TSTP Solution File: LAT337+1 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LAT337+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n011.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 11:27:58 EDT 2023

% Result   : Theorem 5.59s 2.39s
% Output   : Refutation 6.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  122
% Syntax   : Number of formulae    :  200 (  25 unt;  46 typ;   0 def)
%            Number of atoms       :  827 (  14 equ;   0 cnn)
%            Maximal formula atoms :   17 (   5 avg)
%            Number of connectives : 2375 ( 143   ~;   2   |; 526   &;1559   @)
%                                         (   3 <=>; 142  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   70 (  70   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   48 (  46 usr;   2 con; 0-3 aty)
%            Number of variables   :  260 (   0   ^; 206   !;  54   ?; 260   :)

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

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

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

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

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

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

thf(r3_lattices_type,type,
    r3_lattices: $i > $i > $i > $o ).

thf(k23_filter_2_type,type,
    k23_filter_2: $i > $i > $i ).

thf(k22_filter_2_type,type,
    k22_filter_2: $i > $i > $i > $i ).

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

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

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

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

thf(v1_funct_1_type,type,
    v1_funct_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(k1_xboole_0_type,type,
    k1_xboole_0: $i ).

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

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

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

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

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

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

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

thf(m2_lattice4_type,type,
    m2_lattice4: $i > $i > $o ).

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

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

thf(v2_binop_1_type,type,
    v2_binop_1: $i > $i > $o ).

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

thf(v1_binop_1_type,type,
    v1_binop_1: $i > $i > $o ).

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

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

thf(m2_nat_lat_type,type,
    m2_nat_lat: $i > $i > $o ).

thf(r1_lattices_type,type,
    r1_lattices: $i > $i > $i > $o ).

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

thf(74,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/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).

thf(384,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)],[74]) ).

thf(36,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/sandbox2/benchmark/theBenchmark.p',rc9_lattices) ).

thf(185,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)],[36]) ).

thf(19,axiom,
    ? [A: $i] : ( l1_struct_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).

thf(133,plain,
    ? [A: $i] : ( l1_struct_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(46,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(237,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)],[46]) ).

thf(40,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v7_lattices @ A )
        & ( l1_lattices @ A ) )
     => ( ( v1_relat_1 @ ( u1_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 ) )
        & ( v2_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
        & ( v1_partfun1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_lattice2) ).

thf(204,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v7_lattices @ A )
        & ( l1_lattices @ A ) )
     => ( ( v1_relat_1 @ ( u1_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 ) )
        & ( v2_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
        & ( v1_partfun1 @ ( 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)],[40]) ).

thf(20,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(135,plain,
    ! [A: $i] : ( r1_tarski @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(64,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v6_lattices @ A )
        & ( l1_lattices @ A ) )
     => ( ( v1_relat_1 @ ( u1_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 ) )
        & ( v1_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
        & ( v1_partfun1 @ ( u1_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_lattice2) ).

thf(342,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v6_lattices @ A )
        & ( l1_lattices @ A ) )
     => ( ( v1_relat_1 @ ( u1_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 ) )
        & ( v1_binop_1 @ ( u1_lattices @ A ) @ ( u1_struct_0 @ A ) )
        & ( v1_partfun1 @ ( 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)],[64]) ).

thf(60,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ? [B: $i] : ( m2_lattice4 @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_lattice4) ).

thf(327,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ? [B: $i] : ( m2_lattice4 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(62,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ? [B: $i] :
          ( ( m2_lattice4 @ B @ A )
          & ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice4) ).

thf(333,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ? [B: $i] :
          ( ( m2_lattice4 @ B @ A )
          & ~ ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(66,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ? [B: $i] : ( m2_nat_lat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_nat_lat) ).

thf(352,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ? [B: $i] : ( m2_nat_lat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

thf(110,plain,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(68,axiom,
    ? [A: $i] : ( l3_lattices @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).

thf(357,plain,
    ? [A: $i] : ( l3_lattices @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(37,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(196,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)],[37]) ).

thf(59,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m2_lattice4 @ B @ A ) )
     => ( m2_nat_lat @ ( k23_filter_2 @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k23_filter_2) ).

