% Mizar problem: t77_cat_3,cat_3,1768,58 
fof(t77_cat_3,conjecture,(
    ! [A,B] : 
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] : 
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,u2_cat_1(B))
                & m2_relset_1(D,A,u2_cat_1(B)) )
             => ( r1_cat_3(B,C,A,D)
              <=> r3_cat_3(k2_oppcat_1(B),k3_oppcat_1(B,C),A,k5_cat_3(B,A,D)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_cat_1,antisymmetry_r2_hidden,cc1_relset_1,d15_cat_3,d18_cat_3,d2_cat_1,d2_oppcat_1,d3_cat_1,d3_cat_3,d4_cat_3,d4_oppcat_1,d5_cat_3,d6_cat_1,d6_cat_3,dt_g1_cat_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_cat_1,dt_k2_oppcat_1,dt_k2_zfmisc_1,dt_k3_cat_1,dt_k3_cat_3,dt_k3_oppcat_1,dt_k4_cat_1,dt_k4_cat_3,dt_k4_finseq_4,dt_k4_oppcat_1,dt_k5_cat_3,dt_k5_oppcat_1,dt_k6_cat_1,dt_k6_cat_3,dt_k6_oppcat_1,dt_k8_funct_2,dt_l1_cat_1,dt_m1_cat_3,dt_m1_relset_1,dt_m1_subset_1,dt_m2_cat_3,dt_m2_relset_1,dt_u1_cat_1,dt_u2_cat_1,dt_u3_cat_1,dt_u4_cat_1,dt_u5_cat_1,dt_u6_cat_1,existence_l1_cat_1,existence_m1_cat_3,existence_m1_relset_1,existence_m1_subset_1,existence_m2_cat_3,existence_m2_relset_1,fc1_xboole_0,fraenkel_a_3_0_cat_1,free_g1_cat_1,rc1_xboole_0,rc2_xboole_0,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t10_oppcat_1,t11_oppcat_1,t13_oppcat_1,t14_oppcat_1,t17_oppcat_1,t18_cat_1,t19_oppcat_1,t1_cat_3,t1_subset,t2_subset,t2_tarski,t3_subset,t45_cat_3,t4_oppcat_1,t4_subset,t5_oppcat_1,t5_subset,t67_cat_3,t6_boole,t74_cat_3,t75_cat_3,t7_boole,t7_oppcat_1,t8_boole,t8_oppcat_1,t9_oppcat_1]),
    [file(cat_3,t77_cat_3)]).

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

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(d15_cat_3,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C,D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,C,u2_cat_1(A))
                & m2_relset_1(D,C,u2_cat_1(A)) )
             => ( r1_cat_3(A,B,C,D)
              <=> ( m1_cat_3(D,A,B,C)
                  & ! [E] : 
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] : 
                          ( m1_cat_3(F,A,E,C)
                         => ~ ( k4_cat_3(A,C,D) = k4_cat_3(A,C,F)
                              & ! [G] : 
                                  ( m1_subset_1(G,u2_cat_1(A))
                                 => ~ ( r2_hidden(G,k6_cat_1(A,E,B))
                                      & ! [H] : 
                                          ( m1_subset_1(H,u2_cat_1(A))
                                         => ( r2_hidden(H,k6_cat_1(A,E,B))
                                           => ( ! [I] : 
                                                  ( r2_hidden(I,C)
                                                 => k4_cat_1(A,H,k4_finseq_4(C,u2_cat_1(A),D,I)) = k4_finseq_4(C,u2_cat_1(A),F,I) )
                                            <=> G = H ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(cat_3,d15_cat_3),
    []).

fof(d18_cat_3,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C,D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,C,u2_cat_1(A))
                & m2_relset_1(D,C,u2_cat_1(A)) )
             => ( r3_cat_3(A,B,C,D)
              <=> ( m2_cat_3(D,A,B,C)
                  & ! [E] : 
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] : 
                          ( m2_cat_3(F,A,E,C)
                         => ~ ( k3_cat_3(A,C,D) = k3_cat_3(A,C,F)
                              & ! [G] : 
                                  ( m1_subset_1(G,u2_cat_1(A))
                                 => ~ ( r2_hidden(G,k6_cat_1(A,B,E))
                                      & ! [H] : 
                                          ( m1_subset_1(H,u2_cat_1(A))
                                         => ( r2_hidden(H,k6_cat_1(A,B,E))
                                           => ( ! [I] : 
                                                  ( r2_hidden(I,C)
                                                 => k4_cat_1(A,k4_finseq_4(C,u2_cat_1(A),D,I),H) = k4_finseq_4(C,u2_cat_1(A),F,I) )
                                            <=> G = H ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(cat_3,d18_cat_3),
    []).

