TSTP Solution File: LAT345+4 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LAT345+4 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.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 11:28:01 EDT 2023

% Result   : Theorem 110.65s 28.17s
% Output   : Refutation 110.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :  304
% Syntax   : Number of formulae    :  562 (  84 unt;  92 typ;   0 def)
%            Number of atoms       : 2208 ( 305 equ;   0 cnn)
%            Maximal formula atoms :   19 (   4 avg)
%            Number of connectives : 8400 ( 543   ~;  15   |; 964   &;6125   @)
%                                         (  50 <=>; 703  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  140 ( 140   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   94 (  92 usr;  14 con; 0-4 aty)
%            Number of variables   : 1006 (   0   ^; 906   !; 100   ?;1006   :)

% Comments : 
%------------------------------------------------------------------------------
thf(v3_conlat_1_type,type,
    v3_conlat_1: $i > $o ).

thf(v4_conlat_1_type,type,
    v4_conlat_1: $i > $o ).

thf(l2_conlat_1_type,type,
    l2_conlat_1: $i > $o ).

thf(v6_conlat_1_type,type,
    v6_conlat_1: $i > $i > $o ).

thf(v7_conlat_1_type,type,
    v7_conlat_1: $i > $i > $o ).

thf(v9_conlat_1_type,type,
    v9_conlat_1: $i > $i > $o ).

thf(l3_conlat_1_type,type,
    l3_conlat_1: $i > $i > $o ).

thf(k9_conlat_2_type,type,
    k9_conlat_2: $i > $i > $i ).

thf(k7_conlat_2_type,type,
    k7_conlat_2: $i > $i ).

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

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

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

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

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

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

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

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

thf(k2_subset_1_type,type,
    k2_subset_1: $i > $i ).

thf(k5_finsub_1_type,type,
    k5_finsub_1: $i > $i ).

thf(l1_conlat_1_type,type,
    l1_conlat_1: $i > $o ).

thf(v1_conlat_1_type,type,
    v1_conlat_1: $i > $o ).

thf(u1_conlat_1_type,type,
    u1_conlat_1: $i > $i ).

thf(u2_conlat_1_type,type,
    u2_conlat_1: $i > $i ).

thf(k8_funct_2_type,type,
    k8_funct_2: $i > $i > $i > $i > $i ).

thf(k2_conlat_1_type,type,
    k2_conlat_1: $i > $i ).

thf(k12_mcart_1_type,type,
    k12_mcart_1: $i > $i > $i > $i > $i ).

thf(u3_conlat_1_type,type,
    u3_conlat_1: $i > $i ).

thf(r1_conlat_1_type,type,
    r1_conlat_1: $i > $i > $i > $o ).

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

thf(k11_conlat_1_type,type,
    k11_conlat_1: $i > $i ).

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

thf(k4_conlat_2_type,type,
    k4_conlat_2: $i > $i ).

thf(k5_conlat_2_type,type,
    k5_conlat_2: $i > $i ).

thf(k3_conlat_2_type,type,
    k3_conlat_2: $i > $i > $i ).

thf(k15_lattice3_type,type,
    k15_lattice3: $i > $i > $i ).

thf(k1_pre_topc_type,type,
    k1_pre_topc: $i > $i ).

thf(k6_conlat_1_type,type,
    k6_conlat_1: $i > $i ).

thf(k2_conlat_2_type,type,
    k2_conlat_2: $i > $i > $i ).

thf(k5_conlat_1_type,type,
    k5_conlat_1: $i > $i ).

thf(v2_conlat_1_type,type,
    v2_conlat_1: $i > $o ).

thf(k1_conlat_1_type,type,
    k1_conlat_1: $i > $i ).

thf(k1_funct_1_type,type,
    k1_funct_1: $i > $i > $i ).

thf(g3_conlat_1_type,type,
    g3_conlat_1: $i > $i > $i > $i ).

thf(k16_lattice3_type,type,
    k16_lattice3: $i > $i > $i ).

thf(a_2_3_conlat_1_type,type,
    a_2_3_conlat_1: $i > $i > $i ).

thf(a_2_2_conlat_1_type,type,
    a_2_2_conlat_1: $i > $i > $i ).

thf(a_2_1_conlat_1_type,type,
    a_2_1_conlat_1: $i > $i > $i ).

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

thf(k6_relset_1_type,type,
    k6_relset_1: $i > $i > $i > $i ).

thf(a_1_0_domain_1_type,type,
    a_1_0_domain_1: $i > $i ).

thf(a_2_0_conlat_1_type,type,
    a_2_0_conlat_1: $i > $i > $i ).

thf(m3_conlat_1_type,type,
    m3_conlat_1: $i > $i > $i > $o ).

thf(a_2_0_closure1_type,type,
    a_2_0_closure1: $i > $i > $i ).

thf(g2_conlat_1_type,type,
    g2_conlat_1: $i > $i > $i > $i ).

thf(m1_conlat_1_type,type,
    m1_conlat_1: $i > $i > $o ).

thf(m2_conlat_1_type,type,
    m2_conlat_1: $i > $i > $i > $o ).

thf(u4_conlat_1_type,type,
    u4_conlat_1: $i > $i > $i ).

thf(v8_conlat_1_type,type,
    v8_conlat_1: $i > $i > $o ).

thf(u5_conlat_1_type,type,
    u5_conlat_1: $i > $i > $i ).

thf(v11_conlat_1_type,type,
    v11_conlat_1: $i > $i > $o ).

thf(v10_conlat_1_type,type,
    v10_conlat_1: $i > $i > $o ).

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

thf(k8_conlat_1_type,type,
    k8_conlat_1: $i > $i ).

thf(k10_conlat_1_type,type,
    k10_conlat_1: $i > $i ).

thf(k9_conlat_1_type,type,
    k9_conlat_1: $i > $i ).

thf(k1_zf_colla_type,type,
    k1_zf_colla: $i > $i > $i ).

thf(a_1_0_conlat_1_type,type,
    a_1_0_conlat_1: $i > $i ).

thf(r2_conlat_1_type,type,
    r2_conlat_1: $i > $i > $i > $o ).

thf(k12_conlat_1_type,type,
    k12_conlat_1: $i > $i > $i ).

thf(k8_conlat_2_type,type,
    k8_conlat_2: $i > $i > $i ).

thf(k4_conlat_1_type,type,
    k4_conlat_1: $i > $i ).

thf(k1_binop_1_type,type,
    k1_binop_1: $i > $i > $i > $i ).

thf(k7_conlat_1_type,type,
    k7_conlat_1: $i > $i ).

thf(a_2_5_conlat_2_type,type,
    a_2_5_conlat_2: $i > $i > $i ).

thf(m1_lattice4_type,type,
    m1_lattice4: $i > $i > $i > $o ).

thf(k10_conlat_2_type,type,
    k10_conlat_2: $i > $i ).

thf(k1_lattice2_type,type,
    k1_lattice2: $i > $i ).

thf(a_2_4_conlat_2_type,type,
    a_2_4_conlat_2: $i > $i > $i ).

thf(k1_conlat_2_type,type,
    k1_conlat_2: $i > $i > $i ).

thf(k3_conlat_1_type,type,
    k3_conlat_1: $i > $i ).

thf(sk1_type,type,
    sk1: $i ).

thf(sk2_type,type,
    sk2: $i ).

thf(sk24_type,type,
    sk24: $i ).

thf(sk29_type,type,
    sk29: $i ).

thf(sk32_type,type,
    sk32: $i ).

thf(sk48_type,type,
    sk48: $i ).

thf(sk53_type,type,
    sk53: $i ).

thf(sk58_type,type,
    sk58: $i ).

thf(sk69_type,type,
    sk69: $i ).

thf(sk71_type,type,
    sk71: $i ).

thf(sk76_type,type,
    sk76: $i ).

thf(sk77_type,type,
    sk77: $i ).

thf(98,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( v11_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( B
              = ( k6_conlat_1 @ A ) )
          <=> ? [C: $i] :
                ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
                & ? [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
                    & ( B
                      = ( g3_conlat_1 @ A @ C @ D ) )
                    & ( C
                      = ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ k1_xboole_0 ) ) )
                    & ( D
                      = ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ k1_xboole_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_conlat_1) ).

thf(645,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( v11_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( ( B
                = ( k6_conlat_1 @ A ) )
             => ? [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
                  & ? [D: $i] :
                      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
                      & ( B
                        = ( g3_conlat_1 @ A @ C @ D ) )
                      & ( C
                        = ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ k1_xboole_0 ) ) )
                      & ( D
                        = ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ k1_xboole_0 ) ) ) ) )
            & ( ? [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
                  & ? [D: $i] :
                      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
                      & ( B
                        = ( g3_conlat_1 @ A @ C @ D ) )
                      & ( C
                        = ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ k1_xboole_0 ) ) )
                      & ( D
                        = ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ k1_xboole_0 ) ) ) )
             => ( B
                = ( k6_conlat_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(29,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(365,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)],[29]) ).

thf(200,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
     => ( ( v6_conlat_1 @ ( k12_conlat_1 @ A @ B ) @ A )
        & ~ ( v7_conlat_1 @ ( k12_conlat_1 @ A @ B ) @ A )
        & ( v9_conlat_1 @ ( k12_conlat_1 @ A @ B ) @ A )
        & ( l3_conlat_1 @ ( k12_conlat_1 @ A @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_conlat_1) ).

thf(1105,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
     => ( ( v6_conlat_1 @ ( k12_conlat_1 @ A @ B ) @ A )
        & ~ ( v7_conlat_1 @ ( k12_conlat_1 @ A @ B ) @ A )
        & ( v9_conlat_1 @ ( k12_conlat_1 @ A @ B ) @ A )
        & ( l3_conlat_1 @ ( k12_conlat_1 @ A @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(134,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
         => ( ? [C: $i] :
                ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
                & ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A )
                & ( v9_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A )
                & ( l3_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A ) )
          <=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) )
              = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_conlat_1) ).

thf(846,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
         => ( ( ? [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
                  & ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A )
                  & ( v9_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A )
                  & ( l3_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A ) )
             => ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) )
                = B ) )
            & ( ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) )
                = B )
             => ? [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
                  & ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A )
                  & ( v9_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A )
                  & ( l3_conlat_1 @ ( g3_conlat_1 @ A @ C @ B ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(100,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
         => ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B )
            = ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_conlat_1) ).

thf(666,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
         => ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B )
            = ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(201,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( v6_conlat_1 @ ( k5_conlat_1 @ A ) @ A )
        & ~ ( v7_conlat_1 @ ( k5_conlat_1 @ A ) @ A )
        & ( v9_conlat_1 @ ( k5_conlat_1 @ A ) @ A )
        & ( v10_conlat_1 @ ( k5_conlat_1 @ A ) @ A )
        & ( l3_conlat_1 @ ( k5_conlat_1 @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_conlat_1) ).

thf(1110,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( v6_conlat_1 @ ( k5_conlat_1 @ A ) @ A )
        & ~ ( v7_conlat_1 @ ( k5_conlat_1 @ A ) @ A )
        & ( v9_conlat_1 @ ( k5_conlat_1 @ A ) @ A )
        & ( v10_conlat_1 @ ( k5_conlat_1 @ A ) @ A )
        & ( l3_conlat_1 @ ( k5_conlat_1 @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(147,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(909,plain,
    ! [A: $i] : ( r1_tarski @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(92,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(628,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(172,axiom,
    ? [A: $i] :
      ( ( l2_conlat_1 @ A )
      & ~ ( v3_conlat_1 @ A )
      & ( v4_conlat_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_conlat_1) ).

thf(1002,plain,
    ? [A: $i] :
      ( ( l2_conlat_1 @ A )
      & ~ ( v3_conlat_1 @ A )
      & ( v4_conlat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(1005,plain,
    l2_conlat_1 @ sk77,
    inference(cnf,[status(esa)],[1002]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( v4_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( k9_conlat_2 @ ( k7_conlat_2 @ A ) @ ( k9_conlat_2 @ A @ B ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_conlat_2) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ~ ( v3_conlat_1 @ A )
          & ( v4_conlat_1 @ A )
          & ( l2_conlat_1 @ A ) )
       => ! [B: $i] :
            ( ( ( v6_conlat_1 @ B @ A )
              & ~ ( v7_conlat_1 @ B @ A )
              & ( v9_conlat_1 @ B @ A )
              & ( l3_conlat_1 @ B @ A ) )
           => ( ( k9_conlat_2 @ ( k7_conlat_2 @ A ) @ ( k9_conlat_2 @ A @ B ) )
              = B ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(214,plain,
    ~ ! [A: $i] :
        ( ( ~ ( v3_conlat_1 @ A )
          & ( v4_conlat_1 @ A )
          & ( l2_conlat_1 @ A ) )
       => ! [B: $i] :
            ( ( ( v6_conlat_1 @ B @ A )
              & ~ ( v7_conlat_1 @ B @ A )
              & ( v9_conlat_1 @ B @ A )
              & ( l3_conlat_1 @ B @ A ) )
           => ( ( k9_conlat_2 @ ( k7_conlat_2 @ A ) @ ( k9_conlat_2 @ A @ B ) )
              = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(217,plain,
    l2_conlat_1 @ sk1,
    inference(cnf,[status(esa)],[214]) ).

