% Mizar problem: t14_altcat_3,altcat_3,554,22 
fof(t14_altcat_3,conjecture,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k7_altcat_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k7_altcat_1(A)))
             => ( k1_altcat_1(k7_altcat_1(A),B,C) != k1_xboole_0
               => ! [D] : 
                    ( m1_subset_1(D,k1_altcat_1(k7_altcat_1(A),B,C))
                   => ! [E] : 
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,B,C)
                          & m2_relset_1(E,B,C) )
                       => ( E = D
                         => ( v5_altcat_3(D,k7_altcat_1(A),B,C)
                          <=> v2_funct_2(E,B,C) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v6_altcat_1,antisymmetry_r2_hidden,cc1_altcat_1,cc1_funct_1,cc1_relset_1,cc1_setfam_1,cc1_tex_2,cc2_altcat_1,cc2_funct_1,cc2_tex_2,cc3_altcat_1,cc3_tex_2,cc4_tex_2,cc5_tex_2,cc6_tex_2,cc7_tex_2,d10_xboole_0,d16_altcat_1,d1_cqc_lang,d1_funct_2,d1_tarski,d2_funct_2,d3_funct_2,d3_tarski,d4_altcat_1,d4_realset1,d4_xboole_0,d5_funct_1,d8_altcat_3,d9_setfam_1,dt_g2_altcat_1,dt_k1_altcat_1,dt_k1_cqc_lang,dt_k1_funct_1,dt_k1_funct_2,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_altcat_1,dt_k2_funcop_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k3_altcat_1,dt_k3_zfmisc_1,dt_k4_relset_1,dt_k4_xboole_0,dt_k5_altcat_1,dt_k5_relat_1,dt_k7_altcat_1,dt_l1_altcat_1,dt_l1_struct_0,dt_l2_altcat_1,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m3_pboole,dt_u1_altcat_1,dt_u1_struct_0,dt_u2_altcat_1,existence_l1_altcat_1,existence_l1_struct_0,existence_l2_altcat_1,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m3_pboole,fc1_funcop_1,fc1_funct_1,fc1_tex_2,fc1_xboole_0,fc2_altcat_1,fc2_funcop_1,fc2_setfam_1,fc3_altcat_1,fc3_funcop_1,fc4_altcat_1,fc6_funct_1,fc9_funcop_1,free_g2_altcat_1,rc1_funct_1,rc1_setfam_1,rc1_tex_2,rc1_xboole_0,rc2_altcat_1,rc2_funct_1,rc2_tex_2,rc2_xboole_0,rc3_altcat_1,rc3_funct_1,rc3_tex_2,rc4_tex_2,rc5_altcat_1,rc5_funct_1,rc5_tex_2,rc6_altcat_1,rc6_tex_2,rc7_tex_2,redefinition_k4_relset_1,redefinition_m2_relset_1,reflexivity_r1_tarski,s3_funct_1__e16_24_1_2_1_1_1_1__altcat_3,t10_partfun1,t12_relset_1,t13_funcop_1,t18_altcat_1,t19_funcop_1,t1_subset,t1_xboole_1,t22_funct_1,t23_funct_1,t25_funct_1,t2_subset,t39_zfmisc_1,t3_boole,t3_subset,t46_relat_1,t4_boole,t4_realset1,t4_subset,t57_partfun1,t5_subset,t64_relat_1,t65_relat_1,t6_boole,t7_boole,t8_boole,t9_funct_1]),
    [file(altcat_3,t14_altcat_3)]).

fof(abstractness_v6_altcat_1,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ( v6_altcat_1(A)
       => A = g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) ) ) ),
    file(altcat_1,v6_altcat_1),
    []).

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_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(cc1_setfam_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(setfam_1,cc1_setfam_1),
    []).

fof(cc1_tex_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_tex_2(B,k1_zfmisc_1(A))
           => ~ v1_xboole_0(B) ) ) ) ),
    file(tex_2,cc1_tex_2),
    []).

fof(cc2_altcat_1,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_altcat_1(A)
          & v8_altcat_1(A)
          & v9_altcat_1(A) )
       => ( ~ v3_struct_0(A)
          & v10_altcat_1(A) ) ) ) ),
    file(altcat_1,cc2_altcat_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_tex_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_xboole_0(B)
           => v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ),
    file(tex_2,cc2_tex_2),
    []).

fof(cc3_altcat_1,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_altcat_1(A)
          & v10_altcat_1(A)
          & v12_altcat_1(A) )
       => ( ~ v3_struct_0(A)
          & v8_altcat_1(A)
          & v9_altcat_1(A) ) ) ) ),
    file(altcat_1,cc3_altcat_1),
    []).

