TSTP Solution File: TOP034+1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : TOP034+1 : TPTP v8.2.0. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 09:17:27 EDT 2024

% Result   : Theorem 7.50s 3.34s
% Output   : Refutation 8.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  136
% Syntax   : Number of formulae    :  226 (  15 unt;  48 typ;   0 def)
%            Number of atoms       :  938 (   4 equ;   0 cnn)
%            Maximal formula atoms :   17 (   5 avg)
%            Number of connectives : 2346 ( 214   ~;   2   |; 472   &;1372   @)
%                                         (   4 <=>; 282  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   73 (  73   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   50 (  48 usr;   2 con; 0-3 aty)
%            Number of variables   :  322 (   0   ^ 279   !;  43   ?; 322   :)

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

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

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

thf(v2_tsp_2_type,type,
    v2_tsp_2: $i > $i > $o ).

thf(m2_tsp_1_type,type,
    m2_tsp_1: $i > $i > $o ).

thf(r1_borsuk_1_type,type,
    r1_borsuk_1: $i > $i > $o ).

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

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

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

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

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

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

thf(v1_xcmplx_0_type,type,
    v1_xcmplx_0: $i > $o ).

thf(v4_ordinal2_type,type,
    v4_ordinal2: $i > $o ).

thf(v1_xreal_0_type,type,
    v1_xreal_0: $i > $o ).

thf(v1_int_1_type,type,
    v1_int_1: $i > $o ).

thf(v1_rat_1_type,type,
    v1_rat_1: $i > $o ).

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

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

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

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

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

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

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

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

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

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

thf(m1_pre_topc_type,type,
    m1_pre_topc: $i > $i > $o ).

thf(v2_tex_2_type,type,
    v2_tex_2: $i > $i > $o ).

thf(v1_borsuk_1_type,type,
    v1_borsuk_1: $i > $i > $o ).

thf(v2_t_0topsp_type,type,
    v2_t_0topsp: $i > $o ).

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

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

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

thf(v1_tsep_1_type,type,
    v1_tsep_1: $i > $i > $o ).

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

thf(v3_realset2_type,type,
    v3_realset2: $i > $o ).

thf(v1_tdlat_3_type,type,
    v1_tdlat_3: $i > $o ).

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

thf(v2_tdlat_3_type,type,
    v2_tdlat_3: $i > $o ).

thf(v3_tdlat_3_type,type,
    v3_tdlat_3: $i > $o ).

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

thf(v1_funct_2_type,type,
    v1_funct_2: $i > $i > $i > $o ).

thf(v5_pre_topc_type,type,
    v5_pre_topc: $i > $i > $i > $o ).

thf(v3_borsuk_1_type,type,
    v3_borsuk_1: $i > $i > $i > $o ).

thf(v1_tex_3_type,type,
    v1_tex_3: $i > $i > $o ).

thf(v4_tdlat_3_type,type,
    v4_tdlat_3: $i > $o ).

thf(v5_tdlat_3_type,type,
    v5_tdlat_3: $i > $o ).

thf(73,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ( v2_tex_2 @ B @ A )
              & ( v2_tsp_2 @ B @ A ) )
           => ( ( v2_pre_topc @ B )
              & ~ ( v1_borsuk_1 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_tsp_2) ).

thf(340,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ( v2_tex_2 @ B @ A )
              & ( v2_tsp_2 @ B @ A ) )
           => ( ( v2_pre_topc @ B )
              & ~ ( v1_borsuk_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(83,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ~ ( v3_realset2 @ A )
          & ( v2_pre_topc @ A )
          & ( v2_tdlat_3 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ~ ( v3_realset2 @ A )
          & ( v2_pre_topc @ A )
          & ~ ( v2_t_0topsp @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_tsp_1) ).

thf(389,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ~ ( v3_realset2 @ A )
          & ( v2_pre_topc @ A )
          & ( v2_tdlat_3 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ~ ( v3_realset2 @ A )
          & ( v2_pre_topc @ A )
          & ~ ( v2_t_0topsp @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(49,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 )
          & ( v4_pre_topc @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_pre_topc) ).

