TSTP Solution File: LAT292+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LAT292+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.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 : Fri May 19 11:27:24 EDT 2023

% Result   : Theorem 5.62s 2.25s
% Output   : Refutation 5.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  153
% Syntax   : Number of formulae    :  248 (  19 unt;  60 typ;   0 def)
%            Number of atoms       :  911 (  33 equ;   0 cnn)
%            Maximal formula atoms :   17 (   4 avg)
%            Number of connectives : 2383 ( 157   ~;   2   |; 538   &;1503   @)
%                                         (   4 <=>; 179  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   77 (  77   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   62 (  60 usr;   2 con; 0-3 aty)
%            Number of variables   :  312 (   0   ^; 252   !;  60   ?; 312   :)

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

thf(v10_lattices_type,type,
    v10_lattices: $i > $o ).

thf(v17_lattices_type,type,
    v17_lattices: $i > $o ).

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

thf(l3_lattices_type,type,
    l3_lattices: $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(r1_filter_1_type,type,
    r1_filter_1: $i > $i > $o ).

thf(k6_lopclset_type,type,
    k6_lopclset: $i > $i ).

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

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

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

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

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

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

thf(v4_finsub_1_type,type,
    v4_finsub_1: $i > $o ).

thf(v1_finsub_1_type,type,
    v1_finsub_1: $i > $o ).

thf(v3_finsub_1_type,type,
    v3_finsub_1: $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(k2_zfmisc_1_type,type,
    k2_zfmisc_1: $i > $i > $i ).

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

thf(g3_lattices_type,type,
    g3_lattices: $i > $i > $i > $i ).

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

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

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

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

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

thf(l2_lattices_type,type,
    l2_lattices: $i > $o ).

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

thf(l1_lattices_type,type,
    l1_lattices: $i > $o ).

thf(u1_lattices_type,type,
    u1_lattices: $i > $i ).

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

thf(v1_partfun1_type,type,
    v1_partfun1: $i > $i > $i > $o ).

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

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

thf(u2_lattices_type,type,
    u2_lattices: $i > $i ).

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

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

thf(v13_lattices_type,type,
    v13_lattices: $i > $o ).

thf(v14_lattices_type,type,
    v14_lattices: $i > $o ).

thf(v15_lattices_type,type,
    v15_lattices: $i > $o ).

thf(v3_lattices_type,type,
    v3_lattices: $i > $o ).

thf(v4_lattices_type,type,
    v4_lattices: $i > $o ).

thf(v5_lattices_type,type,
    v5_lattices: $i > $o ).

thf(v6_lattices_type,type,
    v6_lattices: $i > $o ).

thf(v7_lattices_type,type,
    v7_lattices: $i > $o ).

thf(v8_lattices_type,type,
    v8_lattices: $i > $o ).

thf(v9_lattices_type,type,
    v9_lattices: $i > $o ).

thf(k1_lopclset_type,type,
    k1_lopclset: $i > $i ).

thf(k4_lopclset_type,type,
    k4_lopclset: $i > $i ).

thf(k12_lopclset_type,type,
    k12_lopclset: $i > $i ).

thf(k11_lopclset_type,type,
    k11_lopclset: $i > $i ).

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

thf(a_1_0_lopclset_type,type,
    a_1_0_lopclset: $i > $i ).

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

thf(v11_lattices_type,type,
    v11_lattices: $i > $o ).

thf(v12_lattices_type,type,
    v12_lattices: $i > $o ).

thf(v16_lattices_type,type,
    v16_lattices: $i > $o ).

thf(k5_lopclset_type,type,
    k5_lopclset: $i > $i ).

thf(16,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ B )
     => ( ( v1_xboole_0 @ B )
        | ( r2_hidden @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

thf(142,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)],[16]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( v1_finset_1 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( v1_finset_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).

thf(152,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)],[20]) ).

thf(77,axiom,
    ? [A: $i] :
      ( ( l1_pre_topc @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v1_pre_topc @ A )
      & ( v2_pre_topc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_pre_topc) ).