thf(170,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ( ( r2_conlat_1 @ A @ B @ C )
              <=> ( r1_tarski @ ( u5_conlat_1 @ A @ C ) @ ( u5_conlat_1 @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_conlat_1) ).

thf(994,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ( ( ( r2_conlat_1 @ A @ B @ C )
                 => ( r1_tarski @ ( u5_conlat_1 @ A @ C ) @ ( u5_conlat_1 @ A @ B ) ) )
                & ( ( r1_tarski @ ( u5_conlat_1 @ A @ C ) @ ( u5_conlat_1 @ A @ B ) )
                 => ( r2_conlat_1 @ A @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(113,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

thf(741,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(34,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ! [C: $i] :
            ( ( m1_subset_1 @ C @ A )
           => ( r2_hidden @ C @ B ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_subset_1) ).

thf(379,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ! [C: $i] :
            ( ( m1_subset_1 @ C @ A )
           => ( r2_hidden @ C @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(62,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v3_conlat_1 @ B )
        & ( l2_conlat_1 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) ) )
     => ( ( r2_hidden @ A @ ( a_2_0_conlat_1 @ B @ C ) )
      <=> ? [D: $i] :
            ( ( m1_subset_1 @ D @ ( u2_conlat_1 @ B ) )
            & ( A = D )
            & ! [E: $i] :
                ( ( m1_subset_1 @ E @ ( u1_conlat_1 @ B ) )
               => ( ( r2_hidden @ E @ C )
                 => ( r1_conlat_1 @ B @ E @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_conlat_1) ).

thf(511,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v3_conlat_1 @ B )
        & ( l2_conlat_1 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) ) )
     => ( ( ( r2_hidden @ A @ ( a_2_0_conlat_1 @ B @ C ) )
         => ? [D: $i] :
              ( ( m1_subset_1 @ D @ ( u2_conlat_1 @ B ) )
              & ( A = D )
              & ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( u1_conlat_1 @ B ) )
                 => ( ( r2_hidden @ E @ C )
                   => ( r1_conlat_1 @ B @ E @ D ) ) ) ) )
        & ( ? [D: $i] :
              ( ( m1_subset_1 @ D @ ( u2_conlat_1 @ B ) )
              & ( A = D )
              & ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( u1_conlat_1 @ B ) )
                 => ( ( r2_hidden @ E @ C )
                   => ( r1_conlat_1 @ B @ E @ D ) ) ) )
         => ( r2_hidden @ A @ ( a_2_0_conlat_1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(103,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
         => ( ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) @ A )
            & ( v9_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) @ A )
            & ( l3_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) @ A )
            & ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
                   => ( ( ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
                        & ( v9_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
                        & ( l3_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
                        & ( r1_tarski @ B @ D ) )
                     => ( r1_tarski @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_conlat_1) ).

thf(677,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
         => ( ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) @ A )
            & ( v9_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) @ A )
            & ( l3_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) @ A )
            & ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
                   => ( ( ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
                        & ( v9_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
                        & ( l3_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
                        & ( r1_tarski @ B @ D ) )
                     => ( r1_tarski @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(35,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
         => ( ( k3_conlat_2 @ A @ B )
            = ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_conlat_2) ).

thf(384,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
         => ( ( k3_conlat_2 @ A @ B )
            = ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(210,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ ( k5_conlat_1 @ A ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_conlat_1) ).

thf(1137,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ ( k5_conlat_1 @ A ) )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(68,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
     => ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_finsub_1) ).

thf(550,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
     => ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(58,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(500,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)],[58]) ).

thf(126,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ~ ( r2_hidden @ C @ B ) )
          <=> ( r2_hidden @ B @ ( k1_zf_colla @ A @ k1_xboole_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zf_colla) ).

thf(797,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ~ ( r2_hidden @ C @ B ) )
             => ( r2_hidden @ B @ ( k1_zf_colla @ A @ k1_xboole_0 ) ) )
            & ( ( r2_hidden @ B @ ( k1_zf_colla @ A @ k1_xboole_0 ) )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ~ ( r2_hidden @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(107,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(698,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(189,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ ( k5_conlat_1 @ A ) )
            = ( k5_conlat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_conlat_1) ).

thf(1063,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ ( k5_conlat_1 @ A ) )
            = ( k5_conlat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(153,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ! [C: $i] :
              ( ( ( v6_conlat_1 @ C @ ( k7_conlat_2 @ A ) )
                & ( l3_conlat_1 @ C @ ( k7_conlat_2 @ A ) ) )
             => ( ( C
                  = ( k8_conlat_2 @ A @ B ) )
              <=> ( ( ( u4_conlat_1 @ ( k7_conlat_2 @ A ) @ C )
                    = ( u5_conlat_1 @ A @ B ) )
                  & ( ( u5_conlat_1 @ ( k7_conlat_2 @ A ) @ C )
                    = ( u4_conlat_1 @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_conlat_2) ).

thf(930,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ! [C: $i] :
              ( ( ( v6_conlat_1 @ C @ ( k7_conlat_2 @ A ) )
                & ( l3_conlat_1 @ C @ ( k7_conlat_2 @ A ) ) )
             => ( ( ( C
                    = ( k8_conlat_2 @ A @ B ) )
                 => ( ( ( u4_conlat_1 @ ( k7_conlat_2 @ A ) @ C )
                      = ( u5_conlat_1 @ A @ B ) )
                    & ( ( u5_conlat_1 @ ( k7_conlat_2 @ A ) @ C )
                      = ( u4_conlat_1 @ A @ B ) ) ) )
                & ( ( ( ( u4_conlat_1 @ ( k7_conlat_2 @ A ) @ C )
                      = ( u5_conlat_1 @ A @ B ) )
                    & ( ( u5_conlat_1 @ ( k7_conlat_2 @ A ) @ C )
                      = ( u4_conlat_1 @ A @ B ) ) )
                 => ( C
                    = ( k8_conlat_2 @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(40,axiom,
    ? [A: $i] :
      ( ( l1_conlat_1 @ A )
      & ( v1_conlat_1 @ A )
      & ~ ( v2_conlat_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_conlat_1) ).

thf(402,plain,
    ? [A: $i] :
      ( ( l1_conlat_1 @ A )
      & ( v1_conlat_1 @ A )
      & ~ ( v2_conlat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(404,plain,
    v1_conlat_1 @ sk29,
    inference(cnf,[status(esa)],[402]) ).

thf(123,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ( ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ A )
            & ( v9_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ A )
            & ( l3_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ A )
            & ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
                   => ( ( ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
                        & ( v9_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
                        & ( l3_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
                        & ( r1_tarski @ B @ C ) )
                     => ( r1_tarski @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_conlat_1) ).

thf(782,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ( ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ A )
            & ( v9_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ A )
            & ( l3_conlat_1 @ ( g3_conlat_1 @ A @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ A )
            & ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
                   => ( ( ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
                        & ( v9_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
                        & ( l3_conlat_1 @ ( g3_conlat_1 @ A @ C @ D ) @ A )
                        & ( r1_tarski @ B @ C ) )
                     => ( r1_tarski @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(44,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ! [B: $i] :
            ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
           => ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lopclset) ).

thf(417,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ! [B: $i] :
            ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
           => ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(75,axiom,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(565,plain,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(109,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( v10_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( B
              = ( k5_conlat_1 @ A ) )
          <=> ? [C: $i] :
                ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
                & ? [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
                    & ( B
                      = ( g3_conlat_1 @ A @ C @ D ) )
                    & ( C
                      = ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ k1_xboole_0 ) )
                    & ( D
                      = ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_conlat_1) ).

thf(702,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( v10_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( ( B
                = ( k5_conlat_1 @ A ) )
             => ? [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
                  & ? [D: $i] :
                      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
                      & ( B
                        = ( g3_conlat_1 @ A @ C @ D ) )
                      & ( C
                        = ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ k1_xboole_0 ) )
                      & ( D
                        = ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ k1_xboole_0 ) ) ) ) ) )
            & ( ? [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
                  & ? [D: $i] :
                      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
                      & ( B
                        = ( g3_conlat_1 @ A @ C @ D ) )
                      & ( C
                        = ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ k1_xboole_0 ) )
                      & ( D
                        = ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ k1_xboole_0 ) ) ) ) )
             => ( B
                = ( k5_conlat_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(26,axiom,
    ? [A: $i] :
      ( ( l1_conlat_1 @ A )
      & ( v1_conlat_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_conlat_1) ).

thf(356,plain,
    ? [A: $i] :
      ( ( l1_conlat_1 @ A )
      & ( v1_conlat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(357,plain,
    v1_conlat_1 @ sk24,
    inference(cnf,[status(esa)],[356]) ).

thf(96,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l1_conlat_1 @ A ) )
     => ~ ( v1_xboole_0 @ ( u1_conlat_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_conlat_1) ).

thf(638,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l1_conlat_1 @ A ) )
     => ~ ( v1_xboole_0 @ ( u1_conlat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(195,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v8_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ~ ( ( v6_conlat_1 @ B @ A )
              & ~ ( v7_conlat_1 @ B @ A )
              & ( v9_conlat_1 @ B @ A )
              & ( l3_conlat_1 @ B @ A )
              & ( B
               != ( k5_conlat_1 @ A ) )
              & ( B
               != ( k6_conlat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_conlat_1) ).

thf(1087,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v8_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ~ ( ( v6_conlat_1 @ B @ A )
              & ~ ( v7_conlat_1 @ B @ A )
              & ( v9_conlat_1 @ B @ A )
              & ( l3_conlat_1 @ B @ A )
              & ( B
               != ( k5_conlat_1 @ A ) )
              & ( B
               != ( k6_conlat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(163,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ( ( r2_conlat_1 @ A @ C @ B )
              <=> ( r1_tarski @ ( u5_conlat_1 @ A @ B ) @ ( u5_conlat_1 @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_conlat_1) ).

thf(969,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ( ( ( r2_conlat_1 @ A @ C @ B )
                 => ( r1_tarski @ ( u5_conlat_1 @ A @ B ) @ ( u5_conlat_1 @ A @ C ) ) )
                & ( ( r1_tarski @ ( u5_conlat_1 @ A @ B ) @ ( u5_conlat_1 @ A @ C ) )
                 => ( r2_conlat_1 @ A @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).

thf(228,plain,
    ! [A: $i,B: $i] :
      ~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(10,axiom,
    ( ( k5_finsub_1 @ k1_xboole_0 )
    = ( k1_tarski @ k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finsub_1) ).

thf(261,plain,
    ( ( k5_finsub_1 @ k1_xboole_0 )
    = ( k1_tarski @ k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(129,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
     => ( ~ ( v7_conlat_1 @ ( k2_conlat_2 @ A @ B ) @ A )
        & ( v9_conlat_1 @ ( k2_conlat_2 @ A @ B ) @ A )
        & ( l3_conlat_1 @ ( k2_conlat_2 @ A @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_conlat_2) ).

thf(817,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
     => ( ~ ( v7_conlat_1 @ ( k2_conlat_2 @ A @ B ) @ A )
        & ( v9_conlat_1 @ ( k2_conlat_2 @ A @ B ) @ A )
        & ( l3_conlat_1 @ ( k2_conlat_2 @ A @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(145,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ! [C: $i] :
            ~ ( ( r2_hidden @ C @ B )
              & ! [D: $i] :
                  ~ ( ( r2_hidden @ D @ B )
                    & ( r2_hidden @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).

thf(902,plain,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ! [C: $i] :
            ~ ( ( r2_hidden @ C @ B )
              & ! [D: $i] :
                  ~ ( ( r2_hidden @ D @ B )
                    & ( r2_hidden @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(175,axiom,
    ! [A: $i] :
      ( ( ( v3_conlat_1 @ A )
        & ( l1_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ( v8_conlat_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_conlat_1) ).

thf(1013,plain,
    ! [A: $i] :
      ( ( ( v3_conlat_1 @ A )
        & ( l1_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ( v8_conlat_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(120,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ B @ C )
        & ( r2_hidden @ C @ D )
        & ( r2_hidden @ D @ E )
        & ( r2_hidden @ E @ F )
        & ( r2_hidden @ F @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_ordinal1) ).

thf(770,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ B @ C )
        & ( r2_hidden @ C @ D )
        & ( r2_hidden @ D @ E )
        & ( r2_hidden @ E @ F )
        & ( r2_hidden @ F @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(216,plain,
    v9_conlat_1 @ sk2 @ sk1,
    inference(cnf,[status(esa)],[214]) ).

thf(151,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) )
         => ( ( k12_conlat_1 @ A @ B )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d24_conlat_1) ).

thf(924,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) )
         => ( ( k12_conlat_1 @ A @ B )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(125,axiom,
    ! [A: $i] :
      ( ( A = k1_xboole_0 )
    <=> ! [B: $i] :
          ~ ( r2_hidden @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).