thf(252,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 )
          & ( v4_pre_topc @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(28,axiom,
    ( ( v1_xboole_0 @ k1_xboole_0 )
    & ( v1_membered @ k1_xboole_0 )
    & ( v2_membered @ k1_xboole_0 )
    & ( v3_membered @ k1_xboole_0 )
    & ( v4_membered @ k1_xboole_0 )
    & ( v5_membered @ k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).

thf(173,plain,
    ( ( v1_xboole_0 @ k1_xboole_0 )
    & ( v1_membered @ k1_xboole_0 )
    & ( v2_membered @ k1_xboole_0 )
    & ( v3_membered @ k1_xboole_0 )
    & ( v4_membered @ k1_xboole_0 )
    & ( v5_membered @ k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(66,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(313,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)],[66]) ).

thf(27,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(170,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(8,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(115,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)],[8]) ).

thf(57,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(276,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)],[57]) ).

thf(65,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ! [B: $i] :
          ( ( m2_tsp_1 @ B @ A )
        <=> ( m1_pre_topc @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_tsp_1) ).

thf(308,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ! [B: $i] :
          ( ( ( m2_tsp_1 @ B @ A )
           => ( m1_pre_topc @ B @ A ) )
          & ( ( m1_pre_topc @ B @ A )
           => ( m2_tsp_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(81,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v3_struct_0 @ B )
            & ( m1_pre_topc @ B @ A ) )
         => ( ( r1_borsuk_1 @ A @ B )
          <=> ? [C: $i] :
                ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
                & ( v5_pre_topc @ C @ A @ B )
                & ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
                & ( v3_borsuk_1 @ C @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_borsuk_1) ).

thf(379,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v3_struct_0 @ B )
            & ( m1_pre_topc @ B @ A ) )
         => ( ( ( r1_borsuk_1 @ A @ B )
             => ? [C: $i] :
                  ( ( v1_funct_1 @ C )
                  & ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
                  & ( v5_pre_topc @ C @ A @ B )
                  & ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
                  & ( v3_borsuk_1 @ C @ A @ B ) ) )
            & ( ? [C: $i] :
                  ( ( v1_funct_1 @ C )
                  & ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
                  & ( v5_pre_topc @ C @ A @ B )
                  & ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
                  & ( v3_borsuk_1 @ C @ A @ B ) )
             => ( r1_borsuk_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(55,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ( v1_tsep_1 @ B @ A )
              & ( v2_tex_2 @ B @ A ) )
           => ( ( v2_pre_topc @ B )
              & ~ ( v2_tsp_2 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_tsp_2) ).

thf(269,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ( v1_tsep_1 @ B @ A )
              & ( v2_tex_2 @ B @ A ) )
           => ( ( v2_pre_topc @ B )
              & ~ ( v2_tsp_2 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( v4_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B )
            & ( v3_membered @ B )
            & ( v4_membered @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc19_membered) ).

thf(189,plain,
    ! [A: $i] :
      ( ( v4_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B )
            & ( v3_membered @ B )
            & ( v4_membered @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(89,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ~ ( v2_t_0topsp @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ~ ( v3_realset2 @ A )
          & ( v2_pre_topc @ A )
          & ~ ( v1_tdlat_3 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_tsp_1) ).

thf(416,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ~ ( v2_t_0topsp @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ~ ( v3_realset2 @ A )
          & ( v2_pre_topc @ A )
          & ~ ( v1_tdlat_3 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

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 ) ) )
         => ( ( v1_xboole_0 @ B )
           => ( v3_tops_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_tops_1) ).

thf(325,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)],[69]) ).

thf(43,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(228,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)],[43]) ).

thf(59,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ? [B: $i] : ( m2_tsp_1 @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_tsp_1) ).

thf(289,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ? [B: $i] : ( m2_tsp_1 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(39,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

thf(216,plain,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(68,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ~ ( v2_t_0topsp @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ~ ( v3_struct_0 @ B )
              & ~ ( v2_tex_2 @ B @ A ) )
           => ( ~ ( v3_struct_0 @ B )
              & ~ ( v3_realset2 @ B )
              & ~ ( v2_t_0topsp @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_tsp_1) ).

