1 @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).

thf(182,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ( v1_relat_1 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(68,axiom,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
         => ( ( v3_tops_1 @ B @ A )
           => ( v2_tops_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_tops_1) ).

thf(331,plain,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
         => ( ( v3_tops_1 @ B @ A )
           => ( v2_tops_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(79,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A )
        & ( m4_yellow_6 @ B @ A ) )
     => ( ~ ( v3_struct_0 @ ( k14_yellow_6 @ A @ B ) )
        & ( v1_pre_topc @ ( k14_yellow_6 @ A @ B ) )
        & ( v2_pre_topc @ ( k14_yellow_6 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc25_yellow_6) ).

thf(370,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A )
        & ( m4_yellow_6 @ B @ A ) )
     => ( ~ ( v3_struct_0 @ ( k14_yellow_6 @ A @ B ) )
        & ( v1_pre_topc @ ( k14_yellow_6 @ A @ B ) )
        & ( v2_pre_topc @ ( k14_yellow_6 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
         => ( ( v1_xboole_0 @ B )
           => ( v3_tops_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_tops_1) ).

thf(363,plain,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
         => ( ( v1_xboole_0 @ B )
           => ( v3_tops_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(31,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( r2_hidden @ C @ A )
        <=> ( r2_hidden @ C @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).

thf(203,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( ( r2_hidden @ C @ A )
           => ( r2_hidden @ C @ B ) )
          & ( ( r2_hidden @ C @ B )
           => ( r2_hidden @ C @ A ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(66,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A ) )
     => ! [B: $i] :
          ( ( m4_yellow_6 @ B @ A )
         => ! [C: $i] :
              ( ( ( v1_pre_topc @ C )
                & ( l1_pre_topc @ C ) )
             => ( ( C
                  = ( k14_yellow_6 @ A @ B ) )
              <=> ( ( ( u1_struct_0 @ C )
                    = ( u1_struct_0 @ A ) )
                  & ( ( u1_pre_topc @ C )
                    = ( a_2_1_yellow_6 @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d27_yellow_6) ).

thf(319,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A ) )
     => ! [B: $i] :
          ( ( m4_yellow_6 @ B @ A )
         => ! [C: $i] :
              ( ( ( v1_pre_topc @ C )
                & ( l1_pre_topc @ C ) )
             => ( ( ( C
                    = ( k14_yellow_6 @ A @ B ) )
                 => ( ( ( u1_struct_0 @ C )
                      = ( u1_struct_0 @ A ) )
                    & ( ( u1_pre_topc @ C )
                      = ( a_2_1_yellow_6 @ A @ B ) ) ) )
                & ( ( ( ( u1_struct_0 @ C )
                      = ( u1_struct_0 @ A ) )
                    & ( ( u1_pre_topc @ C )
                      = ( a_2_1_yellow_6 @ A @ B ) ) )
                 => ( C
                    = ( k14_yellow_6 @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(73,axiom,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
         => ( ( v1_xboole_0 @ B )
           => ( ( v3_pre_topc @ B @ A )
              & ( v4_pre_topc @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_tops_1) ).

thf(351,plain,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
         => ( ( v1_xboole_0 @ B )
           => ( ( v3_pre_topc @ B @ A )
              & ( v4_pre_topc @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(24,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ B )
     => ( ( v1_xboole_0 @ B )
        | ( r2_hidden @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

thf(186,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ B )
     => ( ( v1_xboole_0 @ B )
        | ( r2_hidden @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(5,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_xboole_0 @ A )
      & ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).

thf(119,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_xboole_0 @ A )
      & ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(40,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A ) )
     => ? [B: $i] : ( m4_yellow_6 @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m4_yellow_6) ).

thf(235,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A ) )
     => ? [B: $i] : ( m4_yellow_6 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(65,axiom,
    ! [A: $i] :
      ( ( l1_struct_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_finset_1 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_waybel_7) ).

thf(315,plain,
    ! [A: $i] :
      ( ( l1_struct_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_finset_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(13,axiom,
    ( ( v1_xboole_0 @ k1_xboole_0 )
    & ( v1_relat_1 @ k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).

thf(146,plain,
    ( ( v1_xboole_0 @ k1_xboole_0 )
    & ( v1_relat_1 @ k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(87,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
         => ( ( v1_xboole_0 @ B )
           => ( v2_tops_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_tops_1) ).

thf(422,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
         => ( ( v1_xboole_0 @ B )
           => ( v2_tops_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(20,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).

thf(168,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
       => ( ( r1_tarski @ A @ B )
          & ( r1_tarski @ B @ A ) ) )
      & ( ( ( r1_tarski @ A @ B )
          & ( r1_tarski @ B @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(50,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
      & ~ ( v1_xboole_0 @ B )
      & ( v1_finset_1 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_waybel_7) ).

thf(262,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
      & ~ ( v1_xboole_0 @ B )
      & ( v1_finset_1 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(42,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).

thf(242,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_tarski @ A @ B )
      = ( k2_tarski @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

thf(126,plain,
    ! [A: $i,B: $i] :
      ( ( k2_tarski @ A @ B )
      = ( k2_tarski @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(75,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( m1_subset_1 @ ( u1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_pre_topc) ).

thf(358,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( m1_subset_1 @ ( u1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(9,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).

thf(131,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(30,axiom,
    ! [A: $i,B: $i] :
      ( ( k4_tarski @ A @ B )
      = ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).