fof(d2_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => k2_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B) ) ) ),
    file(cat_1,d2_cat_1),
    []).

fof(d2_oppcat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => k3_oppcat_1(A,B) = B ) ) ),
    file(oppcat_1,d2_oppcat_1),
    []).

fof(d3_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => k3_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) ) ) ),
    file(cat_1,d3_cat_1),
    []).

fof(d3_cat_3,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u2_cat_1(A))
            & m2_relset_1(C,B,u2_cat_1(A)) )
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,B,u1_cat_1(A))
                & m2_relset_1(D,B,u1_cat_1(A)) )
             => ( D = k3_cat_3(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,B)
                   => k4_finseq_4(B,u1_cat_1(A),D,E) = k2_cat_1(A,k4_finseq_4(B,u2_cat_1(A),C,E)) ) ) ) ) ) ),
    file(cat_3,d3_cat_3),
    []).

fof(d4_cat_3,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u2_cat_1(A))
            & m2_relset_1(C,B,u2_cat_1(A)) )
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,B,u1_cat_1(A))
                & m2_relset_1(D,B,u1_cat_1(A)) )
             => ( D = k4_cat_3(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,B)
                   => k4_finseq_4(B,u1_cat_1(A),D,E) = k3_cat_1(A,k4_finseq_4(B,u2_cat_1(A),C,E)) ) ) ) ) ) ),
    file(cat_3,d4_cat_3),
    []).

fof(d4_oppcat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => k5_oppcat_1(A,B) = B ) ) ),
    file(oppcat_1,d4_oppcat_1),
    []).

fof(d5_cat_3,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u2_cat_1(A))
            & m2_relset_1(C,B,u2_cat_1(A)) )
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,B,u2_cat_1(k2_oppcat_1(A)))
                & m2_relset_1(D,B,u2_cat_1(k2_oppcat_1(A))) )
             => ( D = k5_cat_3(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,B)
                   => k4_finseq_4(B,u2_cat_1(k2_oppcat_1(A)),D,E) = k5_oppcat_1(A,k4_finseq_4(B,u2_cat_1(A),C,E)) ) ) ) ) ) ),
    file(cat_3,d5_cat_3),
    []).

fof(d6_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => k6_cat_1(A,B,C) = a_3_0_cat_1(A,B,C) ) ) ) ),
    file(cat_1,d6_cat_1),
    []).

fof(d6_cat_3,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,u2_cat_1(k2_oppcat_1(A)))
            & m2_relset_1(C,B,u2_cat_1(k2_oppcat_1(A))) )
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,B,u2_cat_1(A))
                & m2_relset_1(D,B,u2_cat_1(A)) )
             => ( D = k6_cat_3(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,B)
                   => k4_finseq_4(B,u2_cat_1(A),D,E) = k6_oppcat_1(A,k4_finseq_4(B,u2_cat_1(k2_oppcat_1(A)),C,E)) ) ) ) ) ) ),
    file(cat_3,d6_cat_3),
    []).

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_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

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_cat_1,axiom,(
    ! [A,B] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m1_subset_1(k2_cat_1(A,B),u1_cat_1(A)) ) ),
    file(cat_1,k2_cat_1),
    []).

fof(dt_k2_oppcat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v1_cat_1(k2_oppcat_1(A))
        & v2_cat_1(k2_oppcat_1(A))
        & l1_cat_1(k2_oppcat_1(A)) ) ) ),
    file(oppcat_1,k2_oppcat_1),
    []).

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

fof(dt_k3_cat_1,axiom,(
    ! [A,B] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m1_subset_1(k3_cat_1(A,B),u1_cat_1(A)) ) ),
    file(cat_1,k3_cat_1),
    []).

fof(dt_k3_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u2_cat_1(A))
        & m1_relset_1(C,B,u2_cat_1(A)) )
     => ( v1_funct_1(k3_cat_3(A,B,C))
        & v1_funct_2(k3_cat_3(A,B,C),B,u1_cat_1(A))
        & m2_relset_1(k3_cat_3(A,B,C),B,u1_cat_1(A)) ) ) ),
    file(cat_3,k3_cat_3),
    []).

fof(dt_k3_oppcat_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_subset_1(k3_oppcat_1(A,B),u1_cat_1(k2_oppcat_1(A))) ) ),
    file(oppcat_1,k3_oppcat_1),
    []).

fof(dt_k4_cat_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A))
        & m1_subset_1(C,u2_cat_1(A)) )
     => m1_subset_1(k4_cat_1(A,B,C),u2_cat_1(A)) ) ),
    file(cat_1,k4_cat_1),
    []).