fof(cc3_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_tex_2(B,k1_zfmisc_1(A))
           => ( v1_xboole_0(B)
              & v1_membered(B)
              & v2_membered(B)
              & v3_membered(B)
              & v4_membered(B)
              & v5_membered(B)
              & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc3_tex_2),
    []).

fof(cc4_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_xboole_0(B)
           => ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc4_tex_2),
    []).

fof(cc5_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) )
           => ( ~ v1_xboole_0(B)
              & v1_realset1(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc5_tex_2),
    []).

fof(cc6_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & v1_realset1(B) )
           => ( ~ v1_xboole_0(B)
              & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc6_tex_2),
    []).

fof(cc7_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) )
           => ( ~ v1_xboole_0(B)
              & ~ v1_realset1(B) ) ) ) ) ),
    file(tex_2,cc7_tex_2),
    []).

fof(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d16_altcat_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_altcat_1(B)
            & v10_altcat_1(B)
            & l2_altcat_1(B) )
         => ( B = k7_altcat_1(A)
          <=> ( u1_struct_0(B) = A
              & ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(B))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(B))
                     => k1_altcat_1(B,C,D) = k1_funct_2(C,D) ) ) ) ) ) ) ),
    file(altcat_1,d16_altcat_1),
    []).

fof(d1_cqc_lang,axiom,(
    ! [A,B,C,D] : 
      ( ( A = B
       => k1_cqc_lang(A,B,C,D) = C )
      & ( A != B
       => k1_cqc_lang(A,B,C,D) = D ) ) ),
    file(cqc_lang,d1_cqc_lang),
    []).

fof(d1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    []).

fof(d1_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

fof(d2_funct_2,axiom,(
    ! [A,B,C] : 
      ( C = k1_funct_2(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & k1_relat_1(E) = A
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(funct_2,d2_funct_2),
    []).

fof(d3_funct_2,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( v2_funct_2(C,A,B)
      <=> k2_relat_1(C) = B ) ) ),
    file(funct_2,d3_funct_2),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

fof(d4_altcat_1,axiom,(
    ! [A] : 
      ( l1_altcat_1(A)
     => ( v2_altcat_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                        & k1_altcat_1(A,C,D) != k1_xboole_0
                        & k1_altcat_1(A,B,D) = k1_xboole_0 ) ) ) ) ) ) ),
    file(altcat_1,d4_altcat_1),
    []).

fof(d4_realset1,axiom,(
    ! [A] : 
      ( v1_realset1(A)
    <=> ~ ( ~ v1_xboole_0(A)
          & ! [B] : A != k1_tarski(B) ) ) ),
    file(realset1,d4_realset1),
    []).

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

fof(d5_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    []).

fof(d8_altcat_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,k1_altcat_1(A,B,C))
                 => ( v5_altcat_3(D,A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( k1_altcat_1(A,C,E) != k1_xboole_0
                         => ! [F] : 
                              ( m1_subset_1(F,k1_altcat_1(A,C,E))
                             => ! [G] : 
                                  ( m1_subset_1(G,k1_altcat_1(A,C,E))
                                 => ( k5_altcat_1(A,B,C,E,D,F) = k5_altcat_1(A,B,C,E,D,G)
                                   => F = G ) ) ) ) ) ) ) ) ) ) ),
    file(altcat_3,d8_altcat_3),
    []).

fof(d9_setfam_1,axiom,(
    ! [A] : 
      ( v1_setfam_1(A)
    <=> ~ r2_hidden(k1_xboole_0,A) ) ),
    file(setfam_1,d9_setfam_1),
    []).

fof(dt_g2_altcat_1,axiom,(
    ! [A,B,C] : 
      ( ( 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)) )
     => ( v6_altcat_1(g2_altcat_1(A,B,C))
        & l2_altcat_1(g2_altcat_1(A,B,C)) ) ) ),
    file(altcat_1,g2_altcat_1),
    []).

fof(dt_k1_altcat_1,axiom,(
    $true ),
    file(altcat_1,k1_altcat_1),
    []).

fof(dt_k1_cqc_lang,axiom,(
    $true ),
    file(cqc_lang,k1_cqc_lang),
    []).

