SET007 Axioms: SET007+311.ax


%------------------------------------------------------------------------------
% File     : SET007+311 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Categories of Groups
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : grcat_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  185 (  14 unit)
%            Number of atoms       : 1405 ( 135 equality)
%            Maximal formula depth :   23 (   8 average)
%            Number of connectives : 1447 ( 227 ~  ;   0  |; 850  &)
%                                         (  31 <=>; 339 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   49 (   1 propositional; 0-4 arity)
%            Number of functors    :   93 (  11 constant; 0-6 arity)
%            Number of variables   :  436 (   0 singleton; 395 !;  41 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_grcat_1,axiom,
    ( ~ v3_struct_0(k2_algstr_1)
    & v1_rlvect_1(k2_algstr_1)
    & v3_rlvect_1(k2_algstr_1)
    & v4_rlvect_1(k2_algstr_1)
    & v5_rlvect_1(k2_algstr_1)
    & v6_rlvect_1(k2_algstr_1)
    & v13_vectsp_1(k2_algstr_1)
    & v1_midsp_2(k2_algstr_1)
    & v1_algstr_1(k2_algstr_1)
    & v2_algstr_1(k2_algstr_1)
    & v3_algstr_1(k2_algstr_1)
    & v4_algstr_1(k2_algstr_1)
    & v5_algstr_1(k2_algstr_1)
    & v6_algstr_1(k2_algstr_1) )).

fof(fc2_grcat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
     => ~ v1_xboole_0(k1_grcat_1(A,B)) ) )).

fof(fc3_grcat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
     => ( v1_cat_1(k6_grcat_1(A,B))
        & v2_cat_1(k6_grcat_1(A,B)) ) ) )).

fof(rc1_grcat_1,axiom,(
    ? [A] :
      ( l1_grcat_1(A)
      & v2_grcat_1(A) ) )).

fof(fc4_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => v2_grcat_1(k12_grcat_1(A,B)) ) )).

fof(rc2_grcat_1,axiom,(
    ? [A] :
      ( l1_grcat_1(A)
      & v2_grcat_1(A)
      & v3_grcat_1(A) ) )).

fof(fc5_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => ( v2_grcat_1(k12_grcat_1(A,B))
        & v3_grcat_1(k12_grcat_1(A,B)) ) ) )).

fof(rc3_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => ? [C] :
          ( m1_grcat_1(C,A,B)
          & v2_grcat_1(C)
          & v3_grcat_1(C) ) ) )).

fof(fc6_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ( v2_grcat_1(k13_grcat_1(A))
        & v3_grcat_1(k13_grcat_1(A)) ) ) )).

fof(rc4_grcat_1,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v4_grcat_1(A) ) )).

fof(rc5_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ? [B] :
          ( m1_subset_1(B,A)
          & ~ v3_struct_0(B)
          & v1_rlvect_1(B)
          & v4_rlvect_1(B)
          & v5_rlvect_1(B)
          & v6_rlvect_1(B)
          & v1_algstr_1(B)
          & v2_algstr_1(B)
          & v3_algstr_1(B)
          & v4_algstr_1(B)
          & v5_algstr_1(B)
          & v6_algstr_1(B) ) ) )).

fof(rc6_grcat_1,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v5_grcat_1(A) ) )).

fof(rc7_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v5_grcat_1(A) )
     => ? [B] :
          ( m1_subset_1(B,A)
          & v2_grcat_1(B)
          & v3_grcat_1(B) ) ) )).

fof(fc7_grcat_1,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B) )
     => ~ v1_xboole_0(k17_grcat_1(A,B)) ) )).

fof(rc8_grcat_1,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B) )
     => ? [C] :
          ( m5_grcat_1(C,A,B)
          & ~ v1_xboole_0(C) ) ) )).

fof(rc9_grcat_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B)
        & m4_grcat_1(C,A,B) )
     => ? [D] :
          ( m1_subset_1(D,C)
          & v2_grcat_1(D)
          & v3_grcat_1(D) ) ) )).

fof(fc8_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ~ v1_xboole_0(k19_grcat_1(A)) ) )).

fof(fc9_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( ~ v1_xboole_0(k19_grcat_1(A))
        & v4_grcat_1(k19_grcat_1(A)) ) ) )).

fof(fc10_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => v1_cat_1(k28_grcat_1(A)) ) )).

fof(fc11_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( v1_cat_1(k28_grcat_1(A))
        & v2_cat_1(k28_grcat_1(A)) ) ) )).

fof(fc12_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ~ v1_xboole_0(k29_grcat_1(A)) ) )).

fof(fc13_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( v1_cat_1(k30_grcat_1(A))
        & v2_cat_1(k30_grcat_1(A)) ) ) )).

fof(fc14_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ~ v1_xboole_0(k31_grcat_1(A)) ) )).

fof(fc15_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( v1_cat_1(k32_grcat_1(A))
        & v2_cat_1(k32_grcat_1(A)) ) ) )).

fof(t1_grcat_1,axiom,(
    $true )).

fof(t2_grcat_1,axiom,(
    ! [A,B,C,D] :
      ~ ( r2_hidden(D,C)
        & r1_tarski(C,k2_zfmisc_1(A,B))
        & ! [E] :
            ( m1_subset_1(E,A)
           => ! [F] :
                ( m1_subset_1(F,B)
               => D != k4_tarski(E,F) ) ) ) )).

fof(t3_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ( m1_subset_1(k3_mcart_1(B,C,D),A)
                        & m1_subset_1(k4_mcart_1(B,C,D,E),A) ) ) ) ) ) ) )).

fof(t4_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B,C] :
          ( ( r2_hidden(B,C)
            & r2_hidden(C,A) )
         => r2_hidden(B,A) ) ) )).

fof(t5_grcat_1,axiom,
    ( k1_binop_1(k2_midsp_1,k1_xboole_0,k1_xboole_0) = k1_xboole_0
    & k1_funct_1(k7_vectsp_2,k1_xboole_0) = k1_xboole_0
    & k8_vectsp_2 = k1_xboole_0 )).

fof(t6_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( r2_hidden(k1_tarski(k1_xboole_0),A)
        & r2_hidden(k4_tarski(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),A)
        & r2_hidden(k2_zfmisc_1(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),A)
        & r2_hidden(k2_midsp_1,A)
        & r2_hidden(k7_vectsp_2,A) ) ) )).

fof(t7_grcat_1,axiom,(
    v1_midsp_2(g1_rlvect_1(k1_tarski(k1_xboole_0),k2_midsp_1,k1_algstr_1(k1_xboole_0))) )).

