% Mizar problem: t16_altcat_2,altcat_2,613,52 
fof(t16_altcat_2,conjecture,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v5_altcat_1(k5_altcat_2(A),u1_cat_1(A),k4_altcat_2(A))
        & v4_altcat_1(k5_altcat_2(A),u1_cat_1(A),k4_altcat_2(A)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_altcat_1,cc1_funct_1,cc1_pboole,cc1_realset1,cc1_relat_1,cc1_relset_1,cc2_funct_1,cc2_pboole,cc3_pboole,commutativity_k2_tarski,d1_binop_1,d3_altcat_2,d5_tarski,d7_cat_1,d8_altcat_1,d9_altcat_1,dt_k10_cat_1,dt_k1_binop_1,dt_k1_funct_1,dt_k1_multop_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_altcat_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_altcat_1,dt_k3_zfmisc_1,dt_k4_altcat_1,dt_k4_altcat_2,dt_k4_tarski,dt_k5_altcat_2,dt_k5_cat_1,dt_k6_cat_1,dt_k9_cat_1,dt_l1_cat_1,dt_m1_cat_1,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m3_pboole,dt_u1_cat_1,dt_u2_cat_1,existence_l1_cat_1,existence_m1_cat_1,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m3_pboole,fc12_relat_1,fc1_subset_1,fc2_altcat_1,fc2_pboole,fc2_subset_1,fc3_realset1,fc3_subset_1,fc4_relat_1,fc4_subset_1,fc5_subset_1,fc7_funcop_1,rc1_funcop_1,rc1_funct_1,rc1_pboole,rc1_realset1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_pboole,rc2_realset1,rc2_relat_1,rc2_subset_1,rc3_funct_1,rc3_pboole,rc3_relat_1,rc4_funct_1,rc4_pboole,rc5_funct_1,redefinition_k10_cat_1,redefinition_k4_altcat_1,redefinition_m2_relset_1,reflexivity_r1_tarski,t13_altcat_2,t14_altcat_2,t1_subset,t2_subset,t3_subset,t4_subset,t56_cat_1,t57_cat_1,t58_cat_1,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(altcat_2,t16_altcat_2)]).

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

fof(cc1_altcat_1,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_fraenkel(B) ) ) ),
    file(altcat_1,cc1_altcat_1),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v2_relat_1(B)
           => ~ v3_relat_1(B) ) ) ) ),
    file(pboole,cc1_pboole),
    []).

fof(cc1_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ~ v1_xboole_0(A) ) ),
    file(realset1,cc1_realset1),
    []).

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_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(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

fof(cc2_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v3_relat_1(B)
           => ~ v2_relat_1(B) ) ) ) ),
    file(pboole,cc2_pboole),
    []).

fof(cc3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m3_pboole(D,A,B,C)
         => v1_funcop_1(D) ) ) ),
    file(pboole,cc3_pboole),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(d1_binop_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ),
    file(binop_1,d1_binop_1),
    []).

fof(d3_altcat_2,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_pboole(B,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)))
         => ( B = k4_altcat_2(A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_cat_1(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_cat_1(A))
                   => k1_binop_1(B,C,D) = k6_cat_1(A,C,D) ) ) ) ) ) ),
    file(altcat_2,d3_altcat_2),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(d7_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) != k1_xboole_0
               => ! [D] : 
                    ( m1_subset_1(D,u2_cat_1(A))
                   => ( m1_cat_1(D,A,B,C)
                    <=> r2_hidden(D,k6_cat_1(A,B,C)) ) ) ) ) ) ) ),
    file(cat_1,d7_cat_1),
    []).

fof(d8_altcat_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,k2_zfmisc_1(A,A))
         => ! [C] : 
              ( m3_pboole(C,k3_zfmisc_1(A,A,A),k3_altcat_1(A,B,B),k2_altcat_1(A,B))
             => ( v4_altcat_1(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => ? [E] : 
                        ( r2_hidden(E,k1_binop_1(B,D,D))
                        & ! [F] : 
                            ( m1_subset_1(F,A)
                           => ! [G] : 
                                ( r2_hidden(G,k1_binop_1(B,D,F))
                               => k1_binop_1(k4_altcat_1(A,B,C,D,D,F),G,E) = G ) ) ) ) ) ) ) ) ),
    file(altcat_1,d8_altcat_1),
    []).