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

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_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_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

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_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_altcat_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,k1_altcat_1(A,B,C))
        & m1_subset_1(F,k1_altcat_1(A,C,D)) )
     => m1_subset_1(k5_altcat_1(A,B,C,D,E,F),k1_altcat_1(A,B,D)) ) ),
    file(altcat_1,k5_altcat_1),
    []).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k7_altcat_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v3_struct_0(k7_altcat_1(A))
        & v6_altcat_1(k7_altcat_1(A))
        & v10_altcat_1(k7_altcat_1(A))
        & l2_altcat_1(k7_altcat_1(A)) ) ) ),
    file(altcat_1,k7_altcat_1),
    []).

fof(dt_l1_altcat_1,axiom,(
    ! [A] : 
      ( l1_altcat_1(A)
     => l1_struct_0(A) ) ),
    file(altcat_1,l1_altcat_1),
    []).

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

fof(dt_l2_altcat_1,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => l1_altcat_1(A) ) ),
    file(altcat_1,l2_altcat_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_altcat_1,axiom,(
    ! [A] : 
      ( l1_altcat_1(A)
     => m1_pboole(u1_altcat_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ),
    file(altcat_1,u1_altcat_1),
    []).

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

fof(dt_u2_altcat_1,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => m3_pboole(u2_altcat_1(A),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_altcat_1(u1_struct_0(A),u1_altcat_1(A),u1_altcat_1(A)),k2_altcat_1(u1_struct_0(A),u1_altcat_1(A))) ) ),
    file(altcat_1,u2_altcat_1),
    []).

fof(existence_l1_altcat_1,axiom,(
    ? [A] : l1_altcat_1(A) ),
    file(altcat_1,l1_altcat_1),
    []).

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

fof(existence_l2_altcat_1,axiom,(
    ? [A] : l2_altcat_1(A) ),
    file(altcat_1,l2_altcat_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(fc1_funcop_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B)) ) ),
    file(funcop_1,fc1_funcop_1),
    []).

fof(fc1_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    []).

fof(fc1_tex_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_realset1(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(tex_2,fc1_tex_2),
    []).

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

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_funcop_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A))
      & v1_relat_1(k2_funcop_1(k1_xboole_0,A))
      & v1_funct_1(k2_funcop_1(k1_xboole_0,A))
      & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ),
    file(funcop_1,fc2_funcop_1),
    []).

fof(fc2_setfam_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_setfam_1(k1_tarski(A)) ) ) ),
    file(setfam_1,fc2_setfam_1),
    []).

fof(fc3_altcat_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ 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)) )
     => ( ~ v3_struct_0(g2_altcat_1(A,B,C))
        & v6_altcat_1(g2_altcat_1(A,B,C)) ) ) ),
    file(altcat_1,fc3_altcat_1),
    []).

fof(fc3_funcop_1,axiom,(
    ! [A,B] : 
      ( v1_xboole_0(B)
     => ( v1_xboole_0(k2_funcop_1(B,A))
        & v1_relat_1(k2_funcop_1(B,A))
        & v1_funct_1(k2_funcop_1(B,A))
        & v2_funct_1(k2_funcop_1(B,A)) ) ) ),
    file(funcop_1,fc3_funcop_1),
    []).

fof(fc4_altcat_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v3_struct_0(k7_altcat_1(A))
        & v2_altcat_1(k7_altcat_1(A))
        & v6_altcat_1(k7_altcat_1(A))
        & v10_altcat_1(k7_altcat_1(A))
        & v11_altcat_1(k7_altcat_1(A))
        & v12_altcat_1(k7_altcat_1(A)) ) ) ),
    file(altcat_1,fc4_altcat_1),
    []).

fof(fc6_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => v1_setfam_1(k2_relat_1(A)) ) ),
    file(funct_1,fc6_funct_1),
    []).

fof(fc9_funcop_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v2_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B)) ) ) ),
    file(funcop_1,fc9_funcop_1),
    []).

fof(free_g2_altcat_1,axiom,(
    ! [A,B,C] : 
      ( ( 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)) )
     => ! [D,E,F] : 
          ( g2_altcat_1(A,B,C) = g2_altcat_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(altcat_1,g2_altcat_1),
    []).

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

fof(rc1_setfam_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_setfam_1(A) ) ),
    file(setfam_1,rc1_setfam_1),
    []).

fof(rc1_tex_2,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(tex_2,rc1_tex_2),
    []).

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

fof(rc2_altcat_1,axiom,(
    ? [A] : 
      ( l2_altcat_1(A)
      & v6_altcat_1(A) ) ),
    file(altcat_1,rc2_altcat_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_tex_2,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ),
    file(tex_2,rc2_tex_2),
    []).