thf(789,plain,
    ! [A: $i] :
      ( ( ( A = k1_xboole_0 )
       => ! [B: $i] :
            ~ ( r2_hidden @ B @ A ) )
      & ( ! [B: $i] :
            ~ ( r2_hidden @ B @ A )
       => ( A = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(81,axiom,
    ! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).

thf(591,plain,
    ! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(183,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ? [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
          & ~ ( v7_conlat_1 @ B @ A )
          & ( v9_conlat_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_conlat_1) ).

thf(1040,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ? [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
          & ~ ( v7_conlat_1 @ B @ A )
          & ( v9_conlat_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(97,axiom,
    ? [A: $i] :
      ( ( l1_conlat_1 @ A )
      & ( v1_conlat_1 @ A )
      & ( v2_conlat_1 @ A )
      & ( v3_conlat_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_conlat_1) ).

thf(640,plain,
    ? [A: $i] :
      ( ( l1_conlat_1 @ A )
      & ( v1_conlat_1 @ A )
      & ( v2_conlat_1 @ A )
      & ( v3_conlat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(641,plain,
    v3_conlat_1 @ sk48,
    inference(cnf,[status(esa)],[640]) ).

thf(220,plain,
    ~ ( v3_conlat_1 @ sk1 ),
    inference(cnf,[status(esa)],[214]) ).

thf(1149,plain,
    ( ( v3_conlat_1 @ sk48 )
   != ( v3_conlat_1 @ sk1 ) ),
    inference(paramod_ordered,[status(thm)],[641,220]) ).

thf(1151,plain,
    sk48 != sk1,
    inference(simp,[status(thm)],[1149]) ).

thf(78,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
       => ( ( m1_subset_1 @ B @ A )
        <=> ( r2_hidden @ B @ A ) ) )
      & ( ( v1_xboole_0 @ A )
       => ( ( m1_subset_1 @ B @ A )
        <=> ( v1_xboole_0 @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).

thf(574,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
       => ( ( ( m1_subset_1 @ B @ A )
           => ( r2_hidden @ B @ A ) )
          & ( ( r2_hidden @ B @ A )
           => ( m1_subset_1 @ B @ A ) ) ) )
      & ( ( v1_xboole_0 @ A )
       => ( ( ( m1_subset_1 @ B @ A )
           => ( v1_xboole_0 @ B ) )
          & ( ( v1_xboole_0 @ B )
           => ( m1_subset_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(130,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
    <=> ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).

thf(821,plain,
    ! [A: $i] :
      ( ( ( v1_xboole_0 @ A )
       => ( A = k1_xboole_0 ) )
      & ( ( A = k1_xboole_0 )
       => ( v1_xboole_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(55,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v3_conlat_1 @ B )
        & ( l2_conlat_1 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) ) )
     => ( ( r2_hidden @ A @ ( a_2_1_conlat_1 @ B @ C ) )
      <=> ? [D: $i] :
            ( ( m1_subset_1 @ D @ ( u1_conlat_1 @ B ) )
            & ( A = D )
            & ! [E: $i] :
                ( ( m1_subset_1 @ E @ ( u2_conlat_1 @ B ) )
               => ( ( r2_hidden @ E @ C )
                 => ( r1_conlat_1 @ B @ D @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_conlat_1) ).

thf(480,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v3_conlat_1 @ B )
        & ( l2_conlat_1 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) ) )
     => ( ( ( r2_hidden @ A @ ( a_2_1_conlat_1 @ B @ C ) )
         => ? [D: $i] :
              ( ( m1_subset_1 @ D @ ( u1_conlat_1 @ B ) )
              & ( A = D )
              & ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( u2_conlat_1 @ B ) )
                 => ( ( r2_hidden @ E @ C )
                   => ( r1_conlat_1 @ B @ D @ E ) ) ) ) )
        & ( ? [D: $i] :
              ( ( m1_subset_1 @ D @ ( u1_conlat_1 @ B ) )
              & ( A = D )
              & ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( u2_conlat_1 @ B ) )
                 => ( ( r2_hidden @ E @ C )
                   => ( r1_conlat_1 @ B @ D @ E ) ) ) )
         => ( r2_hidden @ A @ ( a_2_1_conlat_1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(25,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_zfmisc_1) ).

thf(353,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(162,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ( l3_conlat_1 @ B @ A ) )
     => ( ( v6_conlat_1 @ ( k8_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) )
        & ( l3_conlat_1 @ ( k8_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_conlat_2) ).

thf(966,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ( l3_conlat_1 @ B @ A ) )
     => ( ( v6_conlat_1 @ ( k8_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) )
        & ( l3_conlat_1 @ ( k8_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(85,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r1_tarski @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).

thf(602,plain,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r1_tarski @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(38,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) )
      & ~ ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_triang_1) ).

thf(397,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) )
      & ~ ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(140,axiom,
    ~ ! [A: $i] : ( v1_xboole_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_gate_1) ).

thf(877,plain,
    ~ ! [A: $i] : ( v1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(159,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ( v6_conlat_1 @ C @ A )
                & ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ! [D: $i] :
                  ( ( ( v6_conlat_1 @ D @ A )
                    & ~ ( v7_conlat_1 @ D @ A )
                    & ( v9_conlat_1 @ D @ A )
                    & ( l3_conlat_1 @ D @ A ) )
                 => ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ C @ D ) )
                    = ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ C ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_conlat_1) ).

thf(956,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ( v6_conlat_1 @ C @ A )
                & ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ! [D: $i] :
                  ( ( ( v6_conlat_1 @ D @ A )
                    & ~ ( v7_conlat_1 @ D @ A )
                    & ( v9_conlat_1 @ D @ A )
                    & ( l3_conlat_1 @ D @ A ) )
                 => ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ C @ D ) )
                    = ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ C ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(191,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ ( a_2_4_conlat_2 @ A @ B ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_conlat_2) ).

thf(1072,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ ( a_2_4_conlat_2 @ A @ B ) )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(203,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ ( k6_conlat_1 @ A ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_conlat_1) ).

thf(1119,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ ( k6_conlat_1 @ A ) )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_conlat_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( u2_conlat_1 @ A ) )
             => ( ( r1_conlat_1 @ A @ B @ C )
              <=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( u3_conlat_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_conlat_1) ).

thf(411,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_conlat_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( u2_conlat_1 @ A ) )
             => ( ( ( r1_conlat_1 @ A @ B @ C )
                 => ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( u3_conlat_1 @ A ) ) )
                & ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( u3_conlat_1 @ A ) )
                 => ( r1_conlat_1 @ A @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(17,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).

thf(312,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(112,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_conlat_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( u2_conlat_1 @ A ) )
             => ( ~ ( v7_conlat_1 @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ A )
                & ( v9_conlat_1 @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ A )
                & ( l3_conlat_1 @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ A )
                & ~ ( v7_conlat_1 @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) @ A )
                & ( v9_conlat_1 @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) @ A )
                & ( l3_conlat_1 @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_conlat_2) ).

thf(734,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_conlat_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( u2_conlat_1 @ A ) )
             => ( ~ ( v7_conlat_1 @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ A )
                & ( v9_conlat_1 @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ A )
                & ( l3_conlat_1 @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ A )
                & ~ ( v7_conlat_1 @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) @ A )
                & ( v9_conlat_1 @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) @ A )
                & ( l3_conlat_1 @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(221,plain,
    ~ ( v7_conlat_1 @ sk2 @ sk1 ),
    inference(cnf,[status(esa)],[214]) ).

thf(16,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( k1_tarski @ A ) )
    <=> ! [C: $i] :
          ( ( r2_hidden @ C @ B )
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

thf(292,plain,
    ! [A: $i,B: $i] :
      ( ( ( B
          = ( k1_tarski @ A ) )
       => ! [C: $i] :
            ( ( ( r2_hidden @ C @ B )
             => ( C = A ) )
            & ( ( C = A )
             => ( r2_hidden @ C @ B ) ) ) )
      & ( ! [C: $i] :
            ( ( ( r2_hidden @ C @ B )
             => ( C = A ) )
            & ( ( C = A )
             => ( r2_hidden @ C @ B ) ) )
       => ( B
          = ( k1_tarski @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( A
         != ( k1_tarski @ B ) )
        & ( A != k1_xboole_0 )
        & ! [C: $i] :
            ~ ( ( r2_hidden @ C @ A )
              & ( C != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).

thf(233,plain,
    ! [A: $i,B: $i] :
      ~ ( ( A
         != ( k1_tarski @ B ) )
        & ( A != k1_xboole_0 )
        & ! [C: $i] :
            ~ ( ( r2_hidden @ C @ A )
              & ( C != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(155,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ? [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
          & ( v6_conlat_1 @ B @ A )
          & ~ ( v7_conlat_1 @ B @ A )
          & ( v9_conlat_1 @ B @ A )
          & ( v11_conlat_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc16_conlat_1) ).

thf(942,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ? [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
          & ( v6_conlat_1 @ B @ A )
          & ~ ( v7_conlat_1 @ B @ A )
          & ( v9_conlat_1 @ B @ A )
          & ( v11_conlat_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(117,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
     => ! [C: $i] :
          ( ( m3_conlat_1 @ C @ A @ B )
         => ( ~ ( v7_conlat_1 @ C @ A )
            & ( v9_conlat_1 @ C @ A )
            & ( l3_conlat_1 @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_conlat_1) ).

thf(761,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
     => ! [C: $i] :
          ( ( m3_conlat_1 @ C @ A @ B )
         => ( ~ ( v7_conlat_1 @ C @ A )
            & ( v9_conlat_1 @ C @ A )
            & ( l3_conlat_1 @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(187,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ( v6_conlat_1 @ C @ A )
                & ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ C ) )
                = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_conlat_1) ).

thf(1057,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ( v6_conlat_1 @ C @ A )
                & ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ C ) )
                = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(196,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ~ ( v1_xboole_0 @ ( k7_conlat_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_conlat_1) ).

thf(1091,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ~ ( v1_xboole_0 @ ( k7_conlat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(37,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( ( k3_conlat_2 @ A @ ( k2_subset_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
          = ( k5_conlat_1 @ A ) )
        & ( ( k2_conlat_2 @ A @ ( k2_subset_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
          = ( k6_conlat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_conlat_2) ).

thf(392,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( ( k3_conlat_2 @ A @ ( k2_subset_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
          = ( k5_conlat_1 @ A ) )
        & ( ( k2_conlat_2 @ A @ ( k2_subset_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
          = ( k6_conlat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(46,axiom,
    ? [A: $i] :
      ( ( l1_conlat_1 @ A )
      & ( v1_conlat_1 @ A )
      & ~ ( v3_conlat_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_conlat_1) ).

thf(423,plain,
    ? [A: $i] :
      ( ( l1_conlat_1 @ A )
      & ( v1_conlat_1 @ A )
      & ~ ( v3_conlat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(424,plain,
    ~ ( v3_conlat_1 @ sk32 ),
    inference(cnf,[status(esa)],[423]) ).

thf(93,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_conlat_1 @ B @ A )
         => ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_conlat_1) ).

thf(630,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_conlat_1 @ B @ A )
         => ~ ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( k4_tarski @ A @ B )
        = ( k4_tarski @ C @ D ) )
     => ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).

thf(275,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( k4_tarski @ A @ B )
        = ( k4_tarski @ C @ D ) )
     => ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(91,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l1_conlat_1 @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
          & ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc8_conlat_1) ).

thf(625,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l1_conlat_1 @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
          & ~ ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(878,plain,
    ~ ! [A: $i] : ( v1_xboole_0 @ A ),
    inference(polarity_switch,[status(thm)],[877]) ).

thf(879,plain,
    ~ ( v1_xboole_0 @ sk69 ),
    inference(cnf,[status(esa)],[878]) ).

thf(79,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ( m1_conlat_1 @ B @ A ) )
     => ! [C: $i] :
          ( ( m2_conlat_1 @ C @ A @ B )
        <=> ( m1_subset_1 @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_conlat_1) ).

thf(583,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ( m1_conlat_1 @ B @ A ) )
     => ! [C: $i] :
          ( ( ( m2_conlat_1 @ C @ A @ B )
           => ( m1_subset_1 @ C @ B ) )
          & ( ( m1_subset_1 @ C @ B )
           => ( m2_conlat_1 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(179,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ? [B: $i] : ( m1_conlat_1 @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_conlat_1) ).

thf(1027,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ? [B: $i] : ( m1_conlat_1 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(104,axiom,
    ! [A: $i] :
      ( ( l1_conlat_1 @ A )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ( ( v7_conlat_1 @ B @ A )
          <=> ( ( v1_xboole_0 @ ( u4_conlat_1 @ A @ B ) )
              & ( v1_xboole_0 @ ( u5_conlat_1 @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_conlat_1) ).

thf(682,plain,
    ! [A: $i] :
      ( ( l1_conlat_1 @ A )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ( ( ( v7_conlat_1 @ B @ A )
             => ( ( v1_xboole_0 @ ( u4_conlat_1 @ A @ B ) )
                & ( v1_xboole_0 @ ( u5_conlat_1 @ A @ B ) ) ) )
            & ( ( ( v1_xboole_0 @ ( u4_conlat_1 @ A @ B ) )
                & ( v1_xboole_0 @ ( u5_conlat_1 @ A @ B ) ) )
             => ( v7_conlat_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(3,axiom,
    ! [A: $i] : ( m1_subset_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_measure1) ).