thf(403,plain,
    ? [A: $i] :
      ( ( l1_pre_topc @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v1_pre_topc @ A )
      & ( v2_pre_topc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(68,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A )
        & ~ ( v3_struct_0 @ B )
        & ( v10_lattices @ B )
        & ( l3_lattices @ B ) )
     => ( r1_filter_1 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_filter_1) ).

thf(339,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A )
        & ~ ( v3_struct_0 @ B )
        & ( v10_lattices @ B )
        & ( l3_lattices @ B ) )
     => ( r1_filter_1 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(91,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A )
        & ~ ( v3_struct_0 @ B )
        & ( v10_lattices @ B )
        & ( l3_lattices @ B ) )
     => ( ( r1_filter_1 @ A @ B )
       => ( r1_filter_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_filter_1) ).

thf(457,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A )
        & ~ ( v3_struct_0 @ B )
        & ( v10_lattices @ B )
        & ( l3_lattices @ B ) )
     => ( ( r1_filter_1 @ A @ B )
       => ( r1_filter_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(46,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_finset_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).

thf(244,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_finset_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(72,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A )
      & ( v15_lattices @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc11_lattices) ).

thf(365,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A )
      & ( v15_lattices @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ( v1_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( v1_membered @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).

thf(234,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)],[42]) ).

thf(78,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A )
      & ( v15_lattices @ A )
      & ( v16_lattices @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc12_lattices) ).

thf(408,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A )
      & ( v15_lattices @ A )
      & ( v16_lattices @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( ( v1_finsub_1 @ A )
        & ( v3_finsub_1 @ A ) )
     => ( v4_finsub_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finsub_1) ).

thf(115,plain,
    ! [A: $i] :
      ( ( ( v1_finsub_1 @ A )
        & ( v3_finsub_1 @ A ) )
     => ( v4_finsub_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(54,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_pre_topc @ A ) )
     => ( m1_subset_1 @ ( k1_lopclset @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lopclset) ).

thf(276,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_pre_topc @ A ) )
     => ( m1_subset_1 @ ( k1_lopclset @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(88,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( v17_lattices @ A )
        & ~ ( v3_realset2 @ A )
        & ( l3_lattices @ A ) )
     => ( r1_filter_1 @ A @ ( k12_lopclset @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_lopclset) ).

thf(449,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( v17_lattices @ A )
        & ~ ( v3_realset2 @ A )
        & ( l3_lattices @ A ) )
     => ( r1_filter_1 @ A @ ( k12_lopclset @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(73,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v17_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v11_lattices @ A )
          & ( v13_lattices @ A )
          & ( v14_lattices @ A )
          & ( v15_lattices @ A )
          & ( v16_lattices @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_lattices) ).

thf(379,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v17_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v11_lattices @ A )
          & ( v13_lattices @ A )
          & ( v14_lattices @ A )
          & ( v15_lattices @ A )
          & ( v16_lattices @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(34,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/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).

thf(202,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)],[34]) ).

thf(25,axiom,
    ! [A: $i] :
      ( ( l2_lattices @ A )
     => ( l1_struct_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).

thf(174,plain,
    ! [A: $i] :
      ( ( l2_lattices @ A )
     => ( l1_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(58,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ~ ( v3_struct_0 @ ( g3_lattices @ A @ B @ C ) )
        & ( v3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattices) ).

thf(288,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ~ ( v3_struct_0 @ ( g3_lattices @ A @ B @ C ) )
        & ( v3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(84,axiom,
    ? [A: $i] :
      ( ( l1_pre_topc @ A )
      & ( v1_pre_topc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_pre_topc) ).

thf(436,plain,
    ? [A: $i] :
      ( ( l1_pre_topc @ A )
      & ( v1_pre_topc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(50,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v13_lattices @ A )
          & ( v14_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v15_lattices @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_lattices) ).