thf(325,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m2_lattice4 @ B @ A ) )
     => ( m2_nat_lat @ ( k23_filter_2 @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
             => ( ( ~ ( v3_struct_0 @ A )
                  & ( v10_lattices @ A )
                  & ( v17_lattices @ A )
                  & ( l3_lattices @ A )
                  & ( r3_lattices @ A @ B @ C ) )
               => ( ~ ( v3_struct_0 @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                  & ( v10_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                  & ( v17_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                  & ( l3_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_filter_2) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A )
          & ( l3_lattices @ A ) )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
               => ( ( ~ ( v3_struct_0 @ A )
                    & ( v10_lattices @ A )
                    & ( v17_lattices @ A )
                    & ( l3_lattices @ A )
                    & ( r3_lattices @ A @ B @ C ) )
                 => ( ~ ( v3_struct_0 @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                    & ( v10_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                    & ( v17_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                    & ( l3_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(78,plain,
    ~ ! [A: $i] :
        ( ( ~ ( v3_struct_0 @ A )
          & ( v10_lattices @ A )
          & ( l3_lattices @ A ) )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
               => ( ( ~ ( v3_struct_0 @ A )
                    & ( v10_lattices @ A )
                    & ( v17_lattices @ A )
                    & ( l3_lattices @ A )
                    & ( r3_lattices @ A @ B @ C ) )
                 => ( ~ ( v3_struct_0 @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                    & ( v10_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                    & ( v17_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                    & ( l3_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(51,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v6_lattices @ A )
        & ( v8_lattices @ A )
        & ( v9_lattices @ A )
        & ( l3_lattices @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
        & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
     => ( r3_lattices @ A @ B @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).

thf(253,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v6_lattices @ A )
        & ( v8_lattices @ A )
        & ( v9_lattices @ A )
        & ( l3_lattices @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
        & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
     => ( r3_lattices @ A @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(10,axiom,
    ? [A: $i] : ( v1_xboole_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(106,plain,
    ? [A: $i] : ( v1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

thf(121,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(65,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/sandbox2/benchmark/theBenchmark.p',cc4_lattices) ).

thf(348,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)],[65]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ! [B: $i] :
          ( ( m2_nat_lat @ B @ A )
         => ( ~ ( v3_struct_0 @ B )
            & ( v10_lattices @ B )
            & ( l3_lattices @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_nat_lat) ).

thf(233,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ! [B: $i] :
          ( ( m2_nat_lat @ B @ A )
         => ( ~ ( v3_struct_0 @ B )
            & ( v10_lattices @ B )
            & ( l3_lattices @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(49,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(248,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)],[49]) ).

thf(39,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/sandbox2/benchmark/theBenchmark.p',fc3_lattices) ).

thf(201,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)],[39]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(102,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(29,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/sandbox2/benchmark/theBenchmark.p',cc3_lattices) ).

thf(160,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)],[29]) ).

thf(75,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
             => ( ( ~ ( v3_struct_0 @ A )
                  & ( v10_lattices @ A )
                  & ( v15_lattices @ A )
                  & ( v16_lattices @ A )
                  & ( l3_lattices @ A )
                  & ( v12_lattices @ A )
                  & ( r3_lattices @ A @ B @ C ) )
               => ( ~ ( v3_struct_0 @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                  & ( v10_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                  & ( v15_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                  & ( v16_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                  & ( l3_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_filter_2) ).

thf(392,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
             => ( ( ~ ( v3_struct_0 @ A )
                  & ( v10_lattices @ A )
                  & ( v15_lattices @ A )
                  & ( v16_lattices @ A )
                  & ( l3_lattices @ A )
                  & ( v12_lattices @ A )
                  & ( r3_lattices @ A @ B @ C ) )
               => ( ~ ( v3_struct_0 @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                  & ( v10_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                  & ( v15_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                  & ( v16_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) )
                  & ( l3_lattices @ ( k23_filter_2 @ A @ ( k22_filter_2 @ A @ B @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v2_funct_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).

thf(137,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v2_funct_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(4,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(92,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)],[4]) ).

thf(70,axiom,
    ? [A: $i] :
      ( ( l1_struct_0 @ A )
      & ~ ( v3_struct_0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).

thf(361,plain,
    ? [A: $i] :
      ( ( l1_struct_0 @ A )
      & ~ ( v3_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(61,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).