thf(224,plain,
    ! [A: $i] : ( m1_subset_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(156,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k4_conlat_1 @ A )
        = ( k2_conlat_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_conlat_1) ).

thf(948,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k4_conlat_1 @ A )
        = ( k2_conlat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(173,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l1_conlat_1 @ A ) )
     => ? [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
          & ( v6_conlat_1 @ B @ A )
          & ~ ( v7_conlat_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc11_conlat_1) ).

thf(1006,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l1_conlat_1 @ A ) )
     => ? [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
          & ( v6_conlat_1 @ B @ A )
          & ~ ( v7_conlat_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(82,axiom,
    ! [A: $i,B: $i] :
      ( ( ( l1_conlat_1 @ A )
        & ( l3_conlat_1 @ B @ A ) )
     => ( m1_subset_1 @ ( u4_conlat_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u4_conlat_1) ).

thf(593,plain,
    ! [A: $i,B: $i] :
      ( ( ( l1_conlat_1 @ A )
        & ( l3_conlat_1 @ B @ A ) )
     => ( m1_subset_1 @ ( u4_conlat_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(137,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ k1_xboole_0 )
        = ( u2_conlat_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_conlat_1) ).

thf(869,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ k1_xboole_0 )
        = ( u2_conlat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(45,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ B )
               => ( r2_hidden @ D @ C ) )
           => ( r1_tarski @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_subset_1) ).

thf(420,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ B )
               => ( r2_hidden @ D @ C ) )
           => ( r1_tarski @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(135,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
    <=> ! [C: $i] :
          ( ( r2_hidden @ C @ A )
         => ( r2_hidden @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

thf(857,plain,
    ! [A: $i,B: $i] :
      ( ( ( r1_tarski @ A @ B )
       => ! [C: $i] :
            ( ( r2_hidden @ C @ A )
           => ( r2_hidden @ C @ B ) ) )
      & ( ! [C: $i] :
            ( ( r2_hidden @ C @ A )
           => ( r2_hidden @ C @ B ) )
       => ( r1_tarski @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(139,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) )
             => ( ( r3_lattices @ ( k11_conlat_1 @ A ) @ B @ C )
              <=> ( r2_conlat_1 @ A @ ( k12_conlat_1 @ A @ B ) @ ( k12_conlat_1 @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_conlat_1) ).

thf(874,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) )
             => ( ( ( r3_lattices @ ( k11_conlat_1 @ A ) @ B @ C )
                 => ( r2_conlat_1 @ A @ ( k12_conlat_1 @ A @ B ) @ ( k12_conlat_1 @ A @ C ) ) )
                & ( ( r2_conlat_1 @ A @ ( k12_conlat_1 @ A @ B ) @ ( k12_conlat_1 @ A @ C ) )
                 => ( r3_lattices @ ( k11_conlat_1 @ A ) @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(212,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( ( v4_conlat_1 @ ( g2_conlat_1 @ A @ B @ C ) )
        & ( l2_conlat_1 @ ( g2_conlat_1 @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g2_conlat_1) ).

thf(1143,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( ( v4_conlat_1 @ ( g2_conlat_1 @ A @ B @ C ) )
        & ( l2_conlat_1 @ ( g2_conlat_1 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(167,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ? [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
          & ( v6_conlat_1 @ B @ A )
          & ~ ( v7_conlat_1 @ B @ A )
          & ( v9_conlat_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc14_conlat_1) ).

thf(980,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ? [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
          & ( v6_conlat_1 @ B @ A )
          & ~ ( v7_conlat_1 @ B @ A )
          & ( v9_conlat_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(403,plain,
    ~ ( v2_conlat_1 @ sk29 ),
    inference(cnf,[status(esa)],[402]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
         => ( ( k2_conlat_2 @ A @ B )
            = ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_conlat_2) ).

thf(471,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
         => ( ( k2_conlat_2 @ A @ B )
            = ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(225,plain,
    ! [A: $i] : ( m1_subset_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
    inference(cnf,[status(esa)],[224]) ).

thf(70,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( r1_tarski @ B @ C )
         => ( r1_tarski @ ( a_2_0_closure1 @ A @ C ) @ ( a_2_0_closure1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_closure1) ).

thf(554,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( r1_tarski @ B @ C )
         => ( r1_tarski @ ( a_2_0_closure1 @ A @ C ) @ ( a_2_0_closure1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(101,axiom,
    ! [A: $i,B: $i] :
      ( ( ( l1_conlat_1 @ A )
        & ( l3_conlat_1 @ B @ A ) )
     => ( ( v6_conlat_1 @ B @ A )
       => ( B
          = ( g3_conlat_1 @ A @ ( u4_conlat_1 @ A @ B ) @ ( u5_conlat_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v6_conlat_1) ).

thf(669,plain,
    ! [A: $i,B: $i] :
      ( ( ( l1_conlat_1 @ A )
        & ( l3_conlat_1 @ B @ A ) )
     => ( ( v6_conlat_1 @ B @ A )
       => ( B
          = ( g3_conlat_1 @ A @ ( u4_conlat_1 @ A @ B ) @ ( u5_conlat_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(642,plain,
    v2_conlat_1 @ sk48,
    inference(cnf,[status(esa)],[640]) ).

thf(105,axiom,
    ! [A: $i] :
      ( ( l1_conlat_1 @ A )
     => ( ( v3_conlat_1 @ A )
      <=> ( ( v1_xboole_0 @ ( u1_conlat_1 @ A ) )
          | ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_conlat_1) ).

thf(686,plain,
    ! [A: $i] :
      ( ( l1_conlat_1 @ A )
     => ( ( ( v3_conlat_1 @ A )
         => ( ( v1_xboole_0 @ ( u1_conlat_1 @ A ) )
            | ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) ) )
        & ( ( ( v1_xboole_0 @ ( u1_conlat_1 @ A ) )
            | ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) )
         => ( v3_conlat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(192,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ? [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
          & ( v6_conlat_1 @ B @ A )
          & ~ ( v7_conlat_1 @ B @ A )
          & ( v9_conlat_1 @ B @ A )
          & ( v10_conlat_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc15_conlat_1) ).

thf(1075,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ? [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
          & ( v6_conlat_1 @ B @ A )
          & ~ ( v7_conlat_1 @ B @ A )
          & ( v9_conlat_1 @ B @ A )
          & ( v10_conlat_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(171,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ( ( v10_conlat_1 @ B @ A )
          <=> ( ( u4_conlat_1 @ A @ B )
              = ( u1_conlat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_conlat_1) ).

thf(997,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ( ( ( v10_conlat_1 @ B @ A )
             => ( ( u4_conlat_1 @ A @ B )
                = ( u1_conlat_1 @ A ) ) )
            & ( ( ( u4_conlat_1 @ A @ B )
                = ( u1_conlat_1 @ A ) )
             => ( v10_conlat_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(108,axiom,
    ? [A: $i] : ( v1_xboole_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(700,plain,
    ? [A: $i] : ( v1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(701,plain,
    v1_xboole_0 @ sk53,
    inference(cnf,[status(esa)],[700]) ).

thf(208,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k3_conlat_1 @ A )
        = ( k1_conlat_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_conlat_1) ).

thf(1131,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k3_conlat_1 @ A )
        = ( k1_conlat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(188,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ ( k6_conlat_1 @ A ) )
            = ( k6_conlat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_conlat_1) ).

thf(1060,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ ( k6_conlat_1 @ A ) )
            = ( k6_conlat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(148,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ B @ C )
        & ( r2_hidden @ C @ D )
        & ( r2_hidden @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_ordinal1) ).

thf(911,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ B @ C )
        & ( r2_hidden @ C @ D )
        & ( r2_hidden @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(110,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( r2_hidden @ C @ A )
        <=> ( r2_hidden @ C @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).

thf(721,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)],[110]) ).

thf(198,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( r2_conlat_1 @ A @ B @ ( k5_conlat_1 @ A ) )
            & ( r2_conlat_1 @ A @ ( k6_conlat_1 @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_conlat_1) ).

thf(1099,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( r2_conlat_1 @ A @ B @ ( k5_conlat_1 @ A ) )
            & ( r2_conlat_1 @ A @ ( k6_conlat_1 @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(168,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ( ( v11_conlat_1 @ B @ A )
          <=> ( ( u5_conlat_1 @ A @ B )
              = ( u2_conlat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_conlat_1) ).

thf(985,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ( ( ( v11_conlat_1 @ B @ A )
             => ( ( u5_conlat_1 @ A @ B )
                = ( u2_conlat_1 @ A ) ) )
            & ( ( ( u5_conlat_1 @ A @ B )
                = ( u2_conlat_1 @ A ) )
             => ( v11_conlat_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(59,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
             => ( ( r1_tarski @ C @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) )
              <=> ( r1_tarski @ ( k12_mcart_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ B @ C ) @ ( u3_conlat_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_conlat_1) ).

thf(503,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
             => ( ( ( r1_tarski @ C @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) )
                 => ( r1_tarski @ ( k12_mcart_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ B @ C ) @ ( u3_conlat_1 @ A ) ) )
                & ( ( r1_tarski @ ( k12_mcart_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ B @ C ) @ ( u3_conlat_1 @ A ) )
                 => ( r1_tarski @ C @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(86,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ B @ C )
        & ( r2_hidden @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).

thf(605,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ B @ C )
        & ( r2_hidden @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(61,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( l1_conlat_1 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) )
     => ( ( v6_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
        & ( l3_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g3_conlat_1) ).

thf(508,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( l1_conlat_1 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) )
     => ( ( v6_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
        & ( l3_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(150,axiom,
    ? [A: $i] :
      ~ ( v1_xboole_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(921,plain,
    ? [A: $i] :
      ~ ( v1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(118,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
             => ( ( r1_tarski @ B @ C )
               => ( r1_tarski @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ C ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_conlat_1) ).

thf(765,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
             => ( ( r1_tarski @ B @ C )
               => ( r1_tarski @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ C ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(72,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).

thf(558,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(121,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ( ( v9_conlat_1 @ B @ A )
          <=> ( ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( u4_conlat_1 @ A @ B ) )
                = ( u5_conlat_1 @ A @ B ) )
              & ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( u5_conlat_1 @ A @ B ) )
                = ( u4_conlat_1 @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_conlat_1) ).

thf(773,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ( ( ( v9_conlat_1 @ B @ A )
             => ( ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( u4_conlat_1 @ A @ B ) )
                  = ( u5_conlat_1 @ A @ B ) )
                & ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( u5_conlat_1 @ A @ B ) )
                  = ( u4_conlat_1 @ A @ B ) ) ) )
            & ( ( ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( u4_conlat_1 @ A @ B ) )
                  = ( u5_conlat_1 @ A @ B ) )
                & ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( u5_conlat_1 @ A @ B ) )
                  = ( u4_conlat_1 @ A @ B ) ) )
             => ( v9_conlat_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(143,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

thf(888,plain,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(146,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ~ ( ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( u4_conlat_1 @ A @ B ) )
                = ( u5_conlat_1 @ A @ B ) )
              & ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( u5_conlat_1 @ A @ B ) )
                = ( u4_conlat_1 @ A @ B ) )
              & ( v7_conlat_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l21_conlat_2) ).

thf(906,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ~ ( ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( u4_conlat_1 @ A @ B ) )
                = ( u5_conlat_1 @ A @ B ) )
              & ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( u5_conlat_1 @ A @ B ) )
                = ( u4_conlat_1 @ A @ B ) )
              & ( v7_conlat_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(425,plain,
    v1_conlat_1 @ sk32,
    inference(cnf,[status(esa)],[423]) ).

thf(115,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( r2_hidden @ A @ ( a_2_0_closure1 @ B @ C ) )
      <=> ? [D: $i] :
            ( ( m1_subset_1 @ D @ B )
            & ( A = D )
            & ( r1_tarski @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_closure1) ).

thf(745,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( ( r2_hidden @ A @ ( a_2_0_closure1 @ B @ C ) )
         => ? [D: $i] :
              ( ( m1_subset_1 @ D @ B )
              & ( A = D )
              & ( r1_tarski @ C @ D ) ) )
        & ( ? [D: $i] :
              ( ( m1_subset_1 @ D @ B )
              & ( A = D )
              & ( r1_tarski @ C @ D ) )
         => ( r2_hidden @ A @ ( a_2_0_closure1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(50,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( k1_zfmisc_1 @ A ) )
    <=> ! [C: $i] :
          ( ( r2_hidden @ C @ B )
        <=> ( r1_tarski @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).

thf(444,plain,
    ! [A: $i,B: $i] :
      ( ( ( B
          = ( k1_zfmisc_1 @ A ) )
       => ! [C: $i] :
            ( ( ( r2_hidden @ C @ B )
             => ( r1_tarski @ C @ A ) )
            & ( ( r1_tarski @ C @ A )
             => ( r2_hidden @ C @ B ) ) ) )
      & ( ! [C: $i] :
            ( ( ( r2_hidden @ C @ B )
             => ( r1_tarski @ C @ A ) )
            & ( ( r1_tarski @ C @ A )
             => ( r2_hidden @ C @ B ) ) )
       => ( B
          = ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(32,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finsub_1) ).

