% Mizar problem: t25_heyting1,heyting1,762,42 
fof(t25_heyting1,conjecture,(
    ! [A,B] : 
      ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
     => ! [C] : 
          ( m1_subset_1(C,u1_struct_0(k12_normform(A)))
         => ! [D] : 
              ( m1_subset_1(D,u1_struct_0(k12_normform(A)))
             => ~ ( ! [E] : 
                      ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
                     => ( r2_hidden(E,C)
                       => r2_hidden(k1_normform(k5_finsub_1(A),k5_finsub_1(A),E,B),k7_normform(A)) ) )
                  & ! [E] : 
                      ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
                     => ~ ( r2_hidden(E,C)
                          & ! [F] : 
                              ( m2_subset_1(F,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
                             => ~ ( r2_hidden(F,D)
                                  & r1_normform(k5_finsub_1(A),k5_finsub_1(A),F,k1_normform(k5_finsub_1(A),k5_finsub_1(A),E,B)) ) ) ) )
                  & ! [E] : 
                      ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
                     => ~ ( r2_hidden(E,k7_heyting1(A,k3_heyting1(A,C),k3_heyting1(A,D)))
                          & r1_normform(k5_finsub_1(A),k5_finsub_1(A),E,B) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v3_lattices,antisymmetry_r2_hidden,cc1_finset_1,cc1_finsub_1,cc1_relset_1,cc2_finset_1,cc2_finsub_1,cc3_finsub_1,commutativity_k1_normform,commutativity_k3_xboole_0,d3_heyting1,d3_xboole_0,d7_heyting1,dt_g3_lattices,dt_k12_normform,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_normform,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_funct_2,dt_k2_zfmisc_1,dt_k3_funcop_1,dt_k3_heyting1,dt_k3_normform,dt_k3_xboole_0,dt_k5_finsub_1,dt_k5_heyting1,dt_k6_funcop_1,dt_k6_funct_3,dt_k6_normform,dt_k6_relat_1,dt_k7_heyting1,dt_k7_normform,dt_k8_funct_2,dt_k8_normform,dt_k8_setwiseo,dt_k9_relat_1,dt_l1_lattices,dt_l1_struct_0,dt_l2_lattices,dt_l3_lattices,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_m2_subset_1,dt_u1_lattices,dt_u1_struct_0,dt_u2_lattices,existence_l1_lattices,existence_l1_struct_0,existence_l2_lattices,existence_l3_lattices,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,existence_m2_subset_1,fc10_finset_1,fc11_finset_1,fc13_finset_1,fc14_finset_1,fc1_finsub_1,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_finsub_1,fc2_normform,fc3_normform,fc4_normform,fc4_subset_1,fc5_normform,fc6_normform,fraenkel_a_3_4_heyting1,fraenkel_a_3_8_heyting1,free_g3_lattices,idempotence_k1_normform,idempotence_k3_xboole_0,l38_heyting1,rc1_finset_1,rc1_heyting1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc3_struct_0,rc4_finset_1,rc5_struct_0,redefinition_k1_fraenkel,redefinition_k2_funct_2,redefinition_k6_funcop_1,redefinition_k6_funct_3,redefinition_k8_funct_2,redefinition_k8_setwiseo,redefinition_m2_fraenkel,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_normform,reflexivity_r1_tarski,s27_fraenkel__e4_33__heyting1,t15_setwiseo,t1_subset,t2_boole,t2_subset,t2_tarski,t31_normform,t3_subset,t40_normform,t45_normform,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(heyting1,t25_heyting1)]).

fof(abstractness_v3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( v3_lattices(A)
       => A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ) ),
    file(lattices,v3_lattices),
    []).

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

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

fof(cc1_finsub_1,axiom,(
    ! [A] : 
      ( v4_finsub_1(A)
     => ( v1_finsub_1(A)
        & v3_finsub_1(A) ) ) ),
    file(finsub