fof(d9_altcat_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,k2_zfmisc_1(A,A))
         => ! [C] : 
              ( m3_pboole(C,k3_zfmisc_1(A,A,A),k3_altcat_1(A,B,B),k2_altcat_1(A,B))
             => ( v5_altcat_1(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => ? [E] : 
                        ( r2_hidden(E,k1_binop_1(B,D,D))
                        & ! [F] : 
                            ( m1_subset_1(F,A)
                           => ! [G] : 
                                ( r2_hidden(G,k1_binop_1(B,F,D))
                               => k1_binop_1(k4_altcat_1(A,B,C,F,D,D),E,G) = G ) ) ) ) ) ) ) ) ),
    file(altcat_1,d9_altcat_1),
    []).

fof(dt_k10_cat_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_cat_1(k10_cat_1(A,B),A,B,B) ) ),
    file(cat_1,k10_cat_1),
    []).

fof(dt_k1_binop_1,axiom,(
    $true ),
    file(binop_1,k1_binop_1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_multop_1,axiom,(
    $true ),
    file(multop_1,k1_multop_1),
    []).

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_altcat_1,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,k2_zfmisc_1(A,A))
     => m1_pboole(k2_altcat_1(A,B),k3_zfmisc_1(A,A,A)) ) ),
    file(altcat_1,k2_altcat_1),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

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

fof(dt_k3_altcat_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,k2_zfmisc_1(A,A))
        & m1_pboole(C,k2_zfmisc_1(A,A)) )
     => m1_pboole(k3_altcat_1(A,B,C),k3_zfmisc_1(A,A,A)) ) ),
    file(altcat_1,k3_altcat_1),
    []).

fof(dt_k3_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k3_zfmisc_1),
    []).

fof(dt_k4_altcat_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,k2_zfmisc_1(A,A))
        & m3_pboole(C,k3_zfmisc_1(A,A,A),k3_altcat_1(A,B,B),k2_altcat_1(A,B))
        & m1_subset_1(D,A)
        & m1_subset_1(E,A)
        & m1_subset_1(F,A) )
     => ( v1_funct_1(k4_altcat_1(A,B,C,D,E,F))
        & v1_funct_2(k4_altcat_1(A,B,C,D,E,F),k2_zfmisc_1(k1_binop_1(B,E,F),k1_binop_1(B,D,E)),k1_binop_1(B,D,F))
        & m2_relset_1(k4_altcat_1(A,B,C,D,E,F),k2_zfmisc_1(k1_binop_1(B,E,F),k1_binop_1(B,D,E)),k1_binop_1(B,D,F)) ) ) ),
    file(altcat_1,k4_altcat_1),
    []).

fof(dt_k4_altcat_2,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => m1_pboole(k4_altcat_2(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A))) ) ),
    file(altcat_2,k4_altcat_2),
    []).

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

fof(dt_k5_altcat_2,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => m3_pboole(k5_altcat_2(A),k3_zfmisc_1(u1_cat_1(A),u1_cat_1(A),u1_cat_1(A)),k3_altcat_1(u1_cat_1(A),k4_altcat_2(A),k4_altcat_2(A)),k2_altcat_1(u1_cat_1(A),k4_altcat_2(A))) ) ),
    file(altcat_2,k5_altcat_2),
    []).

fof(dt_k5_cat_1,axiom,(
    ! [A,B] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_subset_1(k5_cat_1(A,B),u2_cat_1(A)) ) ),
    file(cat_1,k5_cat_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_k9_cat_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A))
        & m1_subset_1(D,u1_cat_1(A))
        & m1_cat_1(E,A,B,C)
        & m1_cat_1(F,A,C,D) )
     => m1_cat_1(k9_cat_1(A,B,C,D,E,F),A,B,D) ) ),
    file(cat_1,k9_cat_1),
    []).

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

fof(dt_m1_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)) )
     => ! [D] : 
          ( m1_cat_1(D,A,B,C)
         => m1_subset_1(D,u2_cat_1(A)) ) ) ),
    file(cat_1,m1_cat_1),
    []).

fof(dt_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

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_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m3_pboole(D,A,B,C)
         => m1_pboole(D,A) ) ) ),
    file(pboole,m3_pboole),
    []).

