% Mizar problem: t41_grcat_1,grcat_1,1062,38 
fof(t41_grcat_1,conjecture,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] : 
          ( r2_hidden(B,A)
          & r1_grcat_1(B,k2_algstr_1) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_rlvect_1,antisymmetry_r2_hidden,cc1_algstr_1,cc1_classes2,cc1_funct_2,cc1_midsp_2,cc1_relset_1,cc2_algstr_1,cc2_classes2,cc3_algstr_1,cc3_classes2,cc4_algstr_1,cc5_funct_2,cc6_funct_2,d28_grcat_1,d3_algstr_1,d4_algstr_1,dt_g1_rlvect_1,dt_k1_algstr_1,dt_k1_classes2,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_algstr_1,dt_k2_midsp_1,dt_k2_zfmisc_1,dt_k3_mcart_1,dt_k4_mcart_1,dt_k4_tarski,dt_k7_vectsp_1,dt_k7_vectsp_2,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_u2_struct_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_algstr_1,fc1_grcat_1,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_algstr_1,fc2_group_1,fc2_subset_1,fc3_algstr_1,fc4_subset_1,free_g1_rlvect_1,rc1_algstr_1,rc1_classes2,rc1_funct_2,rc1_midsp_2,rc1_subset_1,rc1_xboole_0,rc2_algstr_1,rc2_classes2,rc2_partfun1,rc2_subset_1,rc2_xboole_0,rc3_algstr_1,rc3_struct_0,rc4_struct_0,rc5_struct_0,redefinition_k1_classes2,redefinition_m2_relset_1,reflexivity_r1_tarski,t13_grcat_1,t1_subset,t2_subset,t3_grcat_1,t3_subset,t4_subset,t5_subset,t62_classes2,t6_boole,t6_grcat_1,t7_boole,t8_boole]),
    [file(grcat_1,t41_grcat_1)]).

fof(abstractness_v1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( v1_rlvect_1(A)
       => A = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A)) ) ) ),
    file(rlvect_1,v1_rlvect_1),
    []).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A)
          & v4_algstr_1(A)
          & v5_algstr_1(A) ) ) ) ),
    file(algstr_1,cc1_algstr_1),
    []).

fof(cc1_classes2,axiom,(
    ! [A] : 
      ( v2_classes1(A)
     => v1_classes1(A) ) ),
    file(classes2,cc1_classes2),
    []).

fof(cc1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

fof(cc1_midsp_2,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v1_midsp_2(A) )
       => ( ~ v3_struct_0(A)
          & v13_vectsp_1(A) ) ) ) ),
    file(midsp_2,cc1_midsp_2),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc2_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A)
          & v4_algstr_1(A)
          & v5_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_algstr_1(A) ) ) ) ),
    file(algstr_1,cc2_algstr_1),
    []).

fof(cc2_classes2,axiom,(
    ! [A] : 
      ( v1_classes2(A)
     => ( v1_ordinal1(A)
        & v1_classes1(A)
        & v2_classes1(A) ) ) ),
    file(classes2,cc2_classes2),
    []).

fof(cc3_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_rlvect_1(A) ) ) ) ),
    file(algstr_1,cc3_algstr_1),
    []).

fof(cc3_classes2,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_classes1(A) )
     => v1_classes2(A) ) ),
    file(classes2,cc3_classes2),
    []).

fof(cc4_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A) )
       => ( ~ v3_struct_0(A)
          & v1_algstr_1(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A)
          & v4_algstr_1(A)
          & v5_algstr_1(A)
          & v6_algstr_1(A) ) ) ) ),
    file(algstr_1,cc4_algstr_1),
    []).

fof(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc6_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

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) ) ) ) ),
    file(grcat_1,d28_grcat_1),
    []).

fof(d3_algstr_1,axiom,(
    ! [A] : k1_algstr_1(A) = A ),
    file(algstr_1,d3_algstr_1),
    []).

fof(d4_algstr_1,axiom,(
    k2_algstr_1 = g1_rlvect_1(k1_tarski(k1_xboole_0),k2_midsp_1,k1_algstr_1(k1_xboole_0)) ),
    file(algstr_1,d4_algstr_1),
    []).

fof(dt_g1_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,A) )
     => ( v1_rlvect_1(g1_rlvect_1(A,B,C))
        & l1_rlvect_1(g1_rlvect_1(A,B,C)) ) ) ),
    file(rlvect_1,g1_rlvect_1),
    []).

fof(dt_k1_algstr_1,axiom,(
    ! [A] : m1_subset_1(k1_algstr_1(A),k1_tarski(A)) ),
    file(algstr_1,k1_algstr_1),
    []).

fof(dt_k1_classes2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k1_classes2(A,B),A) ) ),
    file(classes2,k1_classes2),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_algstr_1,axiom,
    ( v1_rlvect_1(k2_algstr_1)
    & l1_rlvect_1(k2_algstr_1) ),
    file(algstr_1,k2_algstr_1),
    []).