thf(257,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v13_lattices @ A )
          & ( v14_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v15_lattices @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(6,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(110,plain,
    ! [A: $i] : ( r1_tarski @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(70,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v11_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A )
      & ( v15_lattices @ A )
      & ( v16_lattices @ A )
      & ( v17_lattices @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc13_lattices) ).

thf(344,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v11_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A )
      & ( v15_lattices @ A )
      & ( v16_lattices @ A )
      & ( v17_lattices @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(31,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

thf(196,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(38,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

thf(216,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(86,axiom,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( l1_struct_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).

thf(443,plain,
    ! [A: $i] :
      ( ( l1_pre_topc @ A )
     => ( l1_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(66,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/sandbox/benchmark/theBenchmark.p',rc6_pre_topc) ).

thf(321,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)],[66]) ).

thf(5,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/sandbox/benchmark/theBenchmark.p',cc18_membered) ).

thf(106,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)],[5]) ).

thf(40,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_finset_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).

thf(221,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_finset_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(53,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc9_lattices) ).

thf(265,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(65,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ B )
        & ( l1_pre_topc @ B ) )
     => ( ( r2_hidden @ A @ ( a_1_0_lopclset @ B ) )
      <=> ? [C: $i] :
            ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
            & ( A = C )
            & ( v3_pre_topc @ C @ B )
            & ( v4_pre_topc @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_lopclset) ).

thf(312,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ B )
        & ( l1_pre_topc @ B ) )
     => ( ( ( r2_hidden @ A @ ( a_1_0_lopclset @ B ) )
         => ? [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
              & ( A = C )
              & ( v3_pre_topc @ C @ B )
              & ( v4_pre_topc @ C @ B ) ) )
        & ( ? [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
              & ( A = C )
              & ( v3_pre_topc @ C @ B )
              & ( v4_pre_topc @ C @ B ) )
         => ( r2_hidden @ A @ ( a_1_0_lopclset @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(35,axiom,
    ? [A: $i] : ( l1_lattices @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).

thf(206,plain,
    ? [A: $i] : ( l1_lattices @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(9,axiom,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(117,plain,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(85,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_lattices) ).

thf(439,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( v3_membered @ A )
     => ( v2_membered @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_membered) ).

thf(102,plain,
    ! [A: $i] :
      ( ( v3_membered @ A )
     => ( v2_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(62,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_pre_topc @ A ) )
     => ( ( k1_lopclset @ A )
        = ( a_1_0_lopclset @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lopclset) ).

thf(302,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_pre_topc @ A ) )
     => ( ( k1_lopclset @ A )
        = ( a_1_0_lopclset @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(51,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( l1_struct_0 @ A ) )
     => ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).

thf(260,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)],[51]) ).

thf(81,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( l1_lattices @ A )
        & ( l2_lattices @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).

thf(429,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( l1_lattices @ A )
        & ( l2_lattices @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(14,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/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).

thf(137,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)],[14]) ).

thf(93,axiom,
    ? [A: $i] : ( l3_lattices @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).

thf(467,plain,
    ? [A: $i] : ( l3_lattices @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(71,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ( ( v1_funct_1 @ ( k5_lopclset @ A ) )
        & ( v1_funct_2 @ ( k5_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) )
        & ( m2_relset_1 @ ( k5_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lopclset) ).

thf(361,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ( ( v1_funct_1 @ ( k5_lopclset @ A ) )
        & ( v1_funct_2 @ ( k5_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) )
        & ( m2_relset_1 @ ( k5_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(67,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v11_lattices @ A )
      & ( v12_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc10_lattices) ).

thf(324,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v11_lattices @ A )
      & ( v12_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(57,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( v17_lattices @ A )
        & ~ ( v3_realset2 @ A )
        & ( l3_lattices @ A ) )
     => ( ( k12_lopclset @ A )
        = ( k6_lopclset @ ( k11_lopclset @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lopclset) ).