fof(t8_grcat_1,axiom,
    ( ! [A] :
        ( m1_subset_1(A,u1_struct_0(k2_algstr_1))
       => A = k1_xboole_0 )
    & ! [A] :
        ( m1_subset_1(A,u1_struct_0(k2_algstr_1))
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k2_algstr_1))
           => k4_rlvect_1(k2_algstr_1,A,B) = k1_xboole_0 ) )
    & ! [A] :
        ( m1_subset_1(A,u1_struct_0(k2_algstr_1))
       => k5_rlvect_1(k2_algstr_1,A) = k1_xboole_0 )
    & k1_rlvect_1(k2_algstr_1) = k1_xboole_0 )).

fof(d1_grcat_1,axiom,(
    $true )).

fof(d2_grcat_1,axiom,(
    $true )).

fof(d3_grcat_1,axiom,(
    $true )).

fof(d4_grcat_1,axiom,(
    $true )).

fof(d6_grcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
         => k2_grcat_1(A,B) = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k1_grcat_1(A,B)) ) ) )).

fof(d7_grcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
         => k3_grcat_1(A,B) = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k1_grcat_1(A,B)) ) ) )).

fof(d8_grcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
         => k4_grcat_1(A,B) = k1_realset1(u5_cat_1(A),k1_grcat_1(A,B)) ) ) )).

fof(d9_grcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
         => k5_grcat_1(A,B) = k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) ) ) )).

fof(t9_grcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
         => r1_cat_2(g1_cat_1(B,k1_grcat_1(A,B),k2_grcat_1(A,B),k3_grcat_1(A,B),k4_grcat_1(A,B),k5_grcat_1(A,B)),A) ) ) )).

fof(d10_grcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
         => k6_grcat_1(A,B) = g1_cat_1(B,k1_grcat_1(A,B),k2_grcat_1(A,B),k3_grcat_1(A,B),k4_grcat_1(A,B),k5_grcat_1(A,B)) ) ) )).

fof(t10_grcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
         => u1_cat_1(k6_grcat_1(A,B)) = B ) ) )).

fof(d11_grcat_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => k7_grcat_1(A) = k6_partfun1(u1_struct_0(A)) ) )).

fof(t11_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k8_funct_2(u1_struct_0(A),u1_struct_0(A),k7_grcat_1(A),B) = B ) ) )).

fof(t12_grcat_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_struct_0(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( k1_partfun1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),k7_grcat_1(A),C) = C
                & k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),C,k7_grcat_1(B)) = C ) ) ) ) )).

fof(d12_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l2_struct_0(B) )
         => k8_grcat_1(A,B) = k2_funcop_1(u1_struct_0(A),k1_rlvect_1(B)) ) ) )).

fof(d13_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v1_grcat_1(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k2_rlvect_1(A,D,E)) = k2_rlvect_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) ) ) ) ) ) )).

fof(t13_grcat_1,axiom,(
    k7_vectsp_1(k2_algstr_1) = k7_vectsp_2 )).

fof(t14_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_rlvect_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ( ( v1_grcat_1(D,A,B)
                          & v1_grcat_1(E,B,C) )
                       => v1_grcat_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) )).

fof(t15_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k8_funct_2(u1_struct_0(A),u1_struct_0(B),k8_grcat_1(A,B),C) = k1_rlvect_1(B) ) ) ) )).

fof(t16_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v5_rlvect_1(B)
            & l1_rlvect_1(B) )
         => v1_grcat_1(k8_grcat_1(A,B),A,B) ) ) )).

fof(d14_grcat_1,axiom,(
    ! [A] :
      ( l1_grcat_1(A)
     => k9_grcat_1(A) = u1_grcat_1(A) ) )).

fof(d15_grcat_1,axiom,(
    ! [A] :
      ( l1_grcat_1(A)
     => k10_grcat_1(A) = u2_grcat_1(A) ) )).

fof(d16_grcat_1,axiom,(
    ! [A] :
      ( l1_grcat_1(A)
     => k11_grcat_1(A) = u3_grcat_1(A) ) )).

fof(t17_grcat_1,axiom,(
    ! [A] :
      ( l1_grcat_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_1(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
                 => ( A = g1_grcat_1(B,C,D)
                   => ( k9_grcat_1(A) = B
                      & k10_grcat_1(A) = C
                      & k11_grcat_1(A) = D ) ) ) ) ) ) )).

fof(d17_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => k12_grcat_1(A,B) = g1_grcat_1(A,B,k8_grcat_1(A,B)) ) ) )).

fof(d18_grcat_1,axiom,(
    ! [A] :
      ( l1_grcat_1(A)
     => ( v3_grcat_1(A)
      <=> v1_grcat_1(k11_grcat_1(A),k9_grcat_1(A),k10_grcat_1(A)) ) ) )).

fof(t18_grcat_1,axiom,(
    ! [A] :
      ( ( v3_grcat_1(A)
        & l1_grcat_1(A) )
     => v1_grcat_1(u3_grcat_1(A),u1_grcat_1(A),u2_grcat_1(A)) ) )).

fof(d19_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v3_grcat_1(C)
                & l1_grcat_1(C) )
             => ( m1_grcat_1(C,A,B)
              <=> ( k9_grcat_1(C) = A
                  & k10_grcat_1(C) = B ) ) ) ) ) )).

fof(t19_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v2_grcat_1(C)
                & l1_grcat_1(C) )
             => ( ( k9_grcat_1(C) = A
                  & k10_grcat_1(C) = B
                  & v1_grcat_1(k11_grcat_1(C),k9_grcat_1(C),k10_grcat_1(C)) )
               => ( v2_grcat_1(C)
                  & m1_grcat_1(C,A,B) ) ) ) ) ) )).

fof(t20_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v1_grcat_1(C,A,B)
               => ( v2_grcat_1(g1_grcat_1(A,B,C))
                  & m1_grcat_1(g1_grcat_1(A,B,C),A,B) ) ) ) ) ) )).

fof(t21_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => v1_grcat_1(k7_grcat_1(A),A,A) ) )).

fof(d20_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => k13_grcat_1(A) = g1_grcat_1(A,A,k7_grcat_1(A)) ) )).

fof(t22_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m1_grcat_1(C,A,B)
             => ? [D] :
                  ( v1_funct_1(D)
                  & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                  & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B))
                  & g1_grcat_1(u1_grcat_1(C),u2_grcat_1(C),u3_grcat_1(C)) = g1_grcat_1(A,B,D)
                  & v1_grcat_1(D,A,B) ) ) ) ) )).

fof(t23_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v2_grcat_1(C)
                & m1_grcat_1(C,A,B) )
             => ? [D] :
                  ( v1_funct_1(D)
                  & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                  & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B))
                  & C = g1_grcat_1(A,B,D) ) ) ) ) )).