thf(321,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ~ ( v2_t_0topsp @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ~ ( v3_struct_0 @ B )
              & ~ ( v2_tex_2 @ B @ A ) )
           => ( ~ ( v3_struct_0 @ B )
              & ~ ( v3_realset2 @ B )
              & ~ ( v2_t_0topsp @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(80,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(376,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)],[80]) ).

thf(10,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(121,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)],[10]) ).

thf(20,axiom,
    ? [A: $i] : ( l1_struct_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).

thf(147,plain,
    ? [A: $i] : ( l1_struct_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(85,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(397,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)],[85]) ).

thf(15,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(133,plain,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(87,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ( v1_borsuk_1 @ B @ A )
              & ( v2_tsp_2 @ B @ A ) )
           => ( ( v2_pre_topc @ B )
              & ~ ( v2_tex_2 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc8_tsp_2) ).

thf(411,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ( v1_borsuk_1 @ B @ A )
              & ( v2_tsp_2 @ B @ A ) )
           => ( ( v2_pre_topc @ B )
              & ~ ( v2_tex_2 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(53,axiom,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( v2_pre_topc @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_pre_topc) ).

thf(265,plain,
    ! [A: $i] :
      ( ( ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( v2_pre_topc @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(36,axiom,
    ! [A: $i] :
      ( ( v3_membered @ A )
     => ( v2_membered @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_membered) ).

thf(206,plain,
    ! [A: $i] :
      ( ( v3_membered @ A )
     => ( v2_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(48,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(248,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)],[48]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( v3_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( v1_xcmplx_0 @ B )
            & ( v1_xreal_0 @ B )
            & ( v1_rat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_membered) ).

thf(117,plain,
    ! [A: $i] :
      ( ( v3_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( v1_xcmplx_0 @ B )
            & ( v1_xreal_0 @ B )
            & ( v1_rat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(34,axiom,
    ! [A: $i] :
      ( ( v1_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( v1_membered @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).

thf(201,plain,
    ! [A: $i] :
      ( ( v1_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( v1_membered @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(78,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ~ ( v2_t_0topsp @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ~ ( v3_struct_0 @ B )
              & ( v2_t_0topsp @ B ) )
           => ( ~ ( v3_struct_0 @ B )
              & ( v2_tex_2 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_tsp_1) ).

thf(366,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ~ ( v2_t_0topsp @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ~ ( v3_struct_0 @ B )
              & ( v2_t_0topsp @ B ) )
           => ( ~ ( v3_struct_0 @ B )
              & ( v2_tex_2 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(5,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(102,plain,
    ! [A: $i] : ( r1_tarski @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(25,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_membered @ A )
      & ( v2_membered @ A )
      & ( v3_membered @ A )
      & ( v4_membered @ A )
      & ( v5_membered @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_membered) ).

thf(160,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_membered @ A )
      & ( v2_membered @ A )
      & ( v3_membered @ A )
      & ( v4_membered @ A )
      & ( v5_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(62,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(297,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)],[62]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ( v1_membered @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_membered) ).

thf(137,plain,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ( v1_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(23,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(156,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)],[23]) ).

thf(76,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ( v3_tdlat_3 @ A )
          & ( v2_t_0topsp @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ( v1_tdlat_3 @ A )
          & ( v3_tdlat_3 @ A )
          & ( v4_tdlat_3 @ A )
          & ( v5_tdlat_3 @ A )
          & ( v2_t_0topsp @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc8_tsp_1) ).

thf(356,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ( v3_tdlat_3 @ A )
          & ( v2_t_0topsp @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ( v1_tdlat_3 @ A )
          & ( v3_tdlat_3 @ A )
          & ( v4_tdlat_3 @ A )
          & ( v5_tdlat_3 @ A )
          & ( v2_t_0topsp @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ( v3_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B )
            & ( v3_membered @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc18_membered) ).

thf(141,plain,
    ! [A: $i] :
      ( ( v3_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B )
            & ( v3_membered @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( v5_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( v1_xcmplx_0 @ B )
            & ( v4_ordinal2 @ B )
            & ( v1_xreal_0 @ B )
            & ( v1_int_1 @ B )
            & ( v1_rat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_membered) ).