fof(dt_k2_midsp_1,axiom,
    ( v1_funct_1(k2_midsp_1)
    & v1_funct_2(k2_midsp_1,k2_zfmisc_1(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0))
    & m2_relset_1(k2_midsp_1,k2_zfmisc_1(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0)) ),
    file(midsp_1,k2_midsp_1),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_mcart_1,axiom,(
    $true ),
    file(mcart_1,k3_mcart_1),
    []).

fof(dt_k4_mcart_1,axiom,(
    $true ),
    file(mcart_1,k4_mcart_1),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k7_vectsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v1_funct_1(k7_vectsp_1(A))
        & v1_funct_2(k7_vectsp_1(A),u1_struct_0(A),u1_struct_0(A))
        & m2_relset_1(k7_vectsp_1(A),u1_struct_0(A),u1_struct_0(A)) ) ) ),
    file(vectsp_1,k7_vectsp_1),
    []).

fof(dt_k7_vectsp_2,axiom,
    ( v1_funct_1(k7_vectsp_2)
    & v1_funct_2(k7_vectsp_2,k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0))
    & m2_relset_1(k7_vectsp_2,k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)) ),
    file(vectsp_2,k7_vectsp_2),
    []).

fof(dt_l1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_struct_0),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_u1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( v1_funct_1(u1_rlvect_1(A))
        & v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(rlvect_1,u1_rlvect_1),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(dt_u2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => m1_subset_1(u2_struct_0(A),u1_struct_0(A)) ) ),
    file(struct_0,u2_struct_0),
    []).

fof(existence_l1_rlvect_1,axiom,(
    ? [A] : l1_rlvect_1(A) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_struct_0),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc1_algstr_1,axiom,
    ( ~ v3_struct_0(k2_algstr_1)
    & v1_rlvect_1(k2_algstr_1) ),
    file(algstr_1,fc1_algstr_1),
    []).

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) ),
    file(grcat_1,fc1_grcat_1),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc2_algstr_1,axiom,
    ( ~ v3_struct_0(k2_algstr_1)
    & v1_rlvect_1(k2_algstr_1)
    & v4_rlvect_1(k2_algstr_1)
    & v5_rlvect_1(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) ),
    file(algstr_1,fc2_algstr_1),
    []).

fof(fc2_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,A) )
     => ( ~ v3_struct_0(g1_rlvect_1(A,B,C))
        & v1_rlvect_1(g1_rlvect_1(A,B,C)) ) ) ),
    file(group_1,fc2_group_1),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc3_algstr_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)
    & 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) ),
    file(algstr_1,fc3_algstr_1),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(free_g1_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_subset_1(C,A) )
     => ! [D,E,F] : 
          ( g1_rlvect_1(A,B,C) = g1_rlvect_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(rlvect_1,g1_rlvect_1),
    []).

fof(rc1_algstr_1,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v1_rlvect_1(A)
      & v5_rlvect_1(A)
      & v1_algstr_1(A)
      & v2_algstr_1(A)
      & v3_algstr_1(A)
      & v4_algstr_1(A)
      & v5_algstr_1(A)
      & v6_algstr_1(A) ) ),
    file(algstr_1,rc1_algstr_1),
    []).

fof(rc1_classes2,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & ~ v1_xboole_0(A)
      & v1_classes1(A)
      & v2_classes1(A)
      & v1_classes2(A) ) ),
    file(classes2,rc1_classes2),
    []).

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

fof(rc1_midsp_2,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v1_rlvect_1(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v13_vectsp_1(A)
      & v1_midsp_2(A) ) ),
    file(midsp_2,rc1_midsp_2),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_algstr_1,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v1_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v1_algstr_1(A)
      & v2_algstr_1(A)
      & v3_algstr_1(A)
      & v4_algstr_1(A)
      & v5_algstr_1(A)
      & v6_algstr_1(A) ) ),
    file(algstr_1,rc2_algstr_1),
    []).

fof(rc2_classes2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] : 
          ( m1_subset_1(B,A)
          & ~ v1_xboole_0(B) ) ) ),
    file(classes2,rc2_classes2),
    []).

fof(rc2_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_algstr_1,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v1_rlvect_1(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v1_algstr_1(A)
      & v2_algstr_1(A)
      & v3_algstr_1(A)
      & v4_algstr_1(A)
      & v5_algstr_1(A)
      & v6_algstr_1(A) ) ),
    file(algstr_1,rc3_algstr_1),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc4_struct_0,axiom,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc4_struct_0),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(redefinition_k1_classes2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A)
        & m1_subset_1(B,A) )
     => k1_classes2(A,B) = k1_tarski(B) ) ),
    file(classes2,k1_classes2),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t13_grcat_1,axiom,(
    k7_vectsp_1(k2_algstr_1) = k7_vectsp_2 ),
    file(grcat_1,t13_grcat_1),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

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) ) ) ) ) ) ) ),
    file(grcat_1,t3_grcat_1),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t62_classes2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => r2_hidden(k1_xboole_0,A) ) ),
    file(classes2,t62_classes2),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

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) ) ) ),
    file(grcat_1,t6_grcat_1),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).