fof(t24_grcat_1,axiom,(
    ! [A] :
      ( ( v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ? [B] :
          ( ~ v3_struct_0(B)
          & v4_rlvect_1(B)
          & v5_rlvect_1(B)
          & v6_rlvect_1(B)
          & l1_rlvect_1(B)
          & ? [C] :
              ( ~ v3_struct_0(C)
              & v4_rlvect_1(C)
              & v5_rlvect_1(C)
              & v6_rlvect_1(C)
              & l1_rlvect_1(C)
              & m1_grcat_1(A,B,C) ) ) ) )).

fof(t25_grcat_1,axiom,(
    ! [A] :
      ( ( v2_grcat_1(A)
        & v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ? [B] :
          ( ~ v3_struct_0(B)
          & v4_rlvect_1(B)
          & v5_rlvect_1(B)
          & v6_rlvect_1(B)
          & l1_rlvect_1(B)
          & ? [C] :
              ( ~ v3_struct_0(C)
              & v4_rlvect_1(C)
              & v5_rlvect_1(C)
              & v6_rlvect_1(C)
              & l1_rlvect_1(C)
              & ? [D] :
                  ( v1_funct_1(D)
                  & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                  & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C))
                  & m1_grcat_1(A,B,C)
                  & A = g1_grcat_1(B,C,D)
                  & v1_grcat_1(D,B,C) ) ) ) ) )).

fof(t26_grcat_1,axiom,(
    ! [A] :
      ( ( v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ! [B] :
          ( ( v3_grcat_1(B)
            & l1_grcat_1(B) )
         => ~ ( k9_grcat_1(A) = k10_grcat_1(B)
              & ! [C] :
                  ( ( ~ v3_struct_0(C)
                    & v4_rlvect_1(C)
                    & v5_rlvect_1(C)
                    & v6_rlvect_1(C)
                    & l1_rlvect_1(C) )
                 => ! [D] :
                      ( ( ~ v3_struct_0(D)
                        & v4_rlvect_1(D)
                        & v5_rlvect_1(D)
                        & v6_rlvect_1(D)
                        & l1_rlvect_1(D) )
                     => ! [E] :
                          ( ( ~ v3_struct_0(E)
                            & v4_rlvect_1(E)
                            & v5_rlvect_1(E)
                            & v6_rlvect_1(E)
                            & l1_rlvect_1(E) )
                         => ~ ( m1_grcat_1(A,D,E)
                              & m1_grcat_1(B,C,D) ) ) ) ) ) ) ) )).

fof(d21_grcat_1,axiom,(
    ! [A] :
      ( ( v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ! [B] :
          ( ( v3_grcat_1(B)
            & l1_grcat_1(B) )
         => ( k9_grcat_1(A) = k10_grcat_1(B)
           => ! [C] :
                ( ( v2_grcat_1(C)
                  & v3_grcat_1(C)
                  & l1_grcat_1(C) )
               => ( C = k15_grcat_1(A,B)
                <=> ! [D] :
                      ( ( ~ v3_struct_0(D)
                        & v4_rlvect_1(D)
                        & v5_rlvect_1(D)
                        & v6_rlvect_1(D)
                        & l1_rlvect_1(D) )
                     => ! [E] :
                          ( ( ~ v3_struct_0(E)
                            & v4_rlvect_1(E)
                            & v5_rlvect_1(E)
                            & v6_rlvect_1(E)
                            & l1_rlvect_1(E) )
                         => ! [F] :
                              ( ( ~ v3_struct_0(F)
                                & v4_rlvect_1(F)
                                & v5_rlvect_1(F)
                                & v6_rlvect_1(F)
                                & l1_rlvect_1(F) )
                             => ! [G] :
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,u1_struct_0(E),u1_struct_0(F))
                                    & m2_relset_1(G,u1_struct_0(E),u1_struct_0(F)) )
                                 => ! [H] :
                                      ( ( v1_funct_1(H)
                                        & v1_funct_2(H,u1_struct_0(D),u1_struct_0(E))
                                        & m2_relset_1(H,u1_struct_0(D),u1_struct_0(E)) )
                                     => ( ( g1_grcat_1(u1_grcat_1(A),u2_grcat_1(A),u3_grcat_1(A)) = g1_grcat_1(E,F,G)
                                          & g1_grcat_1(u1_grcat_1(B),u2_grcat_1(B),u3_grcat_1(B)) = g1_grcat_1(D,E,H) )
                                       => C = g1_grcat_1(D,F,k7_funct_2(u1_struct_0(D),u1_struct_0(E),u1_struct_0(F),H,G)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t27_grcat_1,axiom,(
    $true )).

fof(t28_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_1(C) )
             => ! [D] :
                  ( m1_grcat_1(D,B,C)
                 => ! [E] :
                      ( m1_grcat_1(E,A,B)
                     => m1_grcat_1(k15_grcat_1(D,E),A,C) ) ) ) ) ) )).

fof(t29_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_1(C) )
             => ! [D] :
                  ( m1_grcat_1(D,B,C)
                 => ! [E] :
                      ( m1_grcat_1(E,A,B)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(C))
                            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(C)) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,u1_struct_0(A),u1_struct_0(B))
                                & m2_relset_1(G,u1_struct_0(A),u1_struct_0(B)) )
                             => ( ( D = g1_grcat_1(B,C,F)
                                  & E = g1_grcat_1(A,B,G) )
                               => k16_grcat_1(A,B,C,D,E) = g1_grcat_1(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),G,F)) ) ) ) ) ) ) ) ) )).

fof(t30_grcat_1,axiom,(
    ! [A] :
      ( ( v2_grcat_1(A)
        & v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ! [B] :
          ( ( v2_grcat_1(B)
            & v3_grcat_1(B)
            & l1_grcat_1(B) )
         => ~ ( k9_grcat_1(B) = k10_grcat_1(A)
              & ! [C] :
                  ( ( ~ v3_struct_0(C)
                    & v4_rlvect_1(C)
                    & v5_rlvect_1(C)
                    & v6_rlvect_1(C)
                    & l1_rlvect_1(C) )
                 => ! [D] :
                      ( ( ~ v3_struct_0(D)
                        & v4_rlvect_1(D)
                        & v5_rlvect_1(D)
                        & v6_rlvect_1(D)
                        & l1_rlvect_1(D) )
                     => ! [E] :
                          ( ( ~ v3_struct_0(E)
                            & v4_rlvect_1(E)
                            & v5_rlvect_1(E)
                            & v6_rlvect_1(E)
                            & l1_rlvect_1(E) )
                         => ! [F] :
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
                                & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
                             => ! [G] :
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,u1_struct_0(D),u1_struct_0(E))
                                    & m2_relset_1(G,u1_struct_0(D),u1_struct_0(E)) )
                                 => ~ ( A = g1_grcat_1(C,D,F)
                                      & B = g1_grcat_1(D,E,G)
                                      & k15_grcat_1(B,A) = g1_grcat_1(C,E,k7_funct_2(u1_struct_0(C),u1_struct_0(D),u1_struct_0(E),F,G)) ) ) ) ) ) ) ) ) ) )).