thf(109,plain,
    ! [A: $i] :
      ( ( v5_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( v1_xcmplx_0 @ B )
            & ( v4_ordinal2 @ B )
            & ( v1_xreal_0 @ B )
            & ( v1_int_1 @ B )
            & ( v1_rat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(50,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ~ ( v2_t_0topsp @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ~ ( v3_realset2 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_tsp_1) ).

thf(256,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ~ ( v2_t_0topsp @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ~ ( v3_realset2 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(11,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(124,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)],[11]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( v2_t_0topsp @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ~ ( v3_struct_0 @ B )
           => ( ~ ( v3_struct_0 @ B )
              & ( v2_t_0topsp @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_tsp_1) ).

thf(225,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( v2_t_0topsp @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ~ ( v3_struct_0 @ B )
           => ( ~ ( v3_struct_0 @ B )
              & ( v2_t_0topsp @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc17_membered) ).

thf(128,plain,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(74,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ~ ( v1_tex_3 @ B @ A )
           => ( ( v2_pre_topc @ B )
              & ~ ( v2_tsp_2 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_tsp_2) ).

thf(343,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ~ ( v1_tex_3 @ B @ A )
           => ( ( v2_pre_topc @ B )
              & ~ ( v2_tsp_2 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(44,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(237,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)],[44]) ).

thf(29,axiom,
    ! [A: $i] :
      ( ( v5_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B )
            & ( v3_membered @ B )
            & ( v4_membered @ B )
            & ( v5_membered @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc20_membered) ).

thf(180,plain,
    ! [A: $i] :
      ( ( v5_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B )
            & ( v3_membered @ B )
            & ( v4_membered @ B )
            & ( v5_membered @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(21,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(149,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)],[21]) ).

thf(60,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(291,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)],[60]) ).

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

thf(40,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(219,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)],[40]) ).

thf(47,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ~ ( v3_struct_0 @ B )
              & ~ ( v2_t_0topsp @ B ) )
           => ( ~ ( v3_struct_0 @ B )
              & ~ ( v2_tsp_2 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_tsp_2) ).

thf(245,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ~ ( v3_struct_0 @ B )
              & ~ ( v2_t_0topsp @ B ) )
           => ( ~ ( v3_struct_0 @ B )
              & ~ ( v2_tsp_2 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(37,axiom,
    ! [A: $i] :
      ( ( v5_membered @ A )
     => ( v4_membered @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_membered) ).

thf(208,plain,
    ! [A: $i] :
      ( ( v5_membered @ A )
     => ( v4_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(98,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(64,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ~ ( v3_realset2 @ A )
          & ( v2_pre_topc @ A )
          & ( v2_t_0topsp @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ~ ( v3_realset2 @ A )
          & ( v2_pre_topc @ A )
          & ~ ( v2_tdlat_3 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_tsp_1) ).

thf(303,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ~ ( v3_realset2 @ A )
          & ( v2_pre_topc @ A )
          & ( v2_t_0topsp @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ~ ( v3_realset2 @ A )
          & ( v2_pre_topc @ A )
          & ~ ( v2_tdlat_3 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(58,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(278,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)],[58]) ).

thf(84,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( v2_tsp_2 @ B @ A )
           => ( ( v2_pre_topc @ B )
              & ( v1_tex_3 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_tsp_2) ).

thf(394,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( v2_tsp_2 @ B @ A )
           => ( ( v2_pre_topc @ B )
              & ( v1_tex_3 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(54,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( l1_pre_topc @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_pre_topc) ).

thf(267,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( l1_pre_topc @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

thf(167,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(32,axiom,
    ! [A: $i] :
      ( ( v4_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( v1_xcmplx_0 @ B )
            & ( v1_xreal_0 @ B )
            & ( v1_int_1 @ B )
            & ( v1_rat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_membered) ).

thf(194,plain,
    ! [A: $i] :
      ( ( v4_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( v1_xcmplx_0 @ B )
            & ( v1_xreal_0 @ B )
            & ( v1_int_1 @ B )
            & ( v1_rat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( v4_membered @ A )
     => ( v3_membered @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_membered) ).