fof(dt_k4_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u2_cat_1(A))
        & m1_relset_1(C,B,u2_cat_1(A)) )
     => ( v1_funct_1(k4_cat_3(A,B,C))
        & v1_funct_2(k4_cat_3(A,B,C),B,u1_cat_1(A))
        & m2_relset_1(k4_cat_3(A,B,C),B,u1_cat_1(A)) ) ) ),
    file(cat_3,k4_cat_3),
    []).

fof(dt_k4_finseq_4,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ),
    file(finseq_4,k4_finseq_4),
    []).

fof(dt_k4_oppcat_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) )
     => m1_subset_1(k4_oppcat_1(A,B),u1_cat_1(A)) ) ),
    file(oppcat_1,k4_oppcat_1),
    []).

fof(dt_k5_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u2_cat_1(A))
        & m1_relset_1(C,B,u2_cat_1(A)) )
     => ( v1_funct_1(k5_cat_3(A,B,C))
        & v1_funct_2(k5_cat_3(A,B,C),B,u2_cat_1(k2_oppcat_1(A)))
        & m2_relset_1(k5_cat_3(A,B,C),B,u2_cat_1(k2_oppcat_1(A))) ) ) ),
    file(cat_3,k5_cat_3),
    []).

fof(dt_k5_oppcat_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m1_subset_1(k5_oppcat_1(A,B),u2_cat_1(k2_oppcat_1(A))) ) ),
    file(oppcat_1,k5_oppcat_1),
    []).

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_k6_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,u2_cat_1(k2_oppcat_1(A)))
        & m1_relset_1(C,B,u2_cat_1(k2_oppcat_1(A))) )
     => ( v1_funct_1(k6_cat_3(A,B,C))
        & v1_funct_2(k6_cat_3(A,B,C),B,u2_cat_1(A))
        & m2_relset_1(k6_cat_3(A,B,C),B,u2_cat_1(A)) ) ) ),
    file(cat_3,k6_cat_3),
    []).

fof(dt_k6_oppcat_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) )
     => m1_subset_1(k6_oppcat_1(A,B),u2_cat_1(A)) ) ),
    file(oppcat_1,k6_oppcat_1),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

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

fof(dt_m1_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => ! [D] : 
          ( m1_cat_3(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,C,u2_cat_1(A))
            & m2_relset_1(D,C,u2_cat_1(A)) ) ) ) ),
    file(cat_3,m1_cat_3),
    []).

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_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => ! [D] : 
          ( m2_cat_3(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,C,u2_cat_1(A))
            & m2_relset_1(D,C,u2_cat_1(A)) ) ) ) ),
    file(cat_3,m2_cat_3),
    []).

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_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ~ v1_xboole_0(u1_cat_1(A)) ) ),
    file(cat_1,u1_cat_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(existence_l1_cat_1,axiom,(
    ? [A] : l1_cat_1(A) ),
    file(cat_1,l1_cat_1),
    []).

fof(existence_m1_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => ? [D] : m1_cat_3(D,A,B,C) ) ),
    file(cat_3,m1_cat_3),
    []).

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_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => ? [D] : m2_cat_3(D,A,B,C) ) ),
    file(cat_3,m2_cat_3),
    []).

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

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

fof(fraenkel_a_3_0_cat_1,axiom,(
    ! [A,B,C,D] : 
      ( ( l1_cat_1(B)
        & m1_subset_1(C,u1_cat_1(B))
        & m1_subset_1(D,u1_cat_1(B)) )
     => ( r2_hidden(A,a_3_0_cat_1(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u2_cat_1(B))
            & A = E
            & k2_cat_1(B,E) = C
            & k3_cat_1(B,E) = D ) ) ) ),
    file(cat_1,a_3_0_cat_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(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(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

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(t10_oppcat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(k2_oppcat_1(A)))
         => ( k2_cat_1(A,k6_oppcat_1(A,B)) = k3_cat_1(k2_oppcat_1(A),B)
            & k3_cat_1(A,k6_oppcat_1(A,B)) = k2_cat_1(k2_oppcat_1(A),B) ) ) ) ),
    file(oppcat_1,t10_oppcat_1),
    []).

fof(t11_oppcat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ( k3_oppcat_1(A,k2_cat_1(A,B)) = k3_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B))
            & k3_oppcat_1(A,k3_cat_1(A,B)) = k2_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) ) ) ) ),
    file(oppcat_1,t11_oppcat_1),
    []).

fof(t13_oppcat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( r2_hidden(D,k6_cat_1(A,B,C))
                  <=> r2_hidden(k5_oppcat_1(A,D),k6_cat_1(k2_oppcat_1(A),k3_oppcat_1(A,C),k3_oppcat_1(A,B))) ) ) ) ) ) ),
    file(oppcat_1,t13_oppcat_1),
    []).