thf(285,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( v17_lattices @ A )
        & ~ ( v3_realset2 @ A )
        & ( l3_lattices @ A ) )
     => ( ( k12_lopclset @ A )
        = ( k6_lopclset @ ( k11_lopclset @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(41,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( r2_hidden @ C @ A )
        <=> ( r2_hidden @ C @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).

thf(224,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)],[41]) ).

thf(61,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/sandbox/benchmark/theBenchmark.p',rc7_pre_topc) ).

thf(298,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)],[61]) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).

thf(148,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(26,axiom,
    ? [A: $i] : ( l1_struct_0 @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).

thf(176,plain,
    ? [A: $i] : ( l1_struct_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(79,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ( ( k6_lopclset @ A )
        = ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lopclset) ).

thf(423,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ( ( k6_lopclset @ A )
        = ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(30,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/sandbox/benchmark/theBenchmark.p',free_g1_pre_topc) ).

thf(191,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)],[30]) ).

thf(59,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( v17_lattices @ A )
        & ~ ( v3_realset2 @ A )
        & ( l3_lattices @ A ) )
     => ( ~ ( v3_struct_0 @ ( k12_lopclset @ A ) )
        & ( v10_lattices @ ( k12_lopclset @ A ) )
        & ( l3_lattices @ ( k12_lopclset @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_lopclset) ).

thf(291,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( v17_lattices @ A )
        & ~ ( v3_realset2 @ A )
        & ( l3_lattices @ A ) )
     => ( ~ ( v3_struct_0 @ ( k12_lopclset @ A ) )
        & ( v10_lattices @ ( k12_lopclset @ A ) )
        & ( l3_lattices @ ( k12_lopclset @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(87,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v15_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v13_lattices @ A )
          & ( v14_lattices @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_lattices) ).

thf(445,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v15_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v13_lattices @ A )
          & ( v14_lattices @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(17,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).

thf(144,plain,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(43,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( ( ( v1_funct_1 @ C )
          & ( v1_partfun1 @ C @ A @ B ) )
       => ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_2) ).

thf(236,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( ( ( v1_funct_1 @ C )
          & ( v1_partfun1 @ C @ A @ B ) )
       => ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(29,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( m1_relset_1 @ C @ A @ B )
         => ( ( ( v1_funct_1 @ C )
              & ( v1_funct_2 @ C @ A @ B ) )
           => ( ( v1_funct_1 @ C )
              & ( v1_partfun1 @ C @ A @ B )
              & ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_funct_2) ).

thf(187,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( m1_relset_1 @ C @ A @ B )
         => ( ( ( v1_funct_1 @ C )
              & ( v1_funct_2 @ C @ A @ B ) )
           => ( ( v1_funct_1 @ C )
              & ( v1_partfun1 @ C @ A @ B )
              & ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(24,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).

thf(172,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(39,axiom,
    ! [A: $i] :
      ( ( l1_lattices @ A )
     => ( l1_struct_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).

thf(219,plain,
    ! [A: $i] :
      ( ( l1_lattices @ A )
     => ( l1_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(89,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v4_lattices @ A )
          & ( v5_lattices @ A )
          & ( v6_lattices @ A )
          & ( v7_lattices @ A )
          & ( v8_lattices @ A )
          & ( v9_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattices) ).

thf(451,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v4_lattices @ A )
          & ( v5_lattices @ A )
          & ( v6_lattices @ A )
          & ( v7_lattices @ A )
          & ( v8_lattices @ A )
          & ( v9_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(83,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ~ ( v1_xboole_0 @ ( k1_lopclset @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lopclset) ).

thf(434,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ~ ( v1_xboole_0 @ ( k1_lopclset @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(36,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ! [C: $i] :
          ( ( m1_relset_1 @ C @ A @ B )
         => ( ( ( v1_funct_1 @ C )
              & ( v1_funct_2 @ C @ A @ B ) )
           => ( ( v1_funct_1 @ C )
              & ~ ( v1_xboole_0 @ C )
              & ( v1_partfun1 @ C @ A @ B )
              & ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_funct_2) ).