thf(145,plain,
    ! [A: $i] :
      ( ( v4_membered @ A )
     => ( v3_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(88,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ! [B: $i] :
          ( ( m2_tsp_1 @ B @ A )
         => ( l1_pre_topc @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_tsp_1) ).

thf(414,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ! [B: $i] :
          ( ( m2_tsp_1 @ B @ A )
         => ( l1_pre_topc @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(70,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(327,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)],[70]) ).

thf(86,axiom,
    ? [A: $i] : ( l1_pre_topc @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).

thf(409,plain,
    ? [A: $i] : ( l1_pre_topc @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(33,axiom,
    ! [A: $i] :
      ( ( v1_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( v1_xcmplx_0 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_membered) ).

thf(199,plain,
    ! [A: $i] :
      ( ( v1_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( v1_xcmplx_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(72,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ? [B: $i] : ( m1_pre_topc @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_pre_topc) ).

thf(338,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ? [B: $i] : ( m1_pre_topc @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(22,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

thf(154,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(82,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ( v2_tex_2 @ B @ A )
              & ( v2_tsp_2 @ B @ A ) )
           => ( ( v2_pre_topc @ B )
              & ~ ( v1_tsep_1 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_tsp_2) ).

thf(386,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ( v2_tex_2 @ B @ A )
              & ( v2_tsp_2 @ B @ A ) )
           => ( ( v2_pre_topc @ B )
              & ~ ( v1_tsep_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(35,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(203,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)],[35]) ).

thf(6,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(104,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)],[6]) ).

thf(24,axiom,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(158,plain,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( v1_xcmplx_0 @ B )
            & ( v1_xreal_0 @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_membered) ).

thf(186,plain,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( v1_xcmplx_0 @ B )
            & ( v1_xreal_0 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(17,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(139,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(56,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ( v1_tdlat_3 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ( v2_t_0topsp @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_tsp_1) ).

thf(272,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ( v1_tdlat_3 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ( v2_t_0topsp @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(75,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ( v2_tdlat_3 @ A )
          & ( v2_t_0topsp @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v3_realset2 @ A )
          & ( v2_pre_topc @ A )
          & ( v1_tdlat_3 @ A )
          & ( v2_tdlat_3 @ A )
          & ( v3_tdlat_3 @ A )
          & ( v4_tdlat_3 @ A )
          & ( v5_tdlat_3 @ A )
          & ( v2_t_0topsp @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_tsp_1) ).

thf(346,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ( v2_tdlat_3 @ A )
          & ( v2_t_0topsp @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v3_realset2 @ A )
          & ( v2_pre_topc @ A )
          & ( v1_tdlat_3 @ A )
          & ( v2_tdlat_3 @ A )
          & ( v3_tdlat_3 @ A )
          & ( v4_tdlat_3 @ A )
          & ( v5_tdlat_3 @ A )
          & ( v2_t_0topsp @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(63,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 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc) ).

thf(300,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 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(67,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ~ ( v1_tdlat_3 @ A )
          & ( v3_tdlat_3 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ~ ( v3_realset2 @ A )
          & ( v2_pre_topc @ A )
          & ~ ( v1_tdlat_3 @ A )
          & ~ ( v2_t_0topsp @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc9_tsp_1) ).

thf(315,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ~ ( v1_tdlat_3 @ A )
          & ( v3_tdlat_3 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ~ ( v3_realset2 @ A )
          & ( v2_pre_topc @ A )
          & ~ ( v1_tdlat_3 @ A )
          & ~ ( v2_t_0topsp @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ~ ( v3_struct_0 @ B )
              & ( v2_tsp_2 @ B @ A ) )
           => ( ~ ( v3_struct_0 @ B )
              & ( v2_t_0topsp @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_tsp_2) ).

thf(262,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ~ ( v3_struct_0 @ B )
              & ( v2_tsp_2 @ B @ A ) )
           => ( ~ ( v3_struct_0 @ B )
              & ( v2_t_0topsp @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(38,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( ( v1_membered @ A )
        & ( v2_membered @ A )
        & ( v3_membered @ A )
        & ( v4_membered @ A )
        & ( v5_membered @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc15_membered) ).