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

fof(rc3_altcat_1,axiom,(
    ? [A] : 
      ( l2_altcat_1(A)
      & ~ v3_struct_0(A)
      & v6_altcat_1(A) ) ),
    file(altcat_1,rc3_altcat_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_tex_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc3_tex_2),
    []).

fof(rc4_tex_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc4_tex_2),
    []).

fof(rc5_altcat_1,axiom,(
    ? [A] : 
      ( l2_altcat_1(A)
      & ~ v3_struct_0(A)
      & v6_altcat_1(A)
      & v10_altcat_1(A) ) ),
    file(altcat_1,rc5_altcat_1),
    []).

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(rc5_tex_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_realset1(B) ) ) ),
    file(tex_2,rc5_tex_2),
    []).

fof(rc6_altcat_1,axiom,(
    ? [A] : 
      ( l2_altcat_1(A)
      & ~ v3_struct_0(A)
      & v2_altcat_1(A)
      & v6_altcat_1(A)
      & v11_altcat_1(A)
      & v12_altcat_1(A) ) ),
    file(altcat_1,rc6_altcat_1),
    []).

fof(rc6_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_realset1(B)
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc6_tex_2),
    []).

fof(rc7_tex_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_realset1(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc7_tex_2),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_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(s3_funct_1__e16_24_1_2_1_1_1_1__altcat_3,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A)
        & m1_subset_1(B,u1_struct_0(k7_altcat_1(A)))
        & m1_subset_1(C,u1_struct_0(k7_altcat_1(A)))
        & m1_subset_1(E,C)
        & m1_subset_1(F,C) )
     => ? [G] : 
          ( v1_relat_1(G)
          & v1_funct_1(G)
          & k1_relat_1(G) = B
          & ! [H] : 
              ( r2_hidden(H,B)
             => k1_funct_1(G,H) = k1_cqc_lang(H,D,F,E) ) ) ) ),
    file(altcat_3,s3_funct_1__e16_24_1_2_1_1_1_1__altcat_3),
    []).

fof(t10_partfun1,axiom,(
    k2_relat_1(k1_xboole_0) = k1_xboole_0 ),
    file(partfun1,t10_partfun1),
    []).

fof(t12_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    []).

fof(t13_funcop_1,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    []).

fof(t18_altcat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                      & k1_altcat_1(A,C,D) != k1_xboole_0
                      & k1_altcat_1(A,B,D) != k1_xboole_0
                      & ? [E] : 
                          ( m1_subset_1(E,k1_altcat_1(A,B,C))
                          & ? [F] : 
                              ( m1_subset_1(F,k1_altcat_1(A,C,D))
                              & ? [G] : 
                                  ( v1_relat_1(G)
                                  & v1_funct_1(G)
                                  & ? [H] : 
                                      ( v1_relat_1(H)
                                      & v1_funct_1(H)
                                      & E = G
                                      & F = H
                                      & k5_altcat_1(A,B,C,D,E,F) != k5_relat_1(G,H) ) ) ) ) ) ) ) ) ) ),
    file(altcat_1,t18_altcat_1),
    []).

fof(t19_funcop_1,axiom,(
    ! [A,B] : 
      ( k1_relat_1(k2_funcop_1(A,B)) = A
      & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) ),
    file(funcop_1,t19_funcop_1),
    []).

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

fof(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    []).

fof(t22_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
           => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ),
    file(funct_1,t22_funct_1),
    []).

fof(t23_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ),
    file(funct_1,t23_funct_1),
    []).

fof(t25_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k2_relat_1(k5_relat_1(C,B)))
           => r2_hidden(A,k2_relat_1(B)) ) ) ) ),
    file(funct_1,t25_funct_1),
    []).

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

fof(t39_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,k1_tarski(B))
    <=> ( A = k1_xboole_0
        | A = k1_tarski(B) ) ) ),
    file(zfmisc_1,t39_zfmisc_1),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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

fof(t46_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k2_relat_1(A),k1_relat_1(B))
           => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ),
    file(relat_1,t46_relat_1),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

fof(t4_realset1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_realset1(A)
      <=> ! [B] : ~ v1_xboole_0(k4_xboole_0(A,k1_tarski(B))) ) ) ),
    file(realset1,t4_realset1),
    []).

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(t57_partfun1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_xboole_0,A) )
     => B = k1_xboole_0 ) ),
    file(partfun1,t57_partfun1),
    []).

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(t64_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( ( k1_relat_1(A) = k1_xboole_0
          | k2_relat_1(A) = k1_xboole_0 )
       => A = k1_xboole_0 ) ) ),
    file(relat_1,t64_relat_1),
    []).

fof(t65_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( k1_relat_1(A) = k1_xboole_0
      <=> k2_relat_1(A) = k1_xboole_0 ) ) ),
    file(relat_1,t65_relat_1),
    []).

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(t9_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    []).