thf(208,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ! [C: $i] :
          ( ( m1_relset_1 @ C @ A @ B )
         => ( ( ( v1_funct_1 @ C )
              & ( v1_funct_2 @ C @ A @ B ) )
           => ( ( v1_funct_1 @ C )
              & ~ ( v1_xboole_0 @ C )
              & ( v1_partfun1 @ C @ A @ B )
              & ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(37,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/sandbox/benchmark/theBenchmark.p',t5_subset) ).

thf(213,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)],[37]) ).

thf(32,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/sandbox/benchmark/theBenchmark.p',t4_subset) ).

thf(198,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)],[32]) ).

thf(55,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ( ( v1_funct_1 @ ( k4_lopclset @ A ) )
        & ( v1_funct_2 @ ( k4_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) )
        & ( m2_relset_1 @ ( k4_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lopclset) ).

thf(278,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ( ( v1_funct_1 @ ( k4_lopclset @ A ) )
        & ( v1_funct_2 @ ( k4_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) )
        & ( m2_relset_1 @ ( k4_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(13,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/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).

thf(135,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)],[13]) ).

thf(45,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

thf(241,plain,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(23,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
      & ( v1_relat_1 @ C )
      & ( v1_funct_1 @ C )
      & ( v1_funct_2 @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_2) ).

thf(167,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
      & ( v1_relat_1 @ C )
      & ( v1_funct_1 @ C )
      & ( v1_funct_2 @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(80,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ( v3_lattices @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lattices) ).

thf(426,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ( v3_lattices @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( v4_finsub_1 @ A )
     => ( ( v1_finsub_1 @ A )
        & ( v3_finsub_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finsub_1) ).

thf(112,plain,
    ! [A: $i] :
      ( ( v4_finsub_1 @ A )
     => ( ( v1_finsub_1 @ A )
        & ( v3_finsub_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(69,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/sandbox/benchmark/theBenchmark.p',dt_u1_pre_topc) ).

thf(342,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)],[69]) ).

thf(60,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ( v3_lattices @ ( g3_lattices @ A @ B @ C ) )
        & ( l3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g3_lattices) ).

thf(295,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ( v3_lattices @ ( g3_lattices @ A @ B @ C ) )
        & ( l3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(56,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/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).

thf(282,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)],[56]) ).

thf(19,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(150,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( v17_lattices @ A )
        & ~ ( v3_realset2 @ A )
        & ( l3_lattices @ A ) )
     => ? [B: $i] :
          ( ~ ( v3_struct_0 @ B )
          & ( v2_pre_topc @ B )
          & ( l1_pre_topc @ B )
          & ( r1_filter_1 @ A @ ( k6_lopclset @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_lopclset) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A )
          & ( v17_lattices @ A )
          & ~ ( v3_realset2 @ A )
          & ( l3_lattices @ A ) )
       => ? [B: $i] :
            ( ~ ( v3_struct_0 @ B )
            & ( v2_pre_topc @ B )
            & ( l1_pre_topc @ B )
            & ( r1_filter_1 @ A @ ( k6_lopclset @ B ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(95,plain,
    ~ ! [A: $i] :
        ( ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A )
          & ( v17_lattices @ A )
          & ~ ( v3_realset2 @ A )
          & ( l3_lattices @ A ) )
       => ? [B: $i] :
            ( ~ ( v3_struct_0 @ B )
            & ( v2_pre_topc @ B )
            & ( l1_pre_topc @ B )
            & ( r1_filter_1 @ A @ ( k6_lopclset @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
      & ( v1_finsub_1 @ ( k1_zfmisc_1 @ A ) )
      & ( v3_finsub_1 @ ( k1_zfmisc_1 @ A ) )
      & ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finsub_1) ).