thf(329,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ~ ( v3_struct_0 @ A )
      & ( v3_lattices @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(76,axiom,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( l1_lattices @ A )
        & ( l2_lattices @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).

thf(403,plain,
    ! [A: $i] :
      ( ( l3_lattices @ A )
     => ( ( l1_lattices @ A )
        & ( l2_lattices @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(22,axiom,
    ? [A: $i] : ( l1_lattices @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).

thf(141,plain,
    ? [A: $i] : ( l1_lattices @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(52,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/sandbox2/benchmark/theBenchmark.p',rc13_lattices) ).

thf(256,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)],[52]) ).

thf(16,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(124,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(31,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(173,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)],[31]) ).

thf(18,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).

thf(129,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(25,axiom,
    ? [A: $i] :
      ~ ( v1_xboole_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(148,plain,
    ? [A: $i] :
      ~ ( v1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(34,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(180,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)],[34]) ).

thf(77,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/sandbox2/benchmark/theBenchmark.p',dt_u2_lattices) ).

thf(406,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)],[77]) ).

thf(13,axiom,
    v1_xboole_0 @ k1_xboole_0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(113,plain,
    v1_xboole_0 @ k1_xboole_0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(43,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/sandbox2/benchmark/theBenchmark.p',cc6_lattices) ).

thf(219,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)],[43]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).

thf(98,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(72,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ! [B: $i] :
          ( ( m2_lattice4 @ B @ A )
         => ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).

thf(367,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ! [B: $i] :
          ( ( m2_lattice4 @ B @ A )
         => ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v4_lattices @ A )
        & ( l2_lattices @ A ) )
     => ( ( v1_relat_1 @ ( u2_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 ) )
        & ( v1_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
        & ( v1_partfun1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_lattice2) ).

thf(213,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v4_lattices @ A )
        & ( l2_lattices @ A ) )
     => ( ( v1_relat_1 @ ( u2_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 ) )
        & ( v1_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
        & ( v1_partfun1 @ ( 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)],[42]) ).

thf(27,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
        & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
     => ( ~ ( v1_xboole_0 @ ( k22_filter_2 @ A @ B @ C ) )
        & ( m2_lattice4 @ ( k22_filter_2 @ A @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k22_filter_2) ).

thf(155,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
        & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
     => ( ~ ( v1_xboole_0 @ ( k22_filter_2 @ A @ B @ C ) )
        & ( m2_lattice4 @ ( k22_filter_2 @ A @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(38,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(198,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)],[38]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( l2_lattices @ A )
     => ( l1_struct_0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).

thf(108,plain,
    ! [A: $i] :
      ( ( l2_lattices @ A )
     => ( l1_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(35,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/sandbox2/benchmark/theBenchmark.p',abstractness_v3_lattices) ).

thf(182,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)],[35]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( l1_lattices @ A )
     => ( l1_struct_0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).

thf(127,plain,
    ! [A: $i] :
      ( ( l1_lattices @ A )
     => ( l1_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m2_lattice4 @ B @ A ) )
         => ( ( v11_lattices @ A )
           => ( v11_lattices @ ( k23_filter_2 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_filter_2) ).

thf(359,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m2_lattice4 @ B @ A ) )
         => ( ( v11_lattices @ A )
           => ( v11_lattices @ ( k23_filter_2 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(63,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v5_lattices @ A )
        & ( l2_lattices @ A ) )
     => ( ( v1_relat_1 @ ( u2_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 ) )
        & ( v2_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
        & ( v1_partfun1 @ ( u2_lattices @ A ) @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) @ ( u1_struct_0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattice2) ).

thf(336,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v5_lattices @ A )
        & ( l2_lattices @ A ) )
     => ( ( v1_relat_1 @ ( u2_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 ) )
        & ( v2_binop_1 @ ( u2_lattices @ A ) @ ( u1_struct_0 @ A ) )
        & ( v1_partfun1 @ ( 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)],[63]) ).

thf(32,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(175,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)],[32]) ).

thf(23,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).

thf(143,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(50,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v6_lattices @ A )
        & ( v8_lattices @ A )
        & ( v9_lattices @ A )
        & ( l3_lattices @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
        & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
     => ( ( r3_lattices @ A @ B @ C )
      <=> ( r1_lattices @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).