thf(375,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(213,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v8_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ~ ( ~ ( v7_conlat_1 @ B @ A )
              & ( v9_conlat_1 @ B @ A )
              & ( l3_conlat_1 @ B @ A )
              & ~ ( v10_conlat_1 @ B @ A )
              & ~ ( v11_conlat_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_conlat_1) ).

thf(1146,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v8_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ~ ( ~ ( v7_conlat_1 @ B @ A )
              & ( v9_conlat_1 @ B @ A )
              & ( l3_conlat_1 @ B @ A )
              & ~ ( v10_conlat_1 @ B @ A )
              & ~ ( v11_conlat_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(48,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
               => ( ( r2_hidden @ D @ B )
                <=> ( r2_hidden @ D @ C ) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_setfam_1) ).

thf(430,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
               => ( ( ( r2_hidden @ D @ B )
                   => ( r2_hidden @ D @ C ) )
                  & ( ( r2_hidden @ D @ C )
                   => ( r2_hidden @ D @ B ) ) ) )
           => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(1153,plain,
    ( ( v2_conlat_1 @ sk48 )
   != ( v2_conlat_1 @ sk29 ) ),
    inference(paramod_ordered,[status(thm)],[642,403]) ).

thf(1154,plain,
    sk48 != sk29,
    inference(simp,[status(thm)],[1153]) ).

thf(114,axiom,
    ? [A: $i] : ( l1_conlat_1 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_conlat_1) ).

thf(743,plain,
    ? [A: $i] : ( l1_conlat_1 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(822,plain,
    ( ! [A: $i] :
        ( ( v1_xboole_0 @ A )
       => ( A = k1_xboole_0 ) )
    & ! [A: $i] :
        ( ( A = k1_xboole_0 )
       => ( v1_xboole_0 @ A ) ) ),
    inference(miniscope,[status(thm)],[821]) ).

thf(823,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
      | ( v1_xboole_0 @ A ) ),
    inference(cnf,[status(esa)],[822]) ).

thf(825,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
      | ( v1_xboole_0 @ A ) ),
    inference(lifteq,[status(thm)],[823]) ).

thf(826,plain,
    v1_xboole_0 @ k1_xboole_0,
    inference(simp,[status(thm)],[825]) ).

thf(205,axiom,
    ! [A: $i] :
      ( ( l1_conlat_1 @ A )
     => ? [B: $i] : ( l3_conlat_1 @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_conlat_1) ).

thf(1124,plain,
    ! [A: $i] :
      ( ( l1_conlat_1 @ A )
     => ? [B: $i] : ( l3_conlat_1 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(74,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k7_conlat_2 @ A )
        = ( g2_conlat_1 @ ( u2_conlat_1 @ A ) @ ( u1_conlat_1 @ A ) @ ( k6_relset_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ ( u3_conlat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_conlat_2) ).

thf(562,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k7_conlat_2 @ A )
        = ( g2_conlat_1 @ ( u2_conlat_1 @ A ) @ ( u1_conlat_1 @ A ) @ ( k6_relset_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ ( u3_conlat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(165,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ ( a_2_5_conlat_2 @ A @ B ) )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_conlat_2) ).

thf(975,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ ( a_2_5_conlat_2 @ A @ B ) )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(24,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ( ( A != k1_xboole_0 )
       => ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_subset_1) ).

thf(350,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ( ( A != k1_xboole_0 )
       => ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(102,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( ( u4_conlat_1 @ A @ ( k5_conlat_1 @ A ) )
          = ( u1_conlat_1 @ A ) )
        & ( ( u5_conlat_1 @ A @ ( k6_conlat_1 @ A ) )
          = ( u2_conlat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_conlat_1) ).

thf(672,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( ( u4_conlat_1 @ A @ ( k5_conlat_1 @ A ) )
          = ( u1_conlat_1 @ A ) )
        & ( ( u5_conlat_1 @ A @ ( k6_conlat_1 @ A ) )
          = ( u2_conlat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(88,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(611,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)],[88]) ).

thf(124,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l1_conlat_1 @ A ) )
     => ~ ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_conlat_1) ).

thf(787,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l1_conlat_1 @ A ) )
     => ~ ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(41,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(406,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)],[41]) ).

thf(132,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
     => ( ~ ( v7_conlat_1 @ ( k3_conlat_2 @ A @ B ) @ A )
        & ( v9_conlat_1 @ ( k3_conlat_2 @ A @ B ) @ A )
        & ( l3_conlat_1 @ ( k3_conlat_2 @ A @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_conlat_2) ).

thf(831,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
     => ( ~ ( v7_conlat_1 @ ( k3_conlat_2 @ A @ B ) @ A )
        & ( v9_conlat_1 @ ( k3_conlat_2 @ A @ B ) @ A )
        & ( l3_conlat_1 @ ( k3_conlat_2 @ A @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(219,plain,
    v6_conlat_1 @ sk2 @ sk1,
    inference(cnf,[status(esa)],[214]) ).

thf(141,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
         => ( ~ ( v7_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
            & ( v9_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
            & ( l3_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
            & ~ ( v7_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
            & ( v9_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
            & ( l3_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_conlat_2) ).

thf(880,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) )
         => ( ~ ( v7_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
            & ( v9_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
            & ( l3_conlat_1 @ ( k16_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
            & ~ ( v7_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
            & ( v9_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A )
            & ( l3_conlat_1 @ ( k15_lattice3 @ ( k11_conlat_1 @ A ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(204,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ( v6_conlat_1 @ B @ A )
        & ~ ( v7_conlat_1 @ B @ A )
        & ( v9_conlat_1 @ B @ A )
        & ( l3_conlat_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k1_conlat_2 @ A @ B ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_conlat_2) ).

thf(1122,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ( v6_conlat_1 @ B @ A )
        & ~ ( v7_conlat_1 @ B @ A )
        & ( v9_conlat_1 @ B @ A )
        & ( l3_conlat_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k1_conlat_2 @ A @ B ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(84,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

thf(599,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(33,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ B @ ( k5_finsub_1 @ A ) )
        & ( r1_tarski @ C @ B ) )
     => ( r2_hidden @ C @ ( k5_finsub_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_yellow_8) ).

thf(377,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ B @ ( k5_finsub_1 @ A ) )
        & ( r1_tarski @ C @ B ) )
     => ( r2_hidden @ C @ ( k5_finsub_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(169,axiom,
    ? [A: $i] :
      ( ( l2_conlat_1 @ A )
      & ~ ( v2_conlat_1 @ A )
      & ( v4_conlat_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_conlat_1) ).

thf(990,plain,
    ? [A: $i] :
      ( ( l2_conlat_1 @ A )
      & ~ ( v2_conlat_1 @ A )
      & ( v4_conlat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(28,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_conlat_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( u2_conlat_1 @ A ) )
             => ( ( r1_conlat_1 @ A @ B @ C )
              <=> ( r3_lattices @ ( k11_conlat_1 @ A ) @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_conlat_2) ).

thf(362,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_conlat_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( u2_conlat_1 @ A ) )
             => ( ( ( r1_conlat_1 @ A @ B @ C )
                 => ( r3_lattices @ ( k11_conlat_1 @ A ) @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) ) )
                & ( ( r3_lattices @ ( k11_conlat_1 @ A ) @ ( k8_funct_2 @ ( u1_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k4_conlat_2 @ A ) @ B ) @ ( k8_funct_2 @ ( u2_conlat_1 @ A ) @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) @ ( k5_conlat_2 @ A ) @ C ) )
                 => ( r1_conlat_1 @ A @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(76,axiom,
    ! [A: $i] :
      ( ( l1_conlat_1 @ A )
     => ( ( v2_conlat_1 @ A )
      <=> ( ( v1_xboole_0 @ ( u1_conlat_1 @ A ) )
          & ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_conlat_1) ).

thf(567,plain,
    ! [A: $i] :
      ( ( l1_conlat_1 @ A )
     => ( ( ( v2_conlat_1 @ A )
         => ( ( v1_xboole_0 @ ( u1_conlat_1 @ A ) )
            & ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) ) )
        & ( ( ( v1_xboole_0 @ ( u1_conlat_1 @ A ) )
            & ( v1_xboole_0 @ ( u2_conlat_1 @ A ) ) )
         => ( v2_conlat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(54,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_conlat_1 @ A ) )
         => ( ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ ( k1_tarski @ B ) )
            = ( a_2_2_conlat_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_conlat_1) ).

thf(477,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_conlat_1 @ A ) )
         => ( ( k1_funct_1 @ ( k1_conlat_1 @ A ) @ ( k1_tarski @ B ) )
            = ( a_2_2_conlat_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(36,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( ( k3_conlat_2 @ A @ ( k1_pre_topc @ ( k11_conlat_1 @ A ) ) )
          = ( k6_conlat_1 @ A ) )
        & ( ( k2_conlat_2 @ A @ ( k1_pre_topc @ ( k11_conlat_1 @ A ) ) )
          = ( k5_conlat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_conlat_2) ).

thf(387,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( ( k3_conlat_2 @ A @ ( k1_pre_topc @ ( k11_conlat_1 @ A ) ) )
          = ( k6_conlat_1 @ A ) )
        & ( ( k2_conlat_2 @ A @ ( k1_pre_topc @ ( k11_conlat_1 @ A ) ) )
          = ( k5_conlat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(56,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( ( k6_relset_1 @ A @ B @ ( k6_relset_1 @ A @ B @ C ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k6_relset_1) ).

thf(494,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( ( k6_relset_1 @ A @ B @ ( k6_relset_1 @ A @ B @ C ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(19,axiom,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i] :
                  ~ ( ( ( r2_hidden @ C @ A )
                      | ( r2_hidden @ D @ A ) )
                    & ( B
                      = ( k4_tarski @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_mcart_1) ).

thf(323,plain,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i] :
                  ~ ( ( ( r2_hidden @ C @ A )
                      | ( r2_hidden @ D @ A ) )
                    & ( B
                      = ( k4_tarski @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(180,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ~ ( v7_conlat_1 @ B @ A )
        & ( v9_conlat_1 @ B @ A )
        & ( l3_conlat_1 @ B @ A ) )
     => ( ( v6_conlat_1 @ ( k9_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) )
        & ~ ( v7_conlat_1 @ ( k9_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) )
        & ( v9_conlat_1 @ ( k9_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) )
        & ( l3_conlat_1 @ ( k9_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_conlat_2) ).

thf(1029,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ~ ( v7_conlat_1 @ B @ A )
        & ( v9_conlat_1 @ B @ A )
        & ( l3_conlat_1 @ B @ A ) )
     => ( ( v6_conlat_1 @ ( k9_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) )
        & ~ ( v7_conlat_1 @ ( k9_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) )
        & ( v9_conlat_1 @ ( k9_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) )
        & ( l3_conlat_1 @ ( k9_conlat_2 @ A @ B ) @ ( k7_conlat_2 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(23,axiom,
    ! [A: $i] :
      ~ ( ( A
          = ( k1_tarski @ k1_xboole_0 ) )
        & ( v1_xboole_0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_gate_1) ).

thf(345,plain,
    ! [A: $i] :
      ~ ( ( A
          = ( k1_tarski @ k1_xboole_0 ) )
        & ( v1_xboole_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(69,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
     => ? [C: $i] : ( m3_conlat_1 @ C @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_conlat_1) ).

thf(552,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
     => ? [C: $i] : ( m3_conlat_1 @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(160,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ( m1_conlat_1 @ B @ A ) )
     => ! [C: $i] :
          ( ( m2_conlat_1 @ C @ A @ B )
         => ( ~ ( v7_conlat_1 @ C @ A )
            & ( v9_conlat_1 @ C @ A )
            & ( l3_conlat_1 @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_conlat_1) ).

thf(959,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ( m1_conlat_1 @ B @ A ) )
     => ! [C: $i] :
          ( ( m2_conlat_1 @ C @ A @ B )
         => ( ~ ( v7_conlat_1 @ C @ A )
            & ( v9_conlat_1 @ C @ A )
            & ( l3_conlat_1 @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(184,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( ( ( u4_conlat_1 @ A @ B )
                = k1_xboole_0 )
             => ( B
                = ( k6_conlat_1 @ A ) ) )
            & ( ( ( u5_conlat_1 @ A @ B )
                = k1_xboole_0 )
             => ( B
                = ( k5_conlat_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_conlat_1) ).

thf(1044,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( ( ( u4_conlat_1 @ A @ B )
                = k1_xboole_0 )
             => ( B
                = ( k6_conlat_1 @ A ) ) )
            & ( ( ( u5_conlat_1 @ A @ B )
                = k1_xboole_0 )
             => ( B
                = ( k5_conlat_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(190,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( m1_conlat_1 @ B @ A )
          <=> ! [C: $i] :
                ( ( r2_hidden @ C @ B )
               => ( ~ ( v7_conlat_1 @ C @ A )
                  & ( v9_conlat_1 @ C @ A )
                  & ( l3_conlat_1 @ C @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_conlat_1) ).