thf(154,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
      & ( v1_finsub_1 @ ( k1_zfmisc_1 @ A ) )
      & ( v3_finsub_1 @ ( k1_zfmisc_1 @ A ) )
      & ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(74,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( v17_lattices @ A )
        & ~ ( v3_realset2 @ A )
        & ( l3_lattices @ A ) )
     => ( ~ ( v3_struct_0 @ ( k11_lopclset @ A ) )
        & ( v1_pre_topc @ ( k11_lopclset @ A ) )
        & ( v2_pre_topc @ ( k11_lopclset @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lopclset) ).

thf(386,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( v17_lattices @ A )
        & ~ ( v3_realset2 @ A )
        & ( l3_lattices @ A ) )
     => ( ~ ( v3_struct_0 @ ( k11_lopclset @ A ) )
        & ( v1_pre_topc @ ( k11_lopclset @ A ) )
        & ( v2_pre_topc @ ( k11_lopclset @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(48,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ( ~ ( v3_struct_0 @ ( k6_lopclset @ A ) )
        & ( v10_lattices @ ( k6_lopclset @ A ) )
        & ( l3_lattices @ ( k6_lopclset @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_lopclset) ).

thf(250,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v2_pre_topc @ A )
        & ( l1_pre_topc @ A ) )
     => ( ~ ( v3_struct_0 @ ( k6_lopclset @ A ) )
        & ( v10_lattices @ ( k6_lopclset @ A ) )
        & ( l3_lattices @ ( k6_lopclset @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ( v1_membered @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_membered) ).

thf(104,plain,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ( v1_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(75,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A )
          & ( v11_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v4_lattices @ A )
          & ( v5_lattices @ A )
          & ( v6_lattices @ A )
          & ( v7_lattices @ A )
          & ( v8_lattices @ A )
          & ( v9_lattices @ A )
          & ( v10_lattices @ A )
          & ( v12_lattices @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_lattices) ).

thf(390,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A )
          & ( v11_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v4_lattices @ A )
          & ( v5_lattices @ A )
          & ( v6_lattices @ A )
          & ( v7_lattices @ A )
          & ( v8_lattices @ A )
          & ( v9_lattices @ A )
          & ( v10_lattices @ A )
          & ( v12_lattices @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(15,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/sandbox/benchmark/theBenchmark.p',cc17_membered) ).

thf(139,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)],[15]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [D: $i,E: $i,F: $i] :
          ( ( ( g3_lattices @ A @ B @ C )
            = ( g3_lattices @ D @ E @ F ) )
         => ( ( A = D )
            & ( B = E )
            & ( C = F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).

thf(119,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [D: $i,E: $i,F: $i] :
          ( ( ( g3_lattices @ A @ B @ C )
            = ( g3_lattices @ D @ E @ F ) )
         => ( ( A = D )
            & ( B = E )
            & ( C = F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(47,axiom,
    ! [A: $i] :
      ( ( l2_lattices @ A )
     => ( ( v1_funct_1 @ ( u2_lattices @ A ) )
        & ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
        & ( m2_relset_1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).

thf(246,plain,
    ! [A: $i] :
      ( ( l2_lattices @ A )
     => ( ( v1_funct_1 @ ( u2_lattices @ A ) )
        & ( v1_funct_2 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
        & ( m2_relset_1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(82,axiom,
    ? [A: $i] : ( l1_pre_topc @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_pre_topc) ).

thf(432,plain,
    ? [A: $i] : ( l1_pre_topc @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( v3_lattices @ A )
       => ( A
          = ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).

thf(262,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( v3_lattices @ A )
       => ( A
          = ( g3_lattices @ ( u1_struct_0 @ A ) @ ( u2_lattices @ A ) @ ( u1_lattices @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(28,axiom,
    ! [A: $i] :
      ( ( l1_lattices @ A )
     => ( ( v1_funct_1 @ ( u1_lattices @ A ) )
        & ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
        & ( m2_relset_1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).