thf(210,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( ( v1_membered @ A )
        & ( v2_membered @ A )
        & ( v3_membered @ A )
        & ( v4_membered @ A )
        & ( v5_membered @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(45,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(239,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)],[45]) ).

thf(46,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ( v1_tsep_1 @ B @ A )
              & ( v2_tsp_2 @ B @ A ) )
           => ( ( v2_pre_topc @ B )
              & ~ ( v2_tex_2 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_tsp_2) ).

thf(242,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ( v1_tsep_1 @ B @ A )
              & ( v2_tsp_2 @ B @ A ) )
           => ( ( v2_pre_topc @ B )
              & ~ ( v2_tex_2 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(61,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v3_realset2 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_t_0topsp @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_tsp_1) ).

thf(294,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v3_realset2 @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v2_t_0topsp @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(12,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(126,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)],[12]) ).

thf(71,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v3_struct_0 @ B )
            & ( v2_tsp_2 @ B @ A )
            & ( m2_tsp_1 @ B @ A ) )
         => ? [C: $i] :
              ( ( v1_funct_1 @ C )
              & ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
              & ( v5_pre_topc @ C @ A @ B )
              & ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
              & ( v3_borsuk_1 @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_tsp_2) ).

thf(332,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v3_struct_0 @ B )
            & ( v2_tsp_2 @ B @ A )
            & ( m2_tsp_1 @ B @ A ) )
         => ? [C: $i] :
              ( ( v1_funct_1 @ C )
              & ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
              & ( v5_pre_topc @ C @ A @ B )
              & ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
              & ( v3_borsuk_1 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(14,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(131,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)],[14]) ).

thf(79,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ~ ( v1_tdlat_3 @ A )
          & ( v2_t_0topsp @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ~ ( v3_realset2 @ A )
          & ( v2_pre_topc @ A )
          & ~ ( v1_tdlat_3 @ A )
          & ~ ( v2_tdlat_3 @ A )
          & ~ ( v3_tdlat_3 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_tsp_1) ).

thf(369,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ~ ( v1_tdlat_3 @ A )
          & ( v2_t_0topsp @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ~ ( v3_realset2 @ A )
          & ( v2_pre_topc @ A )
          & ~ ( v1_tdlat_3 @ A )
          & ~ ( v2_tdlat_3 @ A )
          & ~ ( v3_tdlat_3 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v3_struct_0 @ B )
            & ( v2_tsp_2 @ B @ A )
            & ( m2_tsp_1 @ B @ A ) )
         => ( r1_borsuk_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_tsp_2) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ( l1_pre_topc @ A ) )
       => ! [B: $i] :
            ( ( ~ ( v3_struct_0 @ B )
              & ( v2_tsp_2 @ B @ A )
              & ( m2_tsp_1 @ B @ A ) )
           => ( r1_borsuk_1 @ A @ B ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(90,plain,
    ~ ! [A: $i] :
        ( ( ~ ( v3_struct_0 @ A )
          & ( v2_pre_topc @ A )
          & ( l1_pre_topc @ A ) )
       => ! [B: $i] :
            ( ( ~ ( v3_struct_0 @ B )
              & ( v2_tsp_2 @ B @ A )
              & ( m2_tsp_1 @ B @ A ) )
           => ( r1_borsuk_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(41,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ( v2_tex_2 @ B @ A )
              & ( v1_borsuk_1 @ B @ A ) )
           => ( ( v2_pre_topc @ B )
              & ~ ( v2_tsp_2 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc9_tsp_2) ).

thf(222,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ! [B: $i] :
          ( ( m1_pre_topc @ B @ A )
         => ( ( ( v2_tex_2 @ B @ A )
              & ( v1_borsuk_1 @ B @ A ) )
           => ( ( v2_pre_topc @ B )
              & ~ ( v2_tsp_2 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( l1_struct_0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).