thf(1066,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( ( m1_conlat_1 @ B @ A )
             => ! [C: $i] :
                  ( ( r2_hidden @ C @ B )
                 => ( ~ ( v7_conlat_1 @ C @ A )
                    & ( v9_conlat_1 @ C @ A )
                    & ( l3_conlat_1 @ C @ A ) ) ) )
            & ( ! [C: $i] :
                  ( ( r2_hidden @ C @ B )
                 => ( ~ ( v7_conlat_1 @ C @ A )
                    & ( v9_conlat_1 @ C @ A )
                    & ( l3_conlat_1 @ C @ A ) ) )
             => ( m1_conlat_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(122,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
             => ( ( r1_tarski @ B @ C )
               => ( r1_tarski @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ C ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_conlat_1) ).

thf(780,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
             => ( ( r1_tarski @ B @ C )
               => ( r1_tarski @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ C ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(176,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( r2_hidden @ B @ ( k8_conlat_1 @ A ) )
        <=> ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_conlat_1) ).

thf(1015,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( r2_hidden @ B @ ( k8_conlat_1 @ A ) )
           => ( ( v6_conlat_1 @ B @ A )
              & ~ ( v7_conlat_1 @ B @ A )
              & ( v9_conlat_1 @ B @ A )
              & ( l3_conlat_1 @ B @ A ) ) )
          & ( ( ( v6_conlat_1 @ B @ A )
              & ~ ( v7_conlat_1 @ B @ A )
              & ( v9_conlat_1 @ B @ A )
              & ( l3_conlat_1 @ B @ A ) )
           => ( r2_hidden @ B @ ( k8_conlat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(4,axiom,
    ( ( k1_zfmisc_1 @ k1_xboole_0 )
    = ( k1_tarski @ k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).

thf(226,plain,
    ( ( k1_zfmisc_1 @ k1_xboole_0 )
    = ( k1_tarski @ k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(199,axiom,
    ? [A: $i] :
      ( ( l2_conlat_1 @ A )
      & ( v4_conlat_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_conlat_1) ).

thf(1102,plain,
    ? [A: $i] :
      ( ( l2_conlat_1 @ A )
      & ( v4_conlat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(222,plain,
    ( ( k9_conlat_2 @ ( k7_conlat_2 @ sk1 ) @ ( k9_conlat_2 @ sk1 @ sk2 ) )
   != sk2 ),
    inference(cnf,[status(esa)],[214]) ).

thf(223,plain,
    ( ( k9_conlat_2 @ ( k7_conlat_2 @ sk1 ) @ ( k9_conlat_2 @ sk1 @ sk2 ) )
   != sk2 ),
    inference(lifteq,[status(thm)],[222]) ).

thf(87,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l1_conlat_1 @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
          & ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc9_conlat_1) ).

thf(608,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l1_conlat_1 @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
          & ~ ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(181,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ~ ( v3_conlat_1 @ ( k7_conlat_2 @ A ) )
        & ( v4_conlat_1 @ ( k7_conlat_2 @ A ) )
        & ( l2_conlat_1 @ ( k7_conlat_2 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_conlat_2) ).

thf(1034,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ~ ( v3_conlat_1 @ ( k7_conlat_2 @ A ) )
        & ( v4_conlat_1 @ ( k7_conlat_2 @ A ) )
        & ( l2_conlat_1 @ ( k7_conlat_2 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(426,plain,
    l1_conlat_1 @ sk32,
    inference(cnf,[status(esa)],[423]) ).

thf(67,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(548,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)],[67]) ).

thf(152,axiom,
    ! [A: $i] :
      ( ( l1_conlat_1 @ A )
     => ? [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
          & ( v6_conlat_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc10_conlat_1) ).

thf(927,plain,
    ! [A: $i] :
      ( ( l1_conlat_1 @ A )
     => ? [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
          & ( v6_conlat_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(209,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ( v6_conlat_1 @ C @ A )
                & ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ! [D: $i] :
                  ( ( ( v6_conlat_1 @ D @ A )
                    & ~ ( v7_conlat_1 @ D @ A )
                    & ( v9_conlat_1 @ D @ A )
                    & ( l3_conlat_1 @ D @ A ) )
                 => ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ C @ D ) )
                    = ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ C ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_conlat_1) ).

thf(1134,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ( v6_conlat_1 @ C @ A )
                & ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ! [D: $i] :
                  ( ( ( v6_conlat_1 @ D @ A )
                    & ~ ( v7_conlat_1 @ D @ A )
                    & ( v9_conlat_1 @ D @ A )
                    & ( l3_conlat_1 @ D @ A ) )
                 => ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ C @ D ) )
                    = ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ C ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(193,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l1_conlat_1 @ A ) )
     => ? [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
          & ( v6_conlat_1 @ B @ A )
          & ( v8_conlat_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc12_conlat_1) ).

thf(1081,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l1_conlat_1 @ A ) )
     => ? [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
          & ( v6_conlat_1 @ B @ A )
          & ( v8_conlat_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(90,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v3_conlat_1 @ B )
        & ( l2_conlat_1 @ B )
        & ( m1_subset_1 @ C @ ( u1_conlat_1 @ B ) ) )
     => ( ( r2_hidden @ A @ ( a_2_2_conlat_1 @ B @ C ) )
      <=> ? [D: $i] :
            ( ( m1_subset_1 @ D @ ( u2_conlat_1 @ B ) )
            & ( A = D )
            & ( r1_conlat_1 @ B @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_conlat_1) ).

thf(617,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v3_conlat_1 @ B )
        & ( l2_conlat_1 @ B )
        & ( m1_subset_1 @ C @ ( u1_conlat_1 @ B ) ) )
     => ( ( ( r2_hidden @ A @ ( a_2_2_conlat_1 @ B @ C ) )
         => ? [D: $i] :
              ( ( m1_subset_1 @ D @ ( u2_conlat_1 @ B ) )
              & ( A = D )
              & ( r1_conlat_1 @ B @ C @ D ) ) )
        & ( ? [D: $i] :
              ( ( m1_subset_1 @ D @ ( u2_conlat_1 @ B ) )
              & ( A = D )
              & ( r1_conlat_1 @ B @ C @ D ) )
         => ( r2_hidden @ A @ ( a_2_2_conlat_1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(154,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ( ( r2_conlat_1 @ A @ B @ C )
              <=> ( r1_tarski @ ( u4_conlat_1 @ A @ B ) @ ( u4_conlat_1 @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_conlat_1) ).

thf(939,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ( ( ( r2_conlat_1 @ A @ B @ C )
                 => ( r1_tarski @ ( u4_conlat_1 @ A @ B ) @ ( u4_conlat_1 @ A @ C ) ) )
                & ( ( r1_tarski @ ( u4_conlat_1 @ A @ B ) @ ( u4_conlat_1 @ A @ C ) )
                 => ( r2_conlat_1 @ A @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(22,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).

thf(342,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(116,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) )
      <=> ? [C: $i] :
            ( ( m1_subset_1 @ C @ B )
            & ( A = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).

thf(754,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) )
         => ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A = C ) ) )
        & ( ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A = C ) )
         => ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(185,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ( v6_conlat_1 @ C @ A )
                & ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ C )
                = ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_conlat_1) ).

thf(1049,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ( v6_conlat_1 @ C @ A )
                & ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ( ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ C )
                = ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(63,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ( ( r2_hidden @ D @ B )
                <=> ( r2_hidden @ D @ C ) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_subset_1) ).

thf(525,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ( ( ( r2_hidden @ D @ B )
                   => ( r2_hidden @ D @ C ) )
                  & ( ( r2_hidden @ D @ C )
                   => ( r2_hidden @ D @ B ) ) ) )
           => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(1003,plain,
    v4_conlat_1 @ sk77,
    inference(cnf,[status(esa)],[1002]) ).

thf(106,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v3_conlat_1 @ B )
        & ( l2_conlat_1 @ B )
        & ( m1_subset_1 @ C @ ( u2_conlat_1 @ B ) ) )
     => ( ( r2_hidden @ A @ ( a_2_3_conlat_1 @ B @ C ) )
      <=> ? [D: $i] :
            ( ( m1_subset_1 @ D @ ( u1_conlat_1 @ B ) )
            & ( A = D )
            & ( r1_conlat_1 @ B @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_conlat_1) ).

thf(690,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v3_conlat_1 @ B )
        & ( l2_conlat_1 @ B )
        & ( m1_subset_1 @ C @ ( u2_conlat_1 @ B ) ) )
     => ( ( ( r2_hidden @ A @ ( a_2_3_conlat_1 @ B @ C ) )
         => ? [D: $i] :
              ( ( m1_subset_1 @ D @ ( u1_conlat_1 @ B ) )
              & ( A = D )
              & ( r1_conlat_1 @ B @ D @ C ) ) )
        & ( ? [D: $i] :
              ( ( m1_subset_1 @ D @ ( u1_conlat_1 @ B ) )
              & ( A = D )
              & ( r1_conlat_1 @ B @ D @ C ) )
         => ( r2_hidden @ A @ ( a_2_3_conlat_1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(178,axiom,
    ? [A: $i] : ( l2_conlat_1 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_conlat_1) ).

thf(1025,plain,
    ? [A: $i] : ( l2_conlat_1 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(138,axiom,
    ! [A: $i,B: $i] :
      ( ( ( l1_conlat_1 @ A )
        & ( l3_conlat_1 @ B @ A ) )
     => ( m1_subset_1 @ ( u5_conlat_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u5_conlat_1) ).

thf(872,plain,
    ! [A: $i,B: $i] :
      ( ( ( l1_conlat_1 @ A )
        & ( l3_conlat_1 @ B @ A ) )
     => ( m1_subset_1 @ ( u5_conlat_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(14,axiom,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ( ( ( k1_tarski @ B )
             != A )
            & ! [C: $i,D: $i] :
                ~ ( ( C != D )
                  & ( r2_hidden @ C @ A )
                  & ( r2_hidden @ D @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_collsp) ).

thf(282,plain,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ( ( ( k1_tarski @ B )
             != A )
            & ! [C: $i,D: $i] :
                ~ ( ( C != D )
                  & ( r2_hidden @ C @ A )
                  & ( r2_hidden @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(142,axiom,
    v1_xboole_0 @ k1_xboole_0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(887,plain,
    v1_xboole_0 @ k1_xboole_0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B )
            = ( k1_funct_1 @ ( k2_conlat_1 @ ( k7_conlat_2 @ A ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_conlat_2) ).

thf(414,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B )
            = ( k1_funct_1 @ ( k2_conlat_1 @ ( k7_conlat_2 @ A ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(158,axiom,
    ! [A: $i] :
      ( ( ( v2_conlat_1 @ A )
        & ( l1_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ( v7_conlat_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_conlat_1) ).

thf(954,plain,
    ! [A: $i] :
      ( ( ( v2_conlat_1 @ A )
        & ( l1_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ( v7_conlat_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(11,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ ( k1_tarski @ B ) )
    <=> ( ( A = k1_xboole_0 )
        | ( A
          = ( k1_tarski @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).

thf(263,plain,
    ! [A: $i,B: $i] :
      ( ( ( r1_tarski @ A @ ( k1_tarski @ B ) )
       => ( ( A = k1_xboole_0 )
          | ( A
            = ( k1_tarski @ B ) ) ) )
      & ( ( ( A = k1_xboole_0 )
          | ( A
            = ( k1_tarski @ B ) ) )
       => ( r1_tarski @ A @ ( k1_tarski @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(993,plain,
    l2_conlat_1 @ sk76,
    inference(cnf,[status(esa)],[990]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ~ ( ( A
             != ( k1_tarski @ B ) )
            & ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ( C = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_hahnban) ).

thf(331,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ~ ( ( A
             != ( k1_tarski @ B ) )
            & ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ( C = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(49,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(441,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)],[49]) ).

thf(194,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ~ ( v1_xboole_0 @ ( k7_conlat_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_conlat_1) ).

thf(1085,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ~ ( v1_xboole_0 @ ( k7_conlat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(157,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( v4_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k7_conlat_2 @ ( k7_conlat_2 @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_conlat_2) ).

thf(951,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( v4_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k7_conlat_2 @ ( k7_conlat_2 @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
             => ( ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ C ) )
              <=> ( r1_tarski @ ( k12_mcart_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ B @ C ) @ ( u3_conlat_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_conlat_1) ).

thf(359,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
             => ( ( ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ C ) )
                 => ( r1_tarski @ ( k12_mcart_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ B @ C ) @ ( u3_conlat_1 @ A ) ) )
                & ( ( r1_tarski @ ( k12_mcart_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ B @ C ) @ ( u3_conlat_1 @ A ) )
                 => ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(643,plain,
    v1_conlat_1 @ sk48,
    inference(cnf,[status(esa)],[640]) ).

thf(182,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( m1_lattice4 @ ( k10_conlat_2 @ A ) @ ( k1_lattice2 @ ( k11_conlat_1 @ A ) ) @ ( k11_conlat_1 @ ( k7_conlat_2 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_conlat_2) ).