fof(t31_grcat_1,axiom,(
    ! [A] :
      ( ( v2_grcat_1(A)
        & v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ! [B] :
          ( ( v2_grcat_1(B)
            & v3_grcat_1(B)
            & l1_grcat_1(B) )
         => ( k9_grcat_1(B) = k10_grcat_1(A)
           => ( k9_grcat_1(k15_grcat_1(B,A)) = k9_grcat_1(A)
              & k10_grcat_1(k15_grcat_1(B,A)) = k10_grcat_1(B) ) ) ) ) )).

fof(t32_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_1(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v4_rlvect_1(D)
                    & v5_rlvect_1(D)
                    & v6_rlvect_1(D)
                    & l1_rlvect_1(D) )
                 => ! [E] :
                      ( ( v2_grcat_1(E)
                        & m1_grcat_1(E,A,B) )
                     => ! [F] :
                          ( ( v2_grcat_1(F)
                            & m1_grcat_1(F,B,C) )
                         => ! [G] :
                              ( ( v2_grcat_1(G)
                                & m1_grcat_1(G,C,D) )
                             => k16_grcat_1(A,C,D,G,k16_grcat_1(A,B,C,F,E)) = k16_grcat_1(A,B,D,k16_grcat_1(B,C,D,G,F),E) ) ) ) ) ) ) ) )).

fof(t33_grcat_1,axiom,(
    ! [A] :
      ( ( v2_grcat_1(A)
        & v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ! [B] :
          ( ( v2_grcat_1(B)
            & v3_grcat_1(B)
            & l1_grcat_1(B) )
         => ! [C] :
              ( ( v2_grcat_1(C)
                & v3_grcat_1(C)
                & l1_grcat_1(C) )
             => ( ( k9_grcat_1(C) = k10_grcat_1(B)
                  & k9_grcat_1(B) = k10_grcat_1(A) )
               => k15_grcat_1(C,k15_grcat_1(B,A)) = k15_grcat_1(k15_grcat_1(C,B),A) ) ) ) ) )).

fof(t34_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ( k9_grcat_1(k13_grcat_1(A)) = A
        & k10_grcat_1(k13_grcat_1(A)) = A
        & ! [B] :
            ( ( v2_grcat_1(B)
              & v3_grcat_1(B)
              & l1_grcat_1(B) )
           => ( k10_grcat_1(B) = A
             => k15_grcat_1(k13_grcat_1(A),B) = B ) )
        & ! [B] :
            ( ( v2_grcat_1(B)
              & v3_grcat_1(B)
              & l1_grcat_1(B) )
           => ( k9_grcat_1(B) = A
             => k15_grcat_1(B,k13_grcat_1(A)) = B ) ) ) ) )).

fof(d22_grcat_1,axiom,(
    ! [A] :
      ( v4_grcat_1(A)
    <=> ! [B] :
          ( r2_hidden(B,A)
         => ( ~ v3_struct_0(B)
            & v1_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) ) ) ) )).

fof(d23_grcat_1,axiom,(
    ! [A] :
      ( v5_grcat_1(A)
    <=> ! [B] :
          ( r2_hidden(B,A)
         => ( v2_grcat_1(B)
            & v3_grcat_1(B)
            & l1_grcat_1(B) ) ) ) )).

fof(t35_grcat_1,axiom,(
    $true )).

fof(t36_grcat_1,axiom,(
    $true )).

fof(t37_grcat_1,axiom,(
    ! [A] :
      ( ( v2_grcat_1(A)
        & v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v5_grcat_1(k1_tarski(A)) ) ) )).

fof(d24_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v5_grcat_1(C) )
             => ( m4_grcat_1(C,A,B)
              <=> ! [D] :
                    ( m3_grcat_1(D,C)
                   => ( v2_grcat_1(D)
                      & m1_grcat_1(D,A,B) ) ) ) ) ) ) )).

fof(t38_grcat_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_1(C) )
             => ( m4_grcat_1(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,A)
                   => ( v2_grcat_1(D)
                      & m1_grcat_1(D,B,C) ) ) ) ) ) ) )).

fof(t39_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( ( v2_grcat_1(C)
                & m1_grcat_1(C,A,B) )
             => m4_grcat_1(k1_tarski(C),A,B) ) ) ) )).

fof(d25_grcat_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_struct_0(B)
         => ! [C] :
              ( m5_grcat_1(C,A,B)
            <=> ! [D] :
                  ( r2_hidden(D,C)
                 => ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ) )).

fof(d26_grcat_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_struct_0(B)
         => k17_grcat_1(A,B) = k1_funct_2(u1_struct_0(A),u1_struct_0(B)) ) ) )).

fof(d27_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] :
              ( m4_grcat_1(C,A,B)
             => ( C = k18_grcat_1(A,B)
              <=> ! [D] :
                    ( r2_hidden(D,C)
                  <=> ( v2_grcat_1(D)
                      & m1_grcat_1(D,A,B) ) ) ) ) ) ) )).

fof(d28_grcat_1,axiom,(
    ! [A,B] :
      ( r1_grcat_1(A,B)
    <=> ? [C,D,E,F] :
          ( A = k4_mcart_1(C,D,E,F)
          & ? [G] :
              ( ~ v3_struct_0(G)
              & v1_rlvect_1(G)
              & v4_rlvect_1(G)
              & v5_rlvect_1(G)
              & v6_rlvect_1(G)
              & l1_rlvect_1(G)
              & B = G
              & C = u1_struct_0(G)
              & D = u1_rlvect_1(G)
              & E = k7_vectsp_1(G)
              & F = u2_struct_0(G) ) ) ) )).

fof(t40_grcat_1,axiom,(
    ! [A,B,C] :
      ( ( r1_grcat_1(A,B)
        & r1_grcat_1(A,C) )
     => B = C ) )).

fof(t41_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] :
          ( r2_hidden(B,A)
          & r1_grcat_1(B,k2_algstr_1) ) ) )).

fof(d29_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] :
          ( B = k19_grcat_1(A)
        <=> ! [C] :
              ( r2_hidden(C,B)
            <=> ? [D] :
                  ( r2_hidden(D,A)
                  & r1_grcat_1(D,C) ) ) ) ) )).

