% Mizar problem: t53_grcat_1,grcat_1,1721,56 
fof(t53_grcat_1,conjecture,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => u1_cat_1(k32_grcat_1(A)) = k31_grcat_1(A) ) ),
    inference(mizar_bg_added,[status(thm)],[existence_l1_struct_0,dt_k6_cat_1,dt_k7_relat_1,dt_l1_struct_0,rc4_grcat_1,rc6_grcat_1,rc3_struct_0,rc1_funct_2,cc1_funct_2,rc2_partfun1,existence_l2_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_k12_mcart_1,redefinition_k2_partfun1,redefinition_m2_relset_1,dt_k12_mcart_1,dt_k19_grcat_1,dt_k1_realset1,dt_k20_grcat_1,dt_k24_grcat_1,dt_k25_grcat_1,dt_k26_grcat_1,dt_k27_grcat_1,dt_k2_partfun1,dt_k2_zfmisc_1,dt_k3_tarski,dt_l2_struct_0,dt_m1_relset_1,dt_m2_relset_1,fc8_grcat_1,fc9_grcat_1,cc1_relset_1,rc4_struct_0,fc4_subset_1,cc1_algstr_1,cc2_algstr_1,cc3_algstr_1,cc5_funct_2,cc6_funct_2,fraenkel_a_1_1_grcat_1,fraenkel_a_2_0_grcat_1,free_g1_cat_1,reflexivity_r1_tarski,existence_l1_rlvect_1,dt_g1_cat_1,dt_k1_grcat_1,dt_k28_grcat_1,dt_k29_grcat_1,dt_k2_grcat_1,dt_k3_grcat_1,dt_k4_grcat_1,dt_k5_grcat_1,dt_l1_rlvect_1,dt_u2_cat_1,dt_u3_cat_1,dt_u4_cat_1,dt_u5_cat_1,dt_u6_cat_1,fc2_grcat_1,fc10_grcat_1,fc11_grcat_1,fc12_grcat_1,cc4_algstr_1,cc1_midsp_2,d5_grcat_1,d36_grcat_1,d37_grcat_1,d6_grcat_1,d7_grcat_1,d8_grcat_1,d9_grcat_1,antisymmetry_r2_hidden,abstractness_v1_cat_1,existence_l1_cat_1,existence_m1_subset_1,existence_m3_cat_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k30_grcat_1,dt_k6_grcat_1,dt_l1_cat_1,dt_m1_subset_1,dt_m3_cat_2,fc3_grcat_1,fc13_grcat_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,cc1_classes2,cc3_classes2,rc1_classes2,rc2_classes2,fc1_xboole_0,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t2_tarski,fraenkel_a_1_2_grcat_1,d38_grcat_1,d10_grcat_1,dt_k31_grcat_1,dt_k32_grcat_1,dt_u1_cat_1,fc14_grcat_1,fc15_grcat_1,cc2_classes2,rc1_xboole_0,rc2_xboole_0,t6_boole,t7_boole,t8_boole,d39_grcat_1,d40_grcat_1]),
    [file(grcat_1,t53_grcat_1)]).

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

fof(dt_k6_cat_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_subset_1(k6_cat_1(A,B,C),k1_zfmisc_1(u2_cat_1(A))) ) ),
    file(cat_1,k6_cat_1),
    []).

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    []).

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

fof(rc4_grcat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_grcat_1(A) ) ),
    file(grcat_1,rc4_grcat_1),
    []).

fof(rc6_grcat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v5_grcat_1(A) ) ),
    file(grcat_1,rc6_grcat_1),
    []).

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

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(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(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(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_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_k12_mcart_1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,k1_zfmisc_1(A))
        & m1_subset_1(D,k1_zfmisc_1(B)) )
     => k12_mcart_1(A,B,C,D) = k2_zfmisc_1(C,D) ) ),
    file(mcart_1,k12_mcart_1),
    []).

fof(redefinition_k2_partfun1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k2_partfun1(A,B,C,D) = k7_relat_1(C,D) ) ),
    file(partfun1,k2_partfun1),
    []).