thf(1038,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( m1_lattice4 @ ( k10_conlat_2 @ A ) @ ( k1_lattice2 @ ( k11_conlat_1 @ A ) ) @ ( k11_conlat_1 @ ( k7_conlat_2 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(31,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ~ ( ( B != k1_xboole_0 )
          & ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ~ ( r2_hidden @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_subset_1) ).

thf(370,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ~ ( ( B != k1_xboole_0 )
          & ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ~ ( r2_hidden @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(744,plain,
    l1_conlat_1 @ sk58,
    inference(cnf,[status(esa)],[743]) ).

thf(177,axiom,
    ! [A: $i] :
      ( ( l2_conlat_1 @ A )
     => ( l1_conlat_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_conlat_1) ).

thf(1023,plain,
    ! [A: $i] :
      ( ( l2_conlat_1 @ A )
     => ( l1_conlat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(89,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(613,plain,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(186,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( ( ( u4_conlat_1 @ A @ B )
                = k1_xboole_0 )
             => ( v11_conlat_1 @ B @ A ) )
            & ( ( ( u5_conlat_1 @ A @ B )
                = k1_xboole_0 )
             => ( v10_conlat_1 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_conlat_1) ).

thf(1052,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( ( ( u4_conlat_1 @ A @ B )
                = k1_xboole_0 )
             => ( v11_conlat_1 @ B @ A ) )
            & ( ( ( u5_conlat_1 @ A @ B )
                = k1_xboole_0 )
             => ( v10_conlat_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(136,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
         => ~ ( ( B != k1_xboole_0 )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ~ ( r2_hidden @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_setwiseo) ).

thf(864,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
         => ~ ( ( B != k1_xboole_0 )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ~ ( r2_hidden @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
             => ( ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ C ) )
              <=> ( r1_tarski @ C @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_conlat_1) ).

thf(571,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
             => ( ( ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ C ) )
                 => ( r1_tarski @ C @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) )
                & ( ( r1_tarski @ C @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) )
                 => ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(83,axiom,
    ! [A: $i] :
      ( ( l1_conlat_1 @ A )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ( ( v8_conlat_1 @ B @ A )
          <=> ( ( v1_xboole_0 @ ( u4_conlat_1 @ A @ B ) )
              | ( v1_xboole_0 @ ( u5_conlat_1 @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_conlat_1) ).

thf(595,plain,
    ! [A: $i] :
      ( ( l1_conlat_1 @ A )
     => ! [B: $i] :
          ( ( l3_conlat_1 @ B @ A )
         => ( ( ( v8_conlat_1 @ B @ A )
             => ( ( v1_xboole_0 @ ( u4_conlat_1 @ A @ B ) )
                | ( v1_xboole_0 @ ( u5_conlat_1 @ A @ B ) ) ) )
            & ( ( ( v1_xboole_0 @ ( u4_conlat_1 @ A @ B ) )
                | ( v1_xboole_0 @ ( u5_conlat_1 @ A @ B ) ) )
             => ( v8_conlat_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(57,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( A
        = ( a_1_0_domain_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_domain_1) ).

thf(497,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( A
        = ( a_1_0_domain_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(991,plain,
    v4_conlat_1 @ sk76,
    inference(cnf,[status(esa)],[990]) ).

thf(166,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ( m1_conlat_1 @ B @ A ) )
     => ? [C: $i] : ( m2_conlat_1 @ C @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_conlat_1) ).

thf(978,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ( m1_conlat_1 @ B @ A ) )
     => ? [C: $i] : ( m2_conlat_1 @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(211,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ( v6_conlat_1 @ C @ A )
                & ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ C )
                = ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_conlat_1) ).

thf(1140,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ( v6_conlat_1 @ C @ A )
                & ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ B @ C )
                = ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(6,axiom,
    ! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).

thf(231,plain,
    ! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(71,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
     => ! [C: $i] :
          ( ( r1_tarski @ C @ B )
         => ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_setwiseo) ).

thf(556,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
     => ! [C: $i] :
          ( ( r1_tarski @ C @ B )
         => ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(65,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ( ( r2_hidden @ D @ B )
                 => ( r2_hidden @ D @ C ) ) )
           => ( r1_tarski @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_subset_1) ).

thf(539,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ( ( r2_hidden @ D @ B )
                 => ( r2_hidden @ D @ C ) ) )
           => ( r1_tarski @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(144,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).

thf(891,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
       => ( ( r1_tarski @ A @ B )
          & ( r1_tarski @ B @ A ) ) )
      & ( ( ( r1_tarski @ A @ B )
          & ( r1_tarski @ B @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(174,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k8_conlat_1 @ A )
        = ( k7_conlat_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_conlat_1) ).

thf(1010,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k8_conlat_1 @ A )
        = ( k7_conlat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(30,axiom,
    ! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset_1) ).

thf(368,plain,
    ! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(218,plain,
    l3_conlat_1 @ sk2 @ sk1,
    inference(cnf,[status(esa)],[214]) ).

thf(206,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( k1_conlat_2 @ A @ B )
            = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_conlat_2) ).

thf(1126,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ( ( k1_conlat_2 @ A @ B )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(80,axiom,
    ! [A: $i] :
      ( ( l2_conlat_1 @ A )
     => ( ( v4_conlat_1 @ A )
       => ( A
          = ( g2_conlat_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ ( u3_conlat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v4_conlat_1) ).

thf(588,plain,
    ! [A: $i] :
      ( ( l2_conlat_1 @ A )
     => ( ( v4_conlat_1 @ A )
       => ( A
          = ( g2_conlat_1 @ ( u1_conlat_1 @ A ) @ ( u2_conlat_1 @ A ) @ ( u3_conlat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(161,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k7_conlat_1 @ A )
        = ( a_1_0_conlat_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_conlat_1) ).

thf(963,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k7_conlat_1 @ A )
        = ( a_1_0_conlat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( k2_subset_1 @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).

thf(258,plain,
    ! [A: $i] :
      ( ( k2_subset_1 @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(94,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ k1_xboole_0 )
        = ( u1_conlat_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_conlat_1) ).

thf(632,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ k1_xboole_0 )
        = ( u1_conlat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(111,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k11_conlat_1 @ A )
        = ( g3_lattices @ ( k8_conlat_1 @ A ) @ ( k10_conlat_1 @ A ) @ ( k9_conlat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d23_conlat_1) ).

thf(731,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( k11_conlat_1 @ A )
        = ( g3_lattices @ ( k8_conlat_1 @ A ) @ ( k10_conlat_1 @ A ) @ ( k9_conlat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(64,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(536,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(15,axiom,
    ! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).

thf(290,plain,
    ! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(149,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ! [D: $i,E: $i,F: $i] :
          ( ( ( g2_conlat_1 @ A @ B @ C )
            = ( g2_conlat_1 @ D @ E @ F ) )
         => ( ( A = D )
            & ( B = E )
            & ( C = F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g2_conlat_1) ).

thf(914,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ! [D: $i,E: $i,F: $i] :
          ( ( ( g2_conlat_1 @ A @ B @ C )
            = ( g2_conlat_1 @ D @ E @ F ) )
         => ( ( A = D )
            & ( B = E )
            & ( C = F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(202,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ~ ( v7_conlat_1 @ B @ A )
        & ( v9_conlat_1 @ B @ A )
        & ( l3_conlat_1 @ B @ A ) )
     => ( ( k9_conlat_2 @ A @ B )
        = ( k8_conlat_2 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_conlat_2) ).

thf(1116,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ~ ( v7_conlat_1 @ B @ A )
        & ( v9_conlat_1 @ B @ A )
        & ( l3_conlat_1 @ B @ A ) )
     => ( ( k9_conlat_2 @ A @ B )
        = ( k8_conlat_2 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ~ ( ( r2_hidden @ C @ A )
              & ! [D: $i,E: $i] :
                  ( C
                 != ( k4_tarski @ D @ E ) ) )
        & ! [C: $i,D: $i] :
            ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
           => ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
     => ( r1_tarski @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_zfmisc_1) ).

thf(315,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ~ ( ( r2_hidden @ C @ A )
              & ! [D: $i,E: $i] :
                  ( C
                 != ( k4_tarski @ D @ E ) ) )
        & ! [C: $i,D: $i] :
            ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
           => ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
     => ( r1_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(133,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ( ? [C: $i] :
                ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
                & ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
                & ( v9_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
                & ( l3_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A ) )
          <=> ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) )
              = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_conlat_1) ).

thf(835,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ( ( ? [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
                  & ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
                  & ( v9_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
                  & ( l3_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A ) )
             => ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) )
                = B ) )
            & ( ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) )
                = B )
             => ? [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
                  & ~ ( v7_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
                  & ( v9_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A )
                  & ( l3_conlat_1 @ ( g3_conlat_1 @ A @ B @ C ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(405,plain,
    l1_conlat_1 @ sk29,
    inference(cnf,[status(esa)],[402]) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_subset_1) ).

thf(273,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ~ ( ( r2_hidden @ C @ A )
              & ! [D: $i,E: $i] :
                  ( C
                 != ( k4_tarski @ D @ E ) ) )
        & ! [C: $i] :
            ~ ( ( r2_hidden @ C @ B )
              & ! [D: $i,E: $i] :
                  ( C
                 != ( k4_tarski @ D @ E ) ) )
        & ! [C: $i,D: $i] :
            ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
          <=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t112_zfmisc_1) ).

thf(239,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ~ ( ( r2_hidden @ C @ A )
              & ! [D: $i,E: $i] :
                  ( C
                 != ( k4_tarski @ D @ E ) ) )
        & ! [C: $i] :
            ~ ( ( r2_hidden @ C @ B )
              & ! [D: $i,E: $i] :
                  ( C
                 != ( k4_tarski @ D @ E ) ) )
        & ! [C: $i,D: $i] :
            ( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
             => ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
            & ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
             => ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(127,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_conlat_1) ).

thf(801,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(60,axiom,
    ! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).

thf(506,plain,
    ! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(358,plain,
    l1_conlat_1 @ sk24,
    inference(cnf,[status(esa)],[356]) ).

thf(99,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
         => ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_conlat_1) ).

thf(664,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
         => ( r1_tarski @ B @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(39,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
         => ! [C: $i] :
              ( ( r2_hidden @ C @ B )
             => ( m1_subset_1 @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_setwiseo) ).

thf(400,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
         => ! [C: $i] :
              ( ( r2_hidden @ C @ B )
             => ( m1_subset_1 @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(131,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B )
            = ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_conlat_1) ).

thf(828,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
         => ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B )
            = ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_conlat_1 @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(95,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ B @ C )
        & ( r2_hidden @ C @ D )
        & ( r2_hidden @ D @ E )
        & ( r2_hidden @ E @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_ordinal1) ).

thf(635,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ B @ C )
        & ( r2_hidden @ C @ D )
        & ( r2_hidden @ D @ E )
        & ( r2_hidden @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(53,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u2_conlat_1 @ A ) )
         => ( ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ ( k1_tarski @ B ) )
            = ( a_2_3_conlat_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_conlat_1) ).

thf(474,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u2_conlat_1 @ A ) )
         => ( ( k1_funct_1 @ ( k2_conlat_1 @ A ) @ ( k1_tarski @ B ) )
            = ( a_2_3_conlat_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(119,axiom,
    ! [A: $i] :
      ( ( r1_tarski @ A @ k1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).

thf(767,plain,
    ! [A: $i] :
      ( ( r1_tarski @ A @ k1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(197,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( v6_conlat_1 @ ( k6_conlat_1 @ A ) @ A )
        & ~ ( v7_conlat_1 @ ( k6_conlat_1 @ A ) @ A )
        & ( v9_conlat_1 @ ( k6_conlat_1 @ A ) @ A )
        & ( v11_conlat_1 @ ( k6_conlat_1 @ A ) @ A )
        & ( l3_conlat_1 @ ( k6_conlat_1 @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_conlat_1) ).

thf(1093,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( ( v6_conlat_1 @ ( k6_conlat_1 @ A ) @ A )
        & ~ ( v7_conlat_1 @ ( k6_conlat_1 @ A ) @ A )
        & ( v9_conlat_1 @ ( k6_conlat_1 @ A ) @ A )
        & ( v11_conlat_1 @ ( k6_conlat_1 @ A ) @ A )
        & ( l3_conlat_1 @ ( k6_conlat_1 @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(51,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( l1_conlat_1 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) )
     => ! [D: $i,E: $i,F: $i] :
          ( ( ( g3_conlat_1 @ A @ B @ C )
            = ( g3_conlat_1 @ D @ E @ F ) )
         => ( ( A = D )
            & ( B = E )
            & ( C = F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_conlat_1) ).

thf(464,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( l1_conlat_1 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) ) )
     => ! [D: $i,E: $i,F: $i] :
          ( ( ( g3_conlat_1 @ A @ B @ C )
            = ( g3_conlat_1 @ D @ E @ F ) )
         => ( ( A = D )
            & ( B = E )
            & ( C = F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(207,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( m1_conlat_1 @ ( k8_conlat_1 @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_conlat_1) ).