fof(t42_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => r2_hidden(k2_algstr_1,k19_grcat_1(A)) ) )).

fof(t43_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] :
          ( m1_subset_1(B,k19_grcat_1(A))
         => ( ~ v3_struct_0(B)
            & v1_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) ) ) ) )).

fof(d30_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v5_grcat_1(B) )
         => ( B = k20_grcat_1(A)
          <=> ! [C] :
                ( r2_hidden(C,B)
              <=> ? [D] :
                    ( v1_rlvect_1(D)
                    & m2_grcat_1(D,A)
                    & ? [E] :
                        ( v1_rlvect_1(E)
                        & m2_grcat_1(E,A)
                        & v2_grcat_1(C)
                        & m1_grcat_1(C,D,E) ) ) ) ) ) ) )).

fof(d31_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] :
          ( m2_grcat_1(B,A)
         => k23_grcat_1(A,B) = k13_grcat_1(B) ) ) )).

fof(d32_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k20_grcat_1(A),A)
            & m2_relset_1(B,k20_grcat_1(A),A) )
         => ( B = k24_grcat_1(A)
          <=> ! [C] :
                ( m3_grcat_1(C,k20_grcat_1(A))
               => k8_funct_2(k20_grcat_1(A),A,B,C) = k21_grcat_1(A,C) ) ) ) ) )).

fof(d33_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k20_grcat_1(A),A)
            & m2_relset_1(B,k20_grcat_1(A),A) )
         => ( B = k25_grcat_1(A)
          <=> ! [C] :
                ( m3_grcat_1(C,k20_grcat_1(A))
               => k8_funct_2(k20_grcat_1(A),A,B,C) = k22_grcat_1(A,C) ) ) ) ) )).

fof(d34_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k20_grcat_1(A))
            & m2_relset_1(B,A,k20_grcat_1(A)) )
         => ( B = k26_grcat_1(A)
          <=> ! [C] :
                ( m2_grcat_1(C,A)
               => k8_funct_2(A,k20_grcat_1(A),B,C) = k23_grcat_1(A,C) ) ) ) ) )).

fof(t44_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] :
          ( m3_grcat_1(B,k20_grcat_1(A))
         => ! [C] :
              ( m3_grcat_1(C,k20_grcat_1(A))
             => ~ ( k21_grcat_1(A,B) = k22_grcat_1(A,C)
                  & ! [D] :
                      ( ( v1_rlvect_1(D)
                        & m2_grcat_1(D,A) )
                     => ! [E] :
                          ( ( v1_rlvect_1(E)
                            & m2_grcat_1(E,A) )
                         => ! [F] :
                              ( ( v1_rlvect_1(F)
                                & m2_grcat_1(F,A) )
                             => ~ ( m1_grcat_1(B,E,F)
                                  & m1_grcat_1(C,D,E) ) ) ) ) ) ) ) ) )).

fof(t45_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] :
          ( m3_grcat_1(B,k20_grcat_1(A))
         => ! [C] :
              ( m3_grcat_1(C,k20_grcat_1(A))
             => ( k21_grcat_1(A,B) = k22_grcat_1(A,C)
               => r2_hidden(k15_grcat_1(B,C),k20_grcat_1(A)) ) ) ) ) )).

fof(d35_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k2_zfmisc_1(k20_grcat_1(A),k20_grcat_1(A)),k20_grcat_1(A)) )
         => ( B = k27_grcat_1(A)
          <=> ( ! [C] :
                  ( m3_grcat_1(C,k20_grcat_1(A))
                 => ! [D] :
                      ( m3_grcat_1(D,k20_grcat_1(A))
                     => ( r2_hidden(k4_tarski(C,D),k1_relat_1(B))
                      <=> k21_grcat_1(A,C) = k22_grcat_1(A,D) ) ) )
              & ! [C] :
                  ( m3_grcat_1(C,k20_grcat_1(A))
                 => ! [D] :
                      ( m3_grcat_1(D,k20_grcat_1(A))
                     => ( r2_hidden(k4_tarski(C,D),k1_relat_1(B))
                       => k1_funct_1(B,k4_tarski(C,D)) = k15_grcat_1(C,D) ) ) ) ) ) ) ) )).

fof(d36_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => k28_grcat_1(A) = g1_cat_1(k19_grcat_1(A),k20_grcat_1(k19_grcat_1(A)),k24_grcat_1(k19_grcat_1(A)),k25_grcat_1(k19_grcat_1(A)),k27_grcat_1(k19_grcat_1(A)),k26_grcat_1(k19_grcat_1(A))) ) )).

fof(t46_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(k28_grcat_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(k28_grcat_1(A)))
             => ( r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(k28_grcat_1(A))))
              <=> k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) ) ) ) ) )).

fof(t47_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(k28_grcat_1(A)))
         => ! [C] :
              ( m3_grcat_1(C,k20_grcat_1(k19_grcat_1(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(k28_grcat_1(A)))
                 => ! [E] :
                      ( m2_grcat_1(E,k19_grcat_1(A))
                     => ( v2_grcat_1(B)
                        & m3_grcat_1(B,k20_grcat_1(k19_grcat_1(A)))
                        & m1_subset_1(C,u2_cat_1(k28_grcat_1(A)))
                        & v1_rlvect_1(D)
                        & m2_grcat_1(D,k19_grcat_1(A))
                        & m1_subset_1(E,u1_cat_1(k28_grcat_1(A))) ) ) ) ) ) ) )).

fof(t48_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_cat_1(k28_grcat_1(A)))
         => ! [C] :
              ( m2_grcat_1(C,k19_grcat_1(A))
             => ( B = C
               => k5_cat_1(k28_grcat_1(A),B) = k23_grcat_1(k19_grcat_1(A),C) ) ) ) ) )).

fof(t49_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(k28_grcat_1(A)))
         => ! [C] :
              ( m3_grcat_1(C,k20_grcat_1(k19_grcat_1(A)))
             => ( B = C
               => ( k2_cat_1(k28_grcat_1(A),B) = k21_grcat_1(k19_grcat_1(A),C)
                  & k3_cat_1(k28_grcat_1(A),B) = k22_grcat_1(k19_grcat_1(A),C) ) ) ) ) ) )).