thf(183,plain,
    ! [A: $i] :
      ( ( l1_lattices @ A )
     => ( ( v1_funct_1 @ ( u1_lattices @ A ) )
        & ( v1_funct_2 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) )
        & ( m2_relset_1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(63,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( v17_lattices @ A )
        & ~ ( v3_realset2 @ A )
        & ( l3_lattices @ A ) )
     => ( ( v1_pre_topc @ ( k11_lopclset @ A ) )
        & ( v2_pre_topc @ ( k11_lopclset @ A ) )
        & ( l1_pre_topc @ ( k11_lopclset @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_lopclset) ).

thf(305,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( v17_lattices @ A )
        & ~ ( v3_realset2 @ A )
        & ( l3_lattices @ A ) )
     => ( ( v1_pre_topc @ ( k11_lopclset @ A ) )
        & ( v2_pre_topc @ ( k11_lopclset @ A ) )
        & ( l1_pre_topc @ ( k11_lopclset @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(44,axiom,
    ? [A: $i] : ( l2_lattices @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).

thf(239,plain,
    ? [A: $i] : ( l2_lattices @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
    <=> ( m1_relset_1 @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

thf(126,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)],[11]) ).

thf(76,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/sandbox/benchmark/theBenchmark.p',dt_g1_pre_topc) ).

thf(400,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)],[76]) ).

thf(92,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v4_lattices @ A )
          & ( v5_lattices @ A )
          & ( v6_lattices @ A )
          & ( v7_lattices @ A )
          & ( v8_lattices @ A )
          & ( v9_lattices @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).

thf(459,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v4_lattices @ A )
          & ( v5_lattices @ A )
          & ( v6_lattices @ A )
          & ( v7_lattices @ A )
          & ( v8_lattices @ A )
          & ( v9_lattices @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(12,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/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).

thf(131,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)],[12]) ).

thf(27,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
    <=> ( r1_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

thf(178,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)],[27]) ).

thf(22,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
      & ( v1_relat_1 @ C )
      & ( v1_funct_1 @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).

thf(163,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
      & ( v1_relat_1 @ C )
      & ( v1_funct_1 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(33,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).

thf(200,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)],[33]) ).

thf(49,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/sandbox/benchmark/theBenchmark.p',abstractness_v1_pre_topc) ).

thf(254,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)],[49]) ).

thf(94,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v11_lattices @ A )
      & ( v12_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A )
      & ( v15_lattices @ A )
      & ( v16_lattices @ A )
      & ( v17_lattices @ A )
      & ~ ( v3_realset2 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_lopclset) ).

thf(469,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v4_lattices @ A )
      & ( v5_lattices @ A )
      & ( v6_lattices @ A )
      & ( v7_lattices @ A )
      & ( v8_lattices @ A )
      & ( v9_lattices @ A )
      & ( v10_lattices @ A )
      & ( v11_lattices @ A )
      & ( v12_lattices @ A )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A )
      & ( v15_lattices @ A )
      & ( v16_lattices @ A )
      & ( v17_lattices @ A )
      & ~ ( v3_realset2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(64,axiom,
    ? [A: $i] :
      ( ( l1_struct_0 @ A )
      & ~ ( v3_struct_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).

thf(309,plain,
    ? [A: $i] :
      ( ( l1_struct_0 @ A )
      & ~ ( v3_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(90,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v11_lattices @ A )
          & ( v15_lattices @ A )
          & ( v16_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v17_lattices @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_lattices) ).