thf(1129,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ( m1_conlat_1 @ ( k8_conlat_1 @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(644,plain,
    l1_conlat_1 @ sk48,
    inference(cnf,[status(esa)],[640]) ).

thf(992,plain,
    ~ ( v2_conlat_1 @ sk76 ),
    inference(cnf,[status(esa)],[990]) ).

thf(1004,plain,
    ~ ( v3_conlat_1 @ sk77 ),
    inference(cnf,[status(esa)],[1002]) ).

thf(1150,plain,
    ( ( v3_conlat_1 @ sk48 )
   != ( v3_conlat_1 @ sk32 ) ),
    inference(paramod_ordered,[status(thm)],[641,424]) ).

thf(1152,plain,
    sk48 != sk32,
    inference(simp,[status(thm)],[1150]) ).

thf(47,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
         => ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B )
            = ( k1_funct_1 @ ( k1_conlat_1 @ ( k7_conlat_2 @ A ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_conlat_2) ).

thf(427,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) )
         => ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ A ) ) @ ( k2_conlat_1 @ A ) @ B )
            = ( k1_funct_1 @ ( k1_conlat_1 @ ( k7_conlat_2 @ A ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(128,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ B )
        & ( l2_conlat_1 @ B ) )
     => ( ( r2_hidden @ A @ ( a_1_0_conlat_1 @ B ) )
      <=> ? [C: $i,D: $i] :
            ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) )
            & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) )
            & ( A
              = ( g3_conlat_1 @ B @ C @ D ) )
            & ~ ( v7_conlat_1 @ ( g3_conlat_1 @ B @ C @ D ) @ B )
            & ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) @ ( k1_conlat_1 @ B ) @ C )
              = D )
            & ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) @ ( k2_conlat_1 @ B ) @ D )
              = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_conlat_1) ).

thf(803,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ B )
        & ( l2_conlat_1 @ B ) )
     => ( ( ( r2_hidden @ A @ ( a_1_0_conlat_1 @ B ) )
         => ? [C: $i,D: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) )
              & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) )
              & ( A
                = ( g3_conlat_1 @ B @ C @ D ) )
              & ~ ( v7_conlat_1 @ ( g3_conlat_1 @ B @ C @ D ) @ B )
              & ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) @ ( k1_conlat_1 @ B ) @ C )
                = D )
              & ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) @ ( k2_conlat_1 @ B ) @ D )
                = C ) ) )
        & ( ? [C: $i,D: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) )
              & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) )
              & ( A
                = ( g3_conlat_1 @ B @ C @ D ) )
              & ~ ( v7_conlat_1 @ ( g3_conlat_1 @ B @ C @ D ) @ B )
              & ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) @ ( k1_conlat_1 @ B ) @ C )
                = D )
              & ( ( k8_funct_2 @ ( k1_zfmisc_1 @ ( u2_conlat_1 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_conlat_1 @ B ) ) @ ( k2_conlat_1 @ B ) @ D )
                = C ) )
         => ( r2_hidden @ A @ ( a_1_0_conlat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(21,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k1_tarski @ A ) @ B )
    <=> ( r2_hidden @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).

thf(337,plain,
    ! [A: $i,B: $i] :
      ( ( ( r1_tarski @ ( k1_tarski @ A ) @ B )
       => ( r2_hidden @ A @ B ) )
      & ( ( r2_hidden @ A @ B )
       => ( r1_tarski @ ( k1_tarski @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(922,plain,
    ~ ! [A: $i] : ( v1_xboole_0 @ A ),
    inference(miniscope,[status(thm)],[921]) ).

thf(923,plain,
    ~ ( v1_xboole_0 @ sk71 ),
    inference(cnf,[status(esa)],[922]) ).

thf(66,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
     => ! [C: $i] :
          ( ( m3_conlat_1 @ C @ A @ B )
        <=> ( m1_subset_1 @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m3_conlat_1) ).

thf(543,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_conlat_1 @ A ) ) ) ) )
     => ! [C: $i] :
          ( ( ( m3_conlat_1 @ C @ A @ B )
           => ( m1_subset_1 @ C @ B ) )
          & ( ( m1_subset_1 @ C @ B )
           => ( m3_conlat_1 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(215,plain,
    v4_conlat_1 @ sk1,
    inference(cnf,[status(esa)],[214]) ).

thf(73,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ B @ C ) )
     => ( r1_tarski @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).

thf(560,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ B @ C ) )
     => ( r1_tarski @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(164,axiom,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ( v6_conlat_1 @ C @ A )
                & ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ C ) @ C )
                = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_conlat_1) ).

thf(972,plain,
    ! [A: $i] :
      ( ( ~ ( v3_conlat_1 @ A )
        & ( l2_conlat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v6_conlat_1 @ B @ A )
            & ~ ( v7_conlat_1 @ B @ A )
            & ( v9_conlat_1 @ B @ A )
            & ( l3_conlat_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ( v6_conlat_1 @ C @ A )
                & ~ ( v7_conlat_1 @ C @ A )
                & ( v9_conlat_1 @ C @ A )
                & ( l3_conlat_1 @ C @ A ) )
             => ( ( k1_binop_1 @ ( k10_conlat_1 @ A ) @ ( k1_binop_1 @ ( k9_conlat_1 @ A ) @ B @ C ) @ C )
                = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(74185,plain,
    $false,
    inference(cvc4,[status(thm)],[645,365,1105,846,666,1110,909,628,1005,217,994,741,379,511,677,384,1137,550,500,797,698,1063,930,404,782,417,565,702,357,638,1087,969,228,261,817,902,1013,770,216,924,789,591,1040,1151,574,821,480,353,966,602,397,877,956,1072,1119,411,312,734,221,292,233,942,761,220,1057,1091,392,424,630,275,625,879,583,1027,682,224,948,1006,356,593,869,420,857,874,1143,980,403,471,225,554,669,642,686,1075,997,701,1131,1060,911,721,1002,1099,985,503,605,508,921,765,558,773,888,906,425,745,444,375,1146,430,1154,423,402,743,826,1124,562,975,641,350,672,611,787,406,831,219,880,1122,599,377,990,362,567,477,387,494,323,700,1029,345,552,959,1044,1066,780,1015,226,1102,223,608,1034,426,548,927,1134,1081,617,939,342,754,1049,525,1003,690,640,1025,872,282,887,414,954,263,993,331,441,1085,951,359,643,1038,370,744,1023,613,1052,864,571,595,497,991,978,1140,231,556,539,891,1010,368,218,1126,588,963,258,632,731,536,214,290,914,1116,315,835,405,273,239,801,506,358,664,400,828,635,474,767,1093,464,1129,644,992,1004,1152,427,803,337,923,543,215,560,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LAT345+4 : TPTP v8.1.2. Released v3.4.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n022.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Thu May 18 14:33:26 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 0.82/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 8.30/3.33  % [INFO] 	 Parsing done (2488ms). 
% 8.30/3.35  % [INFO] 	 Running in sequential loop mode. 
% 8.74/3.53  % [INFO] 	 eprover registered as external prover. 
% 8.74/3.53  % [INFO] 	 cvc4 registered as external prover. 
% 8.74/3.54  % [INFO] 	 Scanning for conjecture ... 
% 14.57/5.57  % [INFO] 	 Found a conjecture and 49824 axioms. Running axiom selection ... 
% 19.84/8.36  % [INFO] 	 Axiom selection finished. Selected 211 axioms (removed 49613 axioms). 
% 20.34/8.53  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 20.55/8.54  % [INFO] 	 Type checking passed. 
% 20.55/8.55  % [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 ... 
% 110.51/28.16  % External prover 'cvc4' found a proof!
% 110.51/28.16  % [INFO] 	 Killing All external provers ... 
% 110.65/28.16  % Time passed: 27639ms (effective reasoning time: 24808ms)
% 110.65/28.16  % 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)>
% 110.65/28.17  % Axioms used in derivation (211): dt_k9_conlat_2, fraenkel_a_1_0_domain_1, t10_conlat_2, t27_conlat_1, fc1_zfmisc_1, d1_tarski, t28_conlat_1, t24_conlat_1, t7_subset_1, rc14_conlat_1, fc2_conlat_1, t2_collsp, t3_xboole_1, t43_conlat_1, t34_conlat_1, fc1_xboole_0, t48_domain_1, t40_conlat_1, t8_subset_1, t4_ordinal1, t4_conlat_1, t1_subset, d2_conlat_1, t111_zfmisc_1, dt_k2_subset_1, d5_xboole_0, fc1_conlat_1, t9_measure1, t16_setwiseo, t21_conlat_1, rc1_conlat_1, d8_conlat_1, t1_gate_1, d2_conlat_2, dt_m1_conlat_1, t5_conlat_1, d24_conlat_1, t18_conlat_2, rc6_conlat_1, d17_conlat_1, fraenkel_a_2_1_conlat_1, existence_m2_conlat_1, abstractness_v6_conlat_1, t41_zfmisc_1, t23_conlat_1, t25_conlat_1, t11_conlat_1, t41_conlat_1, rc12_conlat_1, dt_k1_conlat_2, t1_conlat_1, t22_conlat_1, d8_conlat_2, d4_subset_1, involutiveness_k6_relset_1, dt_k2_conlat_2, existence_l3_conlat_1, d1_xboole_0, rc5_conlat_1, d9_conlat_1, t42_conlat_1, d5_conlat_1, dt_m3_conlat_1, t6_boole, dt_k10_conlat_2, rc2_subset_1, t1_xboole_1, d20_conlat_1, t36_conlat_1, d3_conlat_2, t5_subset, rc9_conlat_1, t1_yellow_8, t5_conlat_2, t4_conlat_2, existence_m1_relset_1, t1_zfmisc_1, fc2_subset_1, t79_zfmisc_1, d1_conlat_1, t18_setwiseo, t2_tarski, t37_conlat_1, d14_conlat_1, t5_ordinal1, d13_conlat_1, t4_subset, existence_l2_conlat_1, free_g3_conlat_1, t45_conlat_1, rc4_conlat_1, redefinition_m2_conlat_1, d7_conlat_2, t18_conlat_1, t32_lopclset, t7_boole, t3_ordinal1, rc7_conlat_1, d2_subset_1, t31_conlat_1, fc1_subset_1, t33_zfmisc_1, t7_ordinal1, rc1_subset_1, rc10_conlat_1, d12_conlat_1, dt_k5_conlat_1, t4_subset_1, redefinition_m3_conlat_1, t8_conlat_1, cc2_conlat_1, t3_conlat_1, t2_gate_1, t3_subset, redefinition_k9_conlat_2, t47_conlat_1, dt_g2_conlat_1, t55_subset_1, existence_m1_subset_1, t38_conlat_1, t44_setfam_1, d23_conlat_1, dt_k8_conlat_2, d1_zfmisc_1, l21_conlat_2, fraenkel_a_2_3_conlat_1, dt_k6_conlat_1, rc11_conlat_1, existence_l1_conlat_1, t19_conlat_2, dt_g3_conlat_1, d1_conlat_2, rc1_triang_1, t14_setwiseo, d3_tarski, t6_conlat_1, t2_zf_colla, t39_zfmisc_1, t35_conlat_1, fraenkel_a_1_0_conlat_1, reflexivity_r1_tarski, dt_k7_conlat_2, dt_u4_conlat_1, d18_conlat_1, t6_zfmisc_1, rc3_conlat_1, t10_conlat_1, t2_xboole_1, existence_m3_conlat_1, dt_u5_conlat_1, d16_conlat_1, t9_mcart_1, dt_k12_conlat_1, fc3_conlat_1, t10_subset_1, t26_conlat_1, t2_conlat_1, d15_conlat_1, rc15_conlat_1, t28_finsub_1, fraenkel_a_2_2_conlat_1, t3_hahnban, t26_finsub_1, t80_zfmisc_1, rc16_conlat_1, t24_zfmisc_1, t8_boole, t44_conlat_1, rc1_xboole_0, abstractness_v4_conlat_1, t37_zfmisc_1, t23_finsub_1, t6_conlat_2, t2_subset, existence_m1_conlat_1, dt_m2_conlat_1, t11_conlat_2, t33_conlat_1, t20_conlat_1, d10_xboole_0, t39_conlat_1, t32_finsub_1, t48_subset_1, t9_conlat_2, fraenkel_a_2_0_conlat_1, d11_conlat_1, rc8_conlat_1, t6_ordinal1, d19_conlat_1, redefinition_k8_conlat_1, t49_subset_1, t7_tarski, free_g2_conlat_1, t7_conlat_1, cc1_conlat_1, dt_k7_conlat_1, dt_k8_conlat_1, rc2_xboole_0, t112_zfmisc_1, t9_conlat_1, t13_conlat_2, fraenkel_a_2_0_closure1, dt_k3_conlat_2, dt_l2_conlat_1, t19_conlat_1, t63_subset_1, rc13_conlat_1, antisymmetry_r2_hidden, t17_conlat_2, rc2_conlat_1, t1_closure1
% 110.65/28.17  % No. of inferences in proof: 470
% 110.65/28.17  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 27639 ms resp. 24808 ms w/o parsing
% 110.77/28.31  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 110.77/28.32  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------