fof(t14_oppcat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(k2_oppcat_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(k2_oppcat_1(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u2_cat_1(k2_oppcat_1(A)))
                 => ( r2_hidden(D,k6_cat_1(k2_oppcat_1(A),B,C))
                  <=> r2_hidden(k6_oppcat_1(A,D),k6_cat_1(A,k4_oppcat_1(A,C),k4_oppcat_1(A,B))) ) ) ) ) ) ),
    file(oppcat_1,t14_oppcat_1),
    []).

fof(t17_oppcat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(A))
             => ( k2_cat_1(A,C) = k3_cat_1(A,B)
               => k5_oppcat_1(A,k4_cat_1(A,B,C)) = k4_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,C),k5_oppcat_1(A,B)) ) ) ) ) ),
    file(oppcat_1,t17_oppcat_1),
    []).

fof(t18_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( r2_hidden(D,k6_cat_1(A,B,C))
                  <=> ( k2_cat_1(A,D) = B
                      & k3_cat_1(A,D) = C ) ) ) ) ) ) ),
    file(cat_1,t18_cat_1),
    []).

fof(t19_oppcat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(k2_oppcat_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(k2_oppcat_1(A)))
             => ( k2_cat_1(k2_oppcat_1(A),C) = k3_cat_1(k2_oppcat_1(A),B)
               => k6_oppcat_1(A,k4_cat_1(k2_oppcat_1(A),B,C)) = k4_cat_1(A,k6_oppcat_1(A,C),k6_oppcat_1(A,B)) ) ) ) ) ),
    file(oppcat_1,t19_oppcat_1),
    []).

fof(t1_cat_3,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,B)
            & m2_relset_1(C,A,B) )
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => ( ! [E] : 
                    ( r2_hidden(E,A)
                   => k4_finseq_4(A,B,C,E) = k4_finseq_4(A,B,D,E) )
               => C = D ) ) ) ) ),
    file(cat_3,t1_cat_3),
    []).

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

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

fof(t45_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ! [D] : 
          ( m1_subset_1(D,u1_cat_1(C))
         => ! [E] : 
              ( m1_cat_3(E,C,D,A)
             => ( r2_hidden(B,A)
               => k2_cat_1(C,k4_finseq_4(A,u2_cat_1(C),E,B)) = D ) ) ) ) ),
    file(cat_3,t45_cat_3),
    []).

fof(t4_oppcat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => k4_oppcat_1(A,k3_oppcat_1(A,B)) = B ) ) ),
    file(oppcat_1,t4_oppcat_1),
    []).

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_oppcat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(k2_oppcat_1(A)))
         => k3_oppcat_1(A,k4_oppcat_1(A,B)) = B ) ) ),
    file(oppcat_1,t5_oppcat_1),
    []).

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(t67_cat_3,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(C)
        & l1_cat_1(C) )
     => ! [D] : 
          ( m1_subset_1(D,u1_cat_1(C))
         => ! [E] : 
              ( m2_cat_3(E,C,D,A)
             => ( r2_hidden(B,A)
               => k3_cat_1(C,k4_finseq_4(A,u2_cat_1(C),E,B)) = D ) ) ) ) ),
    file(cat_3,t67_cat_3),
    []).

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

fof(t74_cat_3,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] : 
          ( m1_subset_1(C,u1_cat_1(B))
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,u2_cat_1(B))
                & m2_relset_1(D,A,u2_cat_1(B)) )
             => ( m1_cat_3(D,B,C,A)
              <=> m2_cat_3(k5_cat_3(B,A,D),k2_oppcat_1(B),k3_oppcat_1(B,C),A) ) ) ) ) ),
    file(cat_3,t74_cat_3),
    []).

fof(t75_cat_3,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,u2_cat_1(k2_oppcat_1(B)))
            & m2_relset_1(C,A,u2_cat_1(k2_oppcat_1(B))) )
         => ! [D] : 
              ( m1_subset_1(D,u1_cat_1(k2_oppcat_1(B)))
             => ( m2_cat_3(C,k2_oppcat_1(B),D,A)
              <=> m1_cat_3(k6_cat_3(B,A,C),B,k4_oppcat_1(B,D),A) ) ) ) ) ),
    file(cat_3,t75_cat_3),
    []).

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

fof(t7_oppcat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => k6_oppcat_1(A,k5_oppcat_1(A,B)) = B ) ) ),
    file(oppcat_1,t7_oppcat_1),
    []).

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

fof(t8_oppcat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(k2_oppcat_1(A)))
         => k5_oppcat_1(A,k6_oppcat_1(A,B)) = B ) ) ),
    file(oppcat_1,t8_oppcat_1),
    []).

fof(t9_oppcat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ( k2_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) = k3_cat_1(A,B)
            & k3_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) = k2_cat_1(A,B) ) ) ) ),
    file(oppcat_1,t9_oppcat_1),
    []).