thf(454,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( ~ ( v3_struct_0 @ A )
          & ( v11_lattices @ A )
          & ( v15_lattices @ A )
          & ( v16_lattices @ A ) )
       => ( ~ ( v3_struct_0 @ A )
          & ( v17_lattices @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(489,plain,
    $false,
    inference(e,[status(thm)],[142,152,403,339,457,244,365,234,408,115,276,449,379,202,174,288,436,257,110,344,196,216,443,321,106,221,265,312,206,117,439,102,302,260,429,137,467,361,324,285,224,298,148,176,423,191,291,445,144,236,187,172,219,451,434,208,213,198,278,135,241,167,426,112,342,295,282,150,95,154,386,250,104,390,139,119,246,432,262,183,305,239,126,400,459,131,178,163,200,254,469,309,454]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.08  % Problem  : LAT292+1 : TPTP v8.1.2. Released v3.4.0.
% 0.03/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit : 300
% 0.10/0.29  % WCLimit  : 300
% 0.10/0.29  % DateTime : Thu May 18 14:20:35 EDT 2023
% 0.10/0.29  % CPUTime  : 
% 0.64/0.68  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 0.88/0.83  % [INFO] 	 Parsing done (153ms). 
% 0.88/0.84  % [INFO] 	 Running in sequential loop mode. 
% 1.44/1.05  % [INFO] 	 eprover registered as external prover. 
% 1.44/1.05  % [INFO] 	 cvc4 registered as external prover. 
% 1.44/1.05  % [INFO] 	 Scanning for conjecture ... 
% 1.59/1.14  % [INFO] 	 Found a conjecture and 111 axioms. Running axiom selection ... 
% 1.87/1.21  % [INFO] 	 Axiom selection finished. Selected 92 axioms (removed 19 axioms). 
% 2.09/1.30  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.09/1.31  % [INFO] 	 Type checking passed. 
% 2.26/1.31  % [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 ... 
% 5.62/2.25  % External prover 'e' found a proof!
% 5.62/2.25  % [INFO] 	 Killing All external provers ... 
% 5.62/2.25  % Time passed: 1858ms (effective reasoning time: 1404ms)
% 5.62/2.25  % 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)>
% 5.62/2.25  % Axioms used in derivation (92): redefinition_m2_relset_1, cc2_finset_1, existence_l3_lattices, rc1_lopclset, d9_lopclset, cc18_membered, cc3_lattices, existence_m2_relset_1, fc1_finsub_1, rc4_finset_1, symmetry_r1_filter_1, rc12_lattices, cc6_lattices, existence_l1_lattices, t1_subset, rc2_partfun1, cc4_lattices, dt_m2_relset_1, reflexivity_r1_filter_1, dt_k4_lopclset, d4_lopclset, cc2_finsub_1, rc6_pre_topc, dt_k6_lopclset, dt_k12_lopclset, rc11_lattices, rc3_lattices, dt_l1_lattices, dt_l1_pre_topc, t6_boole, existence_l2_lattices, dt_k1_lopclset, fc4_lopclset, free_g1_pre_topc, dt_k11_lopclset, t5_subset, existence_m1_relset_1, dt_l3_lattices, dt_l2_lattices, t2_tarski, rc13_lattices, cc5_lattices, t4_subset, cc1_funct_2, abstractness_v1_pre_topc, t7_boole, dt_g1_pre_topc, rc3_struct_0, cc4_membered, cc1_lattices, rc1_funct_2, t3_subset, cc1_relset_1, rc9_lattices, dt_u1_lattices, existence_m1_subset_1, cc1_finsub_1, fc1_struct_0, cc6_funct_2, existence_l1_pre_topc, fc1_lopclset, reflexivity_r1_tarski, cc17_membered, dt_g3_lattices, fraenkel_a_1_0_lopclset, rc1_pre_topc, rc6_lattices, rc7_pre_topc, free_g3_lattices, cc7_lattices, dt_k5_lopclset, rc3_finset_1, rc1_finset_1, d1_lopclset, cc1_finset_1, abstractness_v3_lattices, t8_boole, dt_u1_pre_topc, rc5_struct_0, t2_subset, cc3_membered, rc2_pre_topc, existence_l1_struct_0, rc10_lattices, cc5_funct_2, dt_u2_lattices, fc14_finset_1, cc16_membered, fc3_lattices, antisymmetry_r2_hidden, t43_lopclset, cc2_lattices
% 5.62/2.25  % No. of inferences in proof: 188
% 5.62/2.25  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1858 ms resp. 1404 ms w/o parsing
% 5.83/2.32  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.83/2.32  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------