thf(250,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v6_lattices @ A )
        & ( v8_lattices @ A )
        & ( v9_lattices @ A )
        & ( l3_lattices @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
        & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
     => ( ( ( r3_lattices @ A @ B @ C )
         => ( r1_lattices @ A @ B @ C ) )
        & ( ( r1_lattices @ A @ B @ C )
         => ( r3_lattices @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(3,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(87,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)],[3]) ).

thf(9,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(104,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(57,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(319,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)],[57]) ).

thf(56,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/sandbox2/benchmark/theBenchmark.p',rc12_lattices) ).

thf(304,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)],[56]) ).

thf(28,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)],[28]) ).

thf(14,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/sandbox2/benchmark/theBenchmark.p',free_g3_lattices) ).

thf(114,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)],[14]) ).

thf(48,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

thf(246,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(54,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/sandbox2/benchmark/theBenchmark.p',cc5_lattices) ).

thf(287,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)],[54]) ).

thf(26,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_xboole_0 @ A )
      & ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).

thf(151,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_xboole_0 @ A )
      & ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(24,axiom,
    ? [A: $i] : ( l2_lattices @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).

thf(146,plain,
    ? [A: $i] : ( l2_lattices @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

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 )
      & ( v13_lattices @ A )
      & ( v14_lattices @ A )
      & ( v15_lattices @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc11_lattices) ).

thf(273,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)],[53]) ).

thf(41,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/sandbox2/benchmark/theBenchmark.p',dt_g3_lattices) ).

thf(210,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)],[41]) ).

thf(47,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/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).

thf(242,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)],[47]) ).

thf(55,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/sandbox2/benchmark/theBenchmark.p',cc7_lattices) ).

thf(294,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)],[55]) ).

thf(5,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(94,plain,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(30,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m2_lattice4 @ B @ A ) )
     => ( ~ ( v3_struct_0 @ ( k23_filter_2 @ A @ B ) )
        & ( v3_lattices @ ( k23_filter_2 @ A @ B ) )
        & ( v4_lattices @ ( k23_filter_2 @ A @ B ) )
        & ( v5_lattices @ ( k23_filter_2 @ A @ B ) )
        & ( v6_lattices @ ( k23_filter_2 @ A @ B ) )
        & ( v7_lattices @ ( k23_filter_2 @ A @ B ) )
        & ( v8_lattices @ ( k23_filter_2 @ A @ B ) )
        & ( v9_lattices @ ( k23_filter_2 @ A @ B ) )
        & ( v10_lattices @ ( k23_filter_2 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_filter_2) ).

thf(163,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m2_lattice4 @ B @ A ) )
     => ( ~ ( v3_struct_0 @ ( k23_filter_2 @ A @ B ) )
        & ( v3_lattices @ ( k23_filter_2 @ A @ B ) )
        & ( v4_lattices @ ( k23_filter_2 @ A @ B ) )
        & ( v5_lattices @ ( k23_filter_2 @ A @ B ) )
        & ( v6_lattices @ ( k23_filter_2 @ A @ B ) )
        & ( v7_lattices @ ( k23_filter_2 @ A @ B ) )
        & ( v8_lattices @ ( k23_filter_2 @ A @ B ) )
        & ( v9_lattices @ ( k23_filter_2 @ A @ B ) )
        & ( v10_lattices @ ( k23_filter_2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(33,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(178,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)],[33]) ).

thf(73,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/sandbox2/benchmark/theBenchmark.p',rc10_lattices) ).

thf(369,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)],[73]) ).

thf(58,axiom,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ( v3_lattices @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_lattices) ).

thf(322,plain,
    ? [A: $i] :
      ( ( l3_lattices @ A )
      & ( v3_lattices @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(67,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(354,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)],[67]) ).

thf(44,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ? [B: $i] :
          ( ( m2_nat_lat @ B @ A )
          & ~ ( v3_struct_0 @ B )
          & ( v3_lattices @ B )
          & ( v4_lattices @ B )
          & ( v5_lattices @ B )
          & ( v6_lattices @ B )
          & ( v7_lattices @ B )
          & ( v8_lattices @ B )
          & ( v9_lattices @ B )
          & ( v10_lattices @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_nat_lat) ).