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(dt_k12_mcart_1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,k1_zfmisc_1(A))
        & m1_subset_1(D,k1_zfmisc_1(B)) )
     => m1_subset_1(k12_mcart_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(mcart_1,k12_mcart_1),
    []).

fof(dt_k19_grcat_1,axiom,(
    $true ),
    file(grcat_1,k19_grcat_1),
    []).

fof(dt_k1_realset1,axiom,(
    $true ),
    file(realset1,k1_realset1),
    []).

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)) ) ) ),
    file(grcat_1,k20_grcat_1),
    []).

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) ) ) ),
    file(grcat_1,k24_grcat_1),
    []).

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) ) ) ),
    file(grcat_1,k25_grcat_1),
    []).

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)) ) ) ),
    file(grcat_1,k26_grcat_1),
    []).

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)) ) ) ),
    file(grcat_1,k27_grcat_1),
    []).

fof(dt_k2_partfun1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => ( v1_funct_1(k2_partfun1(A,B,C,D))
        & m2_relset_1(k2_partfun1(A,B,C,D),A,B) ) ) ),
    file(partfun1,k2_partfun1),
    []).

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

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

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_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(fc8_grcat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ~ v1_xboole_0(k19_grcat_1(A)) ) ),
    file(grcat_1,fc8_grcat_1),
    []).

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)) ) ) ),
    file(grcat_1,fc9_grcat_1),
    []).

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

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(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(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(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(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(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(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 ) ) ) ) ),
    file(grcat_1,a_1_1_grcat_1),
    []).

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) ) ) ) ),
    file(grcat_1,a_2_0_grcat_1),
    []).

fof(free_g1_cat_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & m1_relset_1(E,k2_zfmisc_1(B,B),B)
        & v1_funct_1(F)
        & v1_funct_2(F,A,B)
        & m1_relset_1(F,A,B) )
     => ! [G,H,I,J,K,L] : 
          ( g1_cat_1(A,B,C,D,E,F) = g1_cat_1(G,H,I,J,K,L)
         => ( A = G
            & B = H
            & C = I
            & D = J
            & E = K
            & F = L ) ) ) ),
    file(cat_1,g1_cat_1),
    []).

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

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

fof(dt_g1_cat_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & m1_relset_1(E,k2_zfmisc_1(B,B),B)
        & v1_funct_1(F)
        & v1_funct_2(F,A,B)
        & m1_relset_1(F,A,B) )
     => ( v1_cat_1(g1_cat_1(A,B,C,D,E,F))
        & l1_cat_1(g1_cat_1(A,B,C,D,E,F)) ) ) ),
    file(cat_1,g1_cat_1),
    []).

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))) ) ),
    file(grcat_1,k1_grcat_1),
    []).

fof(dt_k28_grcat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => l1_cat_1(k28_grcat_1(A)) ) ),
    file(grcat_1,k28_grcat_1),
    []).

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)))) ) ),
    file(grcat_1,k29_grcat_1),
    []).

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) ) ) ),
    file(grcat_1,k2_grcat_1),
    []).

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) ) ) ),
    file(grcat_1,k3_grcat_1),
    []).

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)) ) ) ),
    file(grcat_1,k4_grcat_1),
    []).

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)) ) ) ),
    file(grcat_1,k5_grcat_1),
    []).

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

fof(dt_u2_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ~ v1_xboole_0(u2_cat_1(A)) ) ),
    file(cat_1,u2_cat_1),
    []).

fof(dt_u3_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_funct_1(u3_cat_1(A))
        & v1_funct_2(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A))
        & m2_relset_1(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)) ) ) ),
    file(cat_1,u3_cat_1),
    []).

fof(dt_u4_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_funct_1(u4_cat_1(A))
        & v1_funct_2(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A))
        & m2_relset_1(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)) ) ) ),
    file(cat_1,u4_cat_1),
    []).