thf(364,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( l1_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(4,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(100,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(421,plain,
    $false,
    inference(e,[status(thm)],[340,389,252,173,313,170,115,276,308,379,269,189,416,325,228,289,216,321,376,121,147,397,133,411,265,206,248,117,201,366,102,160,297,137,156,356,141,109,256,124,225,128,343,237,180,149,291,259,219,245,208,98,303,278,394,267,167,194,145,414,327,409,199,338,154,386,203,104,158,186,139,272,346,300,315,262,210,239,242,294,126,332,131,369,90,222,364,100]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : TOP034+1 : TPTP v8.2.0. Released v3.4.0.
% 0.05/0.12  % Command  : run_Leo-III %s %d
% 0.13/0.33  % Computer : n002.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Sat May 18 11:09:09 EDT 2024
% 0.13/0.33  % CPUTime  : 
% 1.00/0.96  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.53/1.20  % [INFO] 	 Parsing done (244ms). 
% 1.53/1.21  % [INFO] 	 Running in sequential loop mode. 
% 2.23/1.57  % [INFO] 	 eprover registered as external prover. 
% 2.23/1.57  % [INFO] 	 cvc4 registered as external prover. 
% 2.23/1.58  % [INFO] 	 Scanning for conjecture ... 
% 2.44/1.70  % [INFO] 	 Found a conjecture (or negated_conjecture) and 94 axioms. Running axiom selection ... 
% 2.64/1.81  % [INFO] 	 Axiom selection finished. Selected 87 axioms (removed 7 axioms). 
% 3.12/1.95  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 3.12/1.96  % [INFO] 	 Type checking passed. 
% 3.12/1.97  % [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 ... 
% 7.50/3.34  % External prover 'e' found a proof!
% 7.50/3.34  % [INFO] 	 Killing All external provers ... 
% 7.50/3.34  % Time passed: 2859ms (effective reasoning time: 2117ms)
% 7.50/3.34  % 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)>
% 7.50/3.34  % Axioms used in derivation (87): cc1_tsp_1, rc6_pre_topc, rc1_tops_1, cc6_tops_1, cc17_membered, rc7_pre_topc, cc4_tsp_2, redefinition_m2_relset_1, cc1_tops_1, cc12_membered, cc10_tsp_2, cc8_tsp_1, cc5_tsp_2, redefinition_m2_tsp_1, cc2_tsp_1, cc10_membered, rc3_tops_1, t1_subset, cc6_tsp_2, fc4_subset_1, rc1_membered, dt_m2_tsp_1, cc5_tops_1, cc3_tops_1, cc3_tsp_2, dt_m2_relset_1, cc2_tsp_2, dt_l1_pre_topc, t6_boole, rc2_subset_1, rc5_tops_1, t5_subset, cc19_membered, existence_m1_relset_1, cc7_tsp_1, fc6_membered, rc4_tops_1, cc11_membered, cc6_tsp_1, t4_subset, cc11_tsp_1, cc20_membered, t7_boole, rc3_struct_0, fc1_subset_1, rc1_subset_1, cc4_membered, dt_m1_pre_topc, cc18_membered, existence_m2_tsp_1, existence_m1_pre_topc, t22_tsp_2, t3_subset, cc1_relset_1, cc13_membered, existence_m1_subset_1, cc4_tsp_1, cc15_membered, cc2_tops_1, existence_m2_relset_1, cc7_tsp_2, cc9_tsp_1, fc1_struct_0, existence_l1_pre_topc, reflexivity_r1_tarski, rc2_tops_1, t8_boole, cc13_tsp_1, t2_subset, cc1_membered, cc10_tsp_1, rc5_struct_0, cc4_tops_1, cc2_membered, cc3_membered, cc8_tsp_2, cc5_tsp_1, cc14_membered, existence_l1_struct_0, d20_borsuk_1, cc9_tsp_2, cc16_membered, cc3_tsp_1, cc12_tsp_1, cc1_tsp_2, antisymmetry_r2_hidden, cc1_pre_topc
% 7.50/3.34  % No. of inferences in proof: 178
% 7.50/3.34  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2859 ms resp. 2117 ms w/o parsing
% 7.50/3.44  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.00/3.45  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------