fof(t50_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] :
          ( m1_subset_1(B,u2_cat_1(k28_grcat_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(k28_grcat_1(A)))
             => ! [D] :
                  ( m3_grcat_1(D,k20_grcat_1(k19_grcat_1(A)))
                 => ! [E] :
                      ( m3_grcat_1(E,k20_grcat_1(k19_grcat_1(A)))
                     => ( ( B = D
                          & C = E )
                       => ( ( k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B)
                           => k21_grcat_1(k19_grcat_1(A),E) = k22_grcat_1(k19_grcat_1(A),D) )
                          & ( k21_grcat_1(k19_grcat_1(A),E) = k22_grcat_1(k19_grcat_1(A),D)
                           => k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) )
                          & ( k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B)
                           => r2_hidden(k4_tarski(E,D),k1_relat_1(k27_grcat_1(k19_grcat_1(A)))) )
                          & ( r2_hidden(k4_tarski(E,D),k1_relat_1(k27_grcat_1(k19_grcat_1(A))))
                           => k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) )
                          & ( k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B)
                           => k4_cat_1(k28_grcat_1(A),B,C) = k15_grcat_1(E,D) )
                          & ( k2_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C)
                           => k21_grcat_1(k19_grcat_1(A),D) = k21_grcat_1(k19_grcat_1(A),E) )
                          & ( k21_grcat_1(k19_grcat_1(A),D) = k21_grcat_1(k19_grcat_1(A),E)
                           => k2_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C) )
                          & ( k3_cat_1(k28_grcat_1(A),B) = k3_cat_1(k28_grcat_1(A),C)
                           => k22_grcat_1(k19_grcat_1(A),D) = k22_grcat_1(k19_grcat_1(A),E) )
                          & ( k22_grcat_1(k19_grcat_1(A),D) = k22_grcat_1(k19_grcat_1(A),E)
                           => k3_cat_1(k28_grcat_1(A),B) = k3_cat_1(k28_grcat_1(A),C) ) ) ) ) ) ) ) ) )).

fof(t51_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => r2_hidden(k2_algstr_1,k29_grcat_1(A)) ) )).

fof(d38_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => k30_grcat_1(A) = k6_grcat_1(k28_grcat_1(A),k29_grcat_1(A)) ) )).

fof(t52_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => u1_cat_1(k30_grcat_1(A)) = k29_grcat_1(A) ) )).

fof(d40_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => k32_grcat_1(A) = k6_grcat_1(k30_grcat_1(A),k31_grcat_1(A)) ) )).

fof(t53_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => u1_cat_1(k32_grcat_1(A)) = k31_grcat_1(A) ) )).

fof(t54_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => r2_hidden(k2_algstr_1,k31_grcat_1(A)) ) )).

fof(s1_grcat_1,axiom,
    ( ! [A,B] :
        ( ( r2_hidden(A,f1_s1_grcat_1)
          & r2_hidden(B,f2_s1_grcat_1)
          & p1_s1_grcat_1(A,B) )
       => r2_hidden(f4_s1_grcat_1(A,B),f3_s1_grcat_1) )
   => ? [A] :
        ( v1_funct_1(A)
        & m2_relset_1(A,k2_zfmisc_1(f1_s1_grcat_1,f2_s1_grcat_1),f3_s1_grcat_1)
        & ! [B,C] :
            ( r2_hidden(k4_tarski(B,C),k1_relat_1(A))
          <=> ( r2_hidden(B,f1_s1_grcat_1)
              & r2_hidden(C,f2_s1_grcat_1)
              & p1_s1_grcat_1(B,C) ) )
        & ! [B,C] :
            ( r2_hidden(k4_tarski(B,C),k1_relat_1(A))
           => k1_funct_1(A,k4_tarski(B,C)) = f4_s1_grcat_1(B,C) ) ) )).

fof(s2_grcat_1,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s2_grcat_1)
       => ! [B] :
            ( m1_subset_1(B,f2_s2_grcat_1)
           => ( p1_s2_grcat_1(A,B)
             => r2_hidden(f4_s2_grcat_1(A,B),f3_s2_grcat_1) ) ) )
   => ? [A] :
        ( v1_funct_1(A)
        & m2_relset_1(A,k2_zfmisc_1(f1_s2_grcat_1,f2_s2_grcat_1),f3_s2_grcat_1)
        & ! [B] :
            ( m1_subset_1(B,f1_s2_grcat_1)
           => ! [C] :
                ( m1_subset_1(C,f2_s2_grcat_1)
               => ( r2_hidden(k4_tarski(B,C),k1_relat_1(A))
                <=> p1_s2_grcat_1(B,C) ) ) )
        & ! [B] :
            ( m1_subset_1(B,f1_s2_grcat_1)
           => ! [C] :
                ( m1_subset_1(C,f2_s2_grcat_1)
               => ( r2_hidden(k4_tarski(B,C),k1_relat_1(A))
                 => k1_funct_1(A,k4_tarski(B,C)) = f4_s2_grcat_1(B,C) ) ) ) ) )).

fof(dt_m1_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => ! [C] :
          ( m1_grcat_1(C,A,B)
         => ( v3_grcat_1(C)
            & l1_grcat_1(C) ) ) ) )).

fof(existence_m1_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => ? [C] : m1_grcat_1(C,A,B) ) )).

fof(dt_m2_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] :
          ( m2_grcat_1(B,A)
         => ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) ) ) ) )).

fof(existence_m2_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ? [B] : m2_grcat_1(B,A) ) )).

fof(redefinition_m2_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] :
          ( m2_grcat_1(B,A)
        <=> m1_subset_1(B,A) ) ) )).

fof(dt_m3_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v5_grcat_1(A) )
     => ! [B] :
          ( m3_grcat_1(B,A)
         => ( v3_grcat_1(B)
            & l1_grcat_1(B) ) ) ) )).

fof(existence_m3_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v5_grcat_1(A) )
     => ? [B] : m3_grcat_1(B,A) ) )).

fof(redefinition_m3_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v5_grcat_1(A) )
     => ! [B] :
          ( m3_grcat_1(B,A)
        <=> m1_subset_1(B,A) ) ) )).

fof(dt_m4_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => ! [C] :
          ( m4_grcat_1(C,A,B)
         => ( ~ v1_xboole_0(C)
            & v5_grcat_1(C) ) ) ) )).

fof(existence_m4_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => ? [C] : m4_grcat_1(C,A,B) ) )).

fof(dt_m5_grcat_1,axiom,(
    $true )).

fof(existence_m5_grcat_1,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & l1_struct_0(B) )
     => ? [C] : m5_grcat_1(C,A,B) ) )).

fof(dt_m6_grcat_1,axiom,(
    ! [A,B,C] :
      ( ( l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B)
        & ~ v1_xboole_0(C)
        & m5_grcat_1(C,A,B) )
     => ! [D] :
          ( m6_grcat_1(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
            & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) ) ) ) )).