fof(dt_u5_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_funct_1(u5_cat_1(A))
        & m2_relset_1(u5_cat_1(A),k2_zfmisc_1(u2_cat_1(A),u2_cat_1(A)),u2_cat_1(A)) ) ) ),
    file(cat_1,u5_cat_1),
    []).

fof(dt_u6_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_funct_1(u6_cat_1(A))
        & v1_funct_2(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A))
        & m2_relset_1(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A)) ) ) ),
    file(cat_1,u6_cat_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)) ) ),
    file(grcat_1,fc2_grcat_1),
    []).

fof(fc10_grcat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => v1_cat_1(k28_grcat_1(A)) ) ),
    file(grcat_1,fc10_grcat_1),
    []).

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)) ) ) ),
    file(grcat_1,fc11_grcat_1),
    []).

fof(fc12_grcat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ~ v1_xboole_0(k29_grcat_1(A)) ) ),
    file(grcat_1,fc12_grcat_1),
    []).

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(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(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)) ) ) ),
    file(grcat_1,d5_grcat_1),
    []).

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))) ) ),
    file(grcat_1,d36_grcat_1),
    []).

fof(d37_grcat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => k29_grcat_1(A) = a_1_1_grcat_1(A) ) ),
    file(grcat_1,d37_grcat_1),
    []).

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)) ) ) ),
    file(grcat_1,d6_grcat_1),
    []).

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)) ) ) ),
    file(grcat_1,d7_grcat_1),
    []).

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)) ) ) ),
    file(grcat_1,d8_grcat_1),
    []).

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) ) ) ),
    file(grcat_1,d9_grcat_1),
    []).

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

fof(abstractness_v1_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_cat_1(A)
       => A = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) ) ),
    file(cat_1,v1_cat_1),
    []).

fof(existence_l1_cat_1,axiom,(
    ? [A] : l1_cat_1(A) ),
    file(cat_1,l1_cat_1),
    []).

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

fof(existence_m3_cat_2,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ? [B] : m3_cat_2(B,A) ) ),
    file(cat_2,m3_cat_2),
    []).

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_k30_grcat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => m3_cat_2(k30_grcat_1(A),k28_grcat_1(A)) ) ),
    file(grcat_1,k30_grcat_1),
    []).

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) ) ),
    file(grcat_1,k6_grcat_1),
    []).

fof(dt_l1_cat_1,axiom,(
    $true ),
    file(cat_1,l1_cat_1),
    []).

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

fof(dt_m3_cat_2,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m3_cat_2(B,A)
         => ( v2_cat_1(B)
            & l1_cat_1(B) ) ) ) ),
    file(cat_2,m3_cat_2),
    []).

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)) ) ) ),
    file(grcat_1,fc3_grcat_1),
    []).

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)) ) ) ),
    file(grcat_1,fc13_grcat_1),
    []).

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

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

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

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

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_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(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

fof(fraenkel_a_1_2_grcat_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_classes2(B) )
     => ( r2_hidden(A,a_1_2_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 ) ) ) ) ),
    file(grcat_1,a_1_2_grcat_1),
    []).

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)) ) ),
    file(grcat_1,d38_grcat_1),
    []).

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)) ) ) ),
    file(grcat_1,d10_grcat_1),
    []).

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)))) ) ),
    file(grcat_1,k31_grcat_1),
    []).

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)) ) ),
    file(grcat_1,k32_grcat_1),
    []).

fof(dt_u1_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ~ v1_xboole_0(u1_cat_1(A)) ) ),
    file(cat_1,u1_cat_1),
    []).

fof(fc14_grcat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ~ v1_xboole_0(k31_grcat_1(A)) ) ),
    file(grcat_1,fc14_grcat_1),
    []).

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)) ) ) ),
    file(grcat_1,fc15_grcat_1),
    []).

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

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

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

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

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),
    []).

fof(d39_grcat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => k31_grcat_1(A) = a_1_2_grcat_1(A) ) ),
    file(grcat_1,d39_grcat_1),
    []).

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)) ) ),
    file(grcat_1,d40_grcat_1),
    []).