thf(200,plain,
    ! [A: $i,B: $i] :
      ( ( k4_tarski @ A @ B )
      = ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(47,axiom,
    ! [A: $i] :
      ( ( l1_struct_0 @ A )
     => ? [B: $i] : ( l1_waybel_0 @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_waybel_0) ).

thf(254,plain,
    ! [A: $i] :
      ( ( l1_struct_0 @ A )
     => ? [B: $i] : ( l1_waybel_0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(74,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v25_waybel_0 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v1_yellow_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_waybel_0) ).

thf(354,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v25_waybel_0 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_orders_2 @ A )
          & ( v1_yellow_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(63,axiom,
    ? [A: $i] : ( l1_orders_2 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).

thf(309,plain,
    ? [A: $i] : ( l1_orders_2 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(33,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
    <=> ( r1_tarski @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

thf(215,plain,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
       => ( r1_tarski @ A @ B ) )
      & ( ( r1_tarski @ A @ B )
       => ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(35,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
     => ( m1_subset_1 @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).

thf(222,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
     => ( m1_subset_1 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(26420,plain,
    $false,
    inference(e,[status(thm)],[142,411,129,259,445,154,347,365,138,333,249,408,115,276,247,440,269,417,301,184,344,196,157,93,284,152,289,164,179,292,233,220,349,424,192,252,224,403,188,328,256,237,266,360,311,279,149,406,230,245,303,271,213,198,306,135,226,438,426,162,374,112,123,194,282,414,182,331,370,363,203,319,351,186,119,235,315,146,422,168,262,242,126,358,131,200,254,354,309,215,222]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08  % Problem  : TOP047+1 : TPTP v8.2.0. Released v3.4.0.
% 0.04/0.09  % Command  : run_Leo-III %s %d
% 0.08/0.29  % Computer : n012.cluster.edu
% 0.08/0.29  % Model    : x86_64 x86_64
% 0.08/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29  % Memory   : 8042.1875MB
% 0.08/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29  % CPULimit : 300
% 0.08/0.29  % WCLimit  : 300
% 0.08/0.29  % DateTime : Sat May 18 11:27:54 EDT 2024
% 0.08/0.29  % CPUTime  : 
% 0.78/0.73  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.21/0.90  % [INFO] 	 Parsing done (161ms). 
% 1.21/0.90  % [INFO] 	 Running in sequential loop mode. 
% 1.63/1.14  % [INFO] 	 eprover registered as external prover. 
% 1.63/1.14  % [INFO] 	 cvc4 registered as external prover. 
% 1.63/1.15  % [INFO] 	 Scanning for conjecture ... 
% 1.98/1.24  % [INFO] 	 Found a conjecture (or negated_conjecture) and 101 axioms. Running axiom selection ... 
% 2.18/1.34  % [INFO] 	 Axiom selection finished. Selected 90 axioms (removed 11 axioms). 
% 2.56/1.47  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.62/1.49  % [INFO] 	 Type checking passed. 
% 2.62/1.49  % [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 ... 
% 83.15/14.15  % External prover 'e' found a proof!
% 83.15/14.15  % [INFO] 	 Killing All external provers ... 
% 83.15/14.15  % Time passed: 13761ms (effective reasoning time: 13246ms)
% 83.15/14.15  % 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)>
% 83.15/14.16  % Axioms used in derivation (90): fc4_subset_1, rc1_tops_1, cc6_tops_1, abstractness_v1_orders_2, dt_l1_orders_2, fc25_yellow_6, rc3_finset_1, existence_l1_struct_0, fc14_finset_1, antisymmetry_r2_hidden, redefinition_m2_relset_1, cc1_tops_1, cc2_finset_1, dt_k14_yellow_6, rc4_finset_1, l12_waybel33, d5_tarski, t1_subset, rc3_tops_1, fc4_relat_1, d27_yellow_6, cc5_tops_1, rc3_funct_1, rc4_yellow_6, cc3_tops_1, dt_m2_relset_1, cc1_relat_1, cc11_waybel_0, rc1_funct_1, dt_u1_orders_2, dt_l1_pre_topc, fc24_yellow_6, rc3_relat_1, t6_boole, rc2_subset_1, free_g1_pre_topc, rc2_waybel_7, rc5_tops_1, fc3_subset_1, t5_subset, existence_m1_relset_1, fc2_subset_1, rc3_waybel_7, rc4_funct_1, existence_m4_yellow_6, dt_l1_waybel_0, t2_tarski, rc4_tops_1, existence_l1_waybel_0, t4_subset, abstractness_v1_pre_topc, t7_boole, existence_l1_orders_2, cc1_funct_1, dt_g1_pre_topc, rc3_struct_0, fc1_subset_1, cc13_waybel_0, dt_g1_orders_2, rc2_funct_1, rc1_subset_1, cc2_funct_1, t3_subset, cc1_relset_1, existence_m1_subset_1, commutativity_k2_tarski, fraenkel_a_2_1_yellow_6, fc1_finset_1, cc2_tops_1, rc2_relat_1, existence_m2_relset_1, free_g1_orders_2, fc1_struct_0, existence_l1_pre_topc, rc1_relat_1, reflexivity_r1_tarski, rc1_finset_1, rc2_tops_1, cc1_finset_1, cc7_yellow_6, t8_boole, dt_k3_waybel28, dt_u1_pre_topc, t2_subset, fc12_relat_1, rc5_struct_0, cc4_tops_1, cc2_lattice3, d10_xboole_0, fc2_finset_1
% 83.15/14.16  % No. of inferences in proof: 184
% 83.15/14.16  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 13761 ms resp. 13246 ms w/o parsing
% 83.15/14.26  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 83.15/14.26  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------