fof(existence_m6_grcat_1,axiom,(
    ! [A,B,C] :
      ( ( l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B)
        & ~ v1_xboole_0(C)
        & m5_grcat_1(C,A,B) )
     => ? [D] : m6_grcat_1(D,A,B,C) ) )).

fof(redefinition_m6_grcat_1,axiom,(
    ! [A,B,C] :
      ( ( l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B)
        & ~ v1_xboole_0(C)
        & m5_grcat_1(C,A,B) )
     => ! [D] :
          ( m6_grcat_1(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) )).

fof(dt_m7_grcat_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B)
        & m4_grcat_1(C,A,B) )
     => ! [D] :
          ( m7_grcat_1(D,A,B,C)
         => m1_grcat_1(D,A,B) ) ) )).

fof(existence_m7_grcat_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B)
        & m4_grcat_1(C,A,B) )
     => ? [D] : m7_grcat_1(D,A,B,C) ) )).

fof(redefinition_m7_grcat_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B)
        & m4_grcat_1(C,A,B) )
     => ! [D] :
          ( m7_grcat_1(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) )).

fof(dt_l1_grcat_1,axiom,(
    $true )).

fof(existence_l1_grcat_1,axiom,(
    ? [A] : l1_grcat_1(A) )).

fof(abstractness_v2_grcat_1,axiom,(
    ! [A] :
      ( l1_grcat_1(A)
     => ( v2_grcat_1(A)
       => A = g1_grcat_1(u1_grcat_1(A),u2_grcat_1(A),u3_grcat_1(A)) ) ) )).

fof(dt_k1_grcat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
     => m1_subset_1(k1_grcat_1(A,B),k1_zfmisc_1(u2_cat_1(A))) ) )).

fof(dt_k2_grcat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
     => ( v1_funct_1(k2_grcat_1(A,B))
        & v1_funct_2(k2_grcat_1(A,B),k1_grcat_1(A,B),B)
        & m2_relset_1(k2_grcat_1(A,B),k1_grcat_1(A,B),B) ) ) )).

fof(dt_k3_grcat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
     => ( v1_funct_1(k3_grcat_1(A,B))
        & v1_funct_2(k3_grcat_1(A,B),k1_grcat_1(A,B),B)
        & m2_relset_1(k3_grcat_1(A,B),k1_grcat_1(A,B),B) ) ) )).

fof(dt_k4_grcat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
     => ( v1_funct_1(k4_grcat_1(A,B))
        & m2_relset_1(k4_grcat_1(A,B),k12_mcart_1(u2_cat_1(A),u2_cat_1(A),k1_grcat_1(A,B),k1_grcat_1(A,B)),k1_grcat_1(A,B)) ) ) )).

fof(dt_k5_grcat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
     => ( v1_funct_1(k5_grcat_1(A,B))
        & v1_funct_2(k5_grcat_1(A,B),B,k1_grcat_1(A,B))
        & m2_relset_1(k5_grcat_1(A,B),B,k1_grcat_1(A,B)) ) ) )).

fof(dt_k6_grcat_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
     => m3_cat_2(k6_grcat_1(A,B),A) ) )).

fof(dt_k7_grcat_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ( v1_funct_1(k7_grcat_1(A))
        & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) ) ) )).

fof(dt_k8_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ( v1_funct_1(k8_grcat_1(A,B))
        & v1_funct_2(k8_grcat_1(A,B),u1_struct_0(A),u1_struct_0(B))
        & m2_relset_1(k8_grcat_1(A,B),u1_struct_0(A),u1_struct_0(B)) ) ) )).

fof(dt_k9_grcat_1,axiom,(
    ! [A] :
      ( l1_grcat_1(A)
     => ( ~ v3_struct_0(k9_grcat_1(A))
        & v4_rlvect_1(k9_grcat_1(A))
        & v5_rlvect_1(k9_grcat_1(A))
        & v6_rlvect_1(k9_grcat_1(A))
        & l1_rlvect_1(k9_grcat_1(A)) ) ) )).

fof(dt_k10_grcat_1,axiom,(
    ! [A] :
      ( l1_grcat_1(A)
     => ( ~ v3_struct_0(k10_grcat_1(A))
        & v4_rlvect_1(k10_grcat_1(A))
        & v5_rlvect_1(k10_grcat_1(A))
        & v6_rlvect_1(k10_grcat_1(A))
        & l1_rlvect_1(k10_grcat_1(A)) ) ) )).

fof(dt_k11_grcat_1,axiom,(
    ! [A] :
      ( l1_grcat_1(A)
     => ( v1_funct_1(k11_grcat_1(A))
        & v1_funct_2(k11_grcat_1(A),u1_struct_0(k9_grcat_1(A)),u1_struct_0(k10_grcat_1(A)))
        & m2_relset_1(k11_grcat_1(A),u1_struct_0(k9_grcat_1(A)),u1_struct_0(k10_grcat_1(A))) ) ) )).

fof(dt_k12_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => l1_grcat_1(k12_grcat_1(A,B)) ) )).

fof(dt_k13_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => m1_grcat_1(k13_grcat_1(A),A,A) ) )).

fof(dt_k14_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => ( v2_grcat_1(k14_grcat_1(A,B))
        & m1_grcat_1(k14_grcat_1(A,B),A,B) ) ) )).

fof(redefinition_k14_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => k14_grcat_1(A,B) = k12_grcat_1(A,B) ) )).

fof(dt_k15_grcat_1,axiom,(
    ! [A,B] :
      ( ( v3_grcat_1(A)
        & l1_grcat_1(A)
        & v3_grcat_1(B)
        & l1_grcat_1(B) )
     => ( v2_grcat_1(k15_grcat_1(A,B))
        & v3_grcat_1(k15_grcat_1(A,B))
        & l1_grcat_1(k15_grcat_1(A,B)) ) ) )).

fof(dt_k16_grcat_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B)
        & ~ v3_struct_0(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & l1_rlvect_1(C)
        & m1_grcat_1(D,B,C)
        & m1_grcat_1(E,A,B) )
     => ( v2_grcat_1(k16_grcat_1(A,B,C,D,E))
        & m1_grcat_1(k16_grcat_1(A,B,C,D,E),A,C) ) ) )).

fof(redefinition_k16_grcat_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B)
        & ~ v3_struct_0(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & l1_rlvect_1(C)
        & m1_grcat_1(D,B,C)
        & m1_grcat_1(E,A,B) )
     => k16_grcat_1(A,B,C,D,E) = k15_grcat_1(D,E) ) )).

fof(dt_k17_grcat_1,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & l1_struct_0(B) )
     => m5_grcat_1(k17_grcat_1(A,B),A,B) ) )).