thf(222,plain,
    ! [A: $i] :
      ( ( ~ ( v3_struct_0 @ A )
        & ( v10_lattices @ A )
        & ( l3_lattices @ A ) )
     => ? [B: $i] :
          ( ( m2_nat_lat @ B @ A )
          & ~ ( v3_struct_0 @ B )
          & ( v3_lattices @ B )
          & ( v4_lattices @ B )
          & ( v5_lattices @ B )
          & ( v6_lattices @ B )
          & ( v7_lattices @ B )
          & ( v8_lattices @ B )
          & ( v9_lattices @ B )
          & ( v10_lattices @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(71,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/sandbox2/benchmark/theBenchmark.p',cc2_lattices) ).

thf(364,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)],[71]) ).

thf(7,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(100,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(412,plain,
    $false,
    inference(e,[status(thm)],[384,185,133,237,204,135,342,327,333,352,110,357,196,325,78,253,106,121,348,233,248,201,102,160,392,137,92,361,329,403,141,256,124,173,129,148,180,406,113,219,98,367,213,155,198,108,182,127,359,336,175,143,250,87,104,319,304,158,114,246,287,151,146,273,210,242,294,94,163,178,369,322,354,222,364,100]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LAT337+1 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n011.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu May 18 14:05:48 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.93/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.35/1.03  % [INFO] 	 Parsing done (166ms). 
% 1.35/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.91/1.25  % [INFO] 	 eprover registered as external prover. 
% 1.91/1.25  % [INFO] 	 cvc4 registered as external prover. 
% 1.91/1.26  % [INFO] 	 Scanning for conjecture ... 
% 2.02/1.34  % [INFO] 	 Found a conjecture and 82 axioms. Running axiom selection ... 
% 2.27/1.41  % [INFO] 	 Axiom selection finished. Selected 75 axioms (removed 7 axioms). 
% 2.65/1.50  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.65/1.51  % [INFO] 	 Type checking passed. 
% 2.65/1.51  % [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 ... 
% 5.59/2.38  % External prover 'e' found a proof!
% 5.59/2.38  % [INFO] 	 Killing All external provers ... 
% 5.59/2.38  % Time passed: 1856ms (effective reasoning time: 1339ms)
% 5.59/2.38  % 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)>
% 5.59/2.39  % Axioms used in derivation (75): redefinition_m2_relset_1, dt_m2_nat_lat, t5_subset, dt_l2_lattices, fc5_filter_2, t86_filter_2, rc2_xboole_0, fc1_xboole_0, rc12_lattices, cc6_lattices, existence_l1_lattices, t1_subset, fc4_subset_1, existence_l3_lattices, fc4_lattice2, cc4_lattices, rc3_funct_1, fc2_lattice2, dt_m2_relset_1, fc3_lattice2, dt_m2_lattice4, rc1_funct_1, reflexivity_r3_lattices, rc11_lattices, rc3_lattices, dt_l1_lattices, t6_boole, rc2_subset_1, existence_l2_lattices, existence_m1_relset_1, dt_l3_lattices, rc13_lattices, cc5_lattices, t4_subset, t7_boole, cc1_funct_1, rc3_struct_0, fc1_subset_1, fc5_lattice2, rc2_funct_1, rc1_subset_1, cc1_lattices, t78_filter_2, redefinition_r3_lattices, cc2_funct_1, t3_subset, cc1_relset_1, rc9_lattices, dt_u1_lattices, existence_m1_subset_1, rc1_nat_lat, cc3_lattices, dt_k23_filter_2, existence_m2_relset_1, existence_m2_lattice4, fc1_struct_0, dt_k22_filter_2, rc1_lattice4, reflexivity_r1_tarski, existence_m2_nat_lat, dt_g3_lattices, rc6_lattices, free_g3_lattices, cc7_lattices, abstractness_v3_lattices, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, existence_l1_struct_0, rc10_lattices, dt_u2_lattices, fc3_lattices, antisymmetry_r2_hidden, cc2_lattices
% 5.59/2.39  % No. of inferences in proof: 154
% 5.59/2.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1856 ms resp. 1339 ms w/o parsing
% 6.04/2.45  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.04/2.46  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------