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

fof(existence_m1_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)) )
     => ? [D] : m1_cat_1(D,A,B,C) ) ),
    file(cat_1,m1_cat_1),
    []).

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

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(existence_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ? [D] : m3_pboole(D,A,B,C) ) ),
    file(pboole,m3_pboole),
    []).

fof(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    []).

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

fof(fc2_altcat_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_finset_1(k1_tarski(A))
        & v1_fraenkel(k1_tarski(A))
        & v1_realset1(k1_tarski(A)) ) ) ),
    file(altcat_1,fc2_altcat_1),
    []).

fof(fc2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ~ v1_xboole_0(k1_funct_1(B,C)) ) ),
    file(pboole,fc2_pboole),
    []).

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

fof(fc3_realset1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A))
      & v1_realset1(k1_tarski(A)) ) ),
    file(realset1,fc3_realset1),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_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(fc5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C) )
     => ~ v1_xboole_0(k3_zfmisc_1(A,B,C)) ) ),
    file(subset_1,fc5_subset_1),
    []).

fof(fc7_funcop_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ( v1_relat_1(k1_funct_1(A,B))
        & v1_funct_1(k1_funct_1(A,B)) ) ) ),
    file(funcop_1,fc7_funcop_1),
    []).

fof(rc1_funcop_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funcop_1(A) ) ),
    file(funcop_1,rc1_funcop_1),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_pboole,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(pboole,rc1_pboole),
    []).

fof(rc1_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(realset1,rc1_realset1),
    []).

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

fof(rc2_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v3_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc2_pboole),
    []).

fof(rc2_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_realset1(A) ) ),
    file(realset1,rc2_realset1),
    []).

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_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(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc3_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v2_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc3_pboole),
    []).

fof(rc3_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

fof(rc4_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

fof(rc4_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_funcop_1(B) ) ),
    file(pboole,rc4_pboole),
    []).

fof(rc5_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_funct_1),
    []).

fof(redefinition_k10_cat_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => k10_cat_1(A,B) = k5_cat_1(A,B) ) ),
    file(cat_1,k10_cat_1),
    []).

fof(redefinition_k4_altcat_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,k2_zfmisc_1(A,A))
        & m3_pboole(C,k3_zfmisc_1(A,A,A),k3_altcat_1(A,B,B),k2_altcat_1(A,B))
        & m1_subset_1(D,A)
        & m1_subset_1(E,A)
        & m1_subset_1(F,A) )
     => k4_altcat_1(A,B,C,D,E,F) = k1_multop_1(C,D,E,F) ) ),
    file(altcat_1,k4_altcat_1),
    []).

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_altcat_2,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => r2_hidden(k10_cat_1(A,B),k1_binop_1(k4_altcat_2(A),B,B)) ) ) ),
    file(altcat_2,t13_altcat_2),
    []).

fof(t14_altcat_2,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,u1_cat_1(A))
                 => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                      & k6_cat_1(A,C,D) != k1_xboole_0
                      & ~ ! [E] : 
                            ( m1_cat_1(E,A,B,C)
                           => ! [F] : 
                                ( m1_cat_1(F,A,C,D)
                               => k1_binop_1(k4_altcat_1(u1_cat_1(A),k4_altcat_2(A),k5_altcat_2(A),B,C,D),F,E) = k9_cat_1(A,B,C,D,E,F) ) ) ) ) ) ) ) ),
    file(altcat_2,t14_altcat_2),
    []).

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(t56_cat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => k6_cat_1(A,B,B) != k1_xboole_0 ) ) ),
    file(cat_1,t56_cat_1),
    []).

fof(t57_cat_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_cat_1(D,A,B,C)
                 => ( k6_cat_1(A,B,C) != k1_xboole_0
                   => k9_cat_1(A,B,C,C,D,k10_cat_1(A,C)) = D ) ) ) ) ) ),
    file(cat_1,t57_cat_1),
    []).

fof(t58_cat_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_cat_1(D,A,B,C)
                 => ( k6_cat_1(A,B,C) != k1_xboole_0
                   => k9_cat_1(A,B,B,C,k10_cat_1(A,B),D) = D ) ) ) ) ) ),
    file(cat_1,t58_cat_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(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),
    []).