fof(dt_k18_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => m4_grcat_1(k18_grcat_1(A,B),A,B) ) )).

fof(dt_k19_grcat_1,axiom,(
    $true )).

fof(dt_k20_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ( ~ v1_xboole_0(k20_grcat_1(A))
        & v5_grcat_1(k20_grcat_1(A)) ) ) )).

fof(dt_k21_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A)
        & m1_subset_1(B,k20_grcat_1(A)) )
     => ( v1_rlvect_1(k21_grcat_1(A,B))
        & m2_grcat_1(k21_grcat_1(A,B),A) ) ) )).

fof(redefinition_k21_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A)
        & m1_subset_1(B,k20_grcat_1(A)) )
     => k21_grcat_1(A,B) = k9_grcat_1(B) ) )).

fof(dt_k22_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A)
        & m1_subset_1(B,k20_grcat_1(A)) )
     => ( v1_rlvect_1(k22_grcat_1(A,B))
        & m2_grcat_1(k22_grcat_1(A,B),A) ) ) )).

fof(redefinition_k22_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A)
        & m1_subset_1(B,k20_grcat_1(A)) )
     => k22_grcat_1(A,B) = k10_grcat_1(B) ) )).

fof(dt_k23_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A)
        & m1_subset_1(B,A) )
     => ( v2_grcat_1(k23_grcat_1(A,B))
        & m3_grcat_1(k23_grcat_1(A,B),k20_grcat_1(A)) ) ) )).

fof(dt_k24_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ( v1_funct_1(k24_grcat_1(A))
        & v1_funct_2(k24_grcat_1(A),k20_grcat_1(A),A)
        & m2_relset_1(k24_grcat_1(A),k20_grcat_1(A),A) ) ) )).

fof(dt_k25_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ( v1_funct_1(k25_grcat_1(A))
        & v1_funct_2(k25_grcat_1(A),k20_grcat_1(A),A)
        & m2_relset_1(k25_grcat_1(A),k20_grcat_1(A),A) ) ) )).

fof(dt_k26_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ( v1_funct_1(k26_grcat_1(A))
        & v1_funct_2(k26_grcat_1(A),A,k20_grcat_1(A))
        & m2_relset_1(k26_grcat_1(A),A,k20_grcat_1(A)) ) ) )).

fof(dt_k27_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ( v1_funct_1(k27_grcat_1(A))
        & m2_relset_1(k27_grcat_1(A),k2_zfmisc_1(k20_grcat_1(A),k20_grcat_1(A)),k20_grcat_1(A)) ) ) )).

fof(dt_k28_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => l1_cat_1(k28_grcat_1(A)) ) )).

fof(dt_k29_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => m1_subset_1(k29_grcat_1(A),k1_zfmisc_1(u1_cat_1(k28_grcat_1(A)))) ) )).

fof(dt_k30_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => m3_cat_2(k30_grcat_1(A),k28_grcat_1(A)) ) )).

fof(dt_k31_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => m1_subset_1(k31_grcat_1(A),k1_zfmisc_1(u1_cat_1(k30_grcat_1(A)))) ) )).

fof(dt_k32_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => m3_cat_2(k32_grcat_1(A),k30_grcat_1(A)) ) )).

fof(dt_u1_grcat_1,axiom,(
    ! [A] :
      ( l1_grcat_1(A)
     => ( ~ v3_struct_0(u1_grcat_1(A))
        & v4_rlvect_1(u1_grcat_1(A))
        & v5_rlvect_1(u1_grcat_1(A))
        & v6_rlvect_1(u1_grcat_1(A))
        & l1_rlvect_1(u1_grcat_1(A)) ) ) )).

fof(dt_u2_grcat_1,axiom,(
    ! [A] :
      ( l1_grcat_1(A)
     => ( ~ v3_struct_0(u2_grcat_1(A))
        & v4_rlvect_1(u2_grcat_1(A))
        & v5_rlvect_1(u2_grcat_1(A))
        & v6_rlvect_1(u2_grcat_1(A))
        & l1_rlvect_1(u2_grcat_1(A)) ) ) )).

fof(dt_u3_grcat_1,axiom,(
    ! [A] :
      ( l1_grcat_1(A)
     => ( v1_funct_1(u3_grcat_1(A))
        & v1_funct_2(u3_grcat_1(A),u1_struct_0(u1_grcat_1(A)),u1_struct_0(u2_grcat_1(A)))
        & m2_relset_1(u3_grcat_1(A),u1_struct_0(u1_grcat_1(A)),u1_struct_0(u2_grcat_1(A))) ) ) )).

fof(dt_g1_grcat_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => ( v2_grcat_1(g1_grcat_1(A,B,C))
        & l1_grcat_1(g1_grcat_1(A,B,C)) ) ) )).

fof(free_g1_grcat_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => ! [D,E,F] :
          ( g1_grcat_1(A,B,C) = g1_grcat_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) )).

fof(d5_grcat_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
         => k1_grcat_1(A,B) = k3_tarski(a_2_0_grcat_1(A,B)) ) ) )).

fof(d37_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => k29_grcat_1(A) = a_1_0_grcat_1(A) ) )).

fof(d39_grcat_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => k31_grcat_1(A) = a_1_1_grcat_1(A) ) )).

fof(fraenkel_a_2_0_grcat_1,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u1_cat_1(B))) )
     => ( r2_hidden(A,a_2_0_grcat_1(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,u1_cat_1(B))
            & m1_subset_1(E,u1_cat_1(B))
            & A = k6_cat_1(B,D,E)
            & r2_hidden(D,C)
            & r2_hidden(E,C) ) ) ) )).

fof(fraenkel_a_1_0_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_classes2(B) )
     => ( r2_hidden(A,a_1_0_grcat_1(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_cat_1(k28_grcat_1(B)))
            & A = C
            & ? [D] :
                ( ~ v3_struct_0(D)
                & v3_rlvect_1(D)
                & v4_rlvect_1(D)
                & v5_rlvect_1(D)
                & v6_rlvect_1(D)
                & l1_rlvect_1(D)
                & C = D ) ) ) ) )).

fof(fraenkel_a_1_1_grcat_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_classes2(B) )
     => ( r2_hidden(A,a_1_1_grcat_1(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_cat_1(k30_grcat_1(B)))
            & A = C
            & ? [D] :
                ( ~ v3_struct_0(D)
                & v3_rlvect_1(D)
                & v4_rlvect_1(D)
                & v5_rlvect_1(D)
                & v6_rlvect_1(D)
                & v1_midsp_2(D)
                & l1_rlvect_1(D)
                & C = D ) ) ) ) )).
%------------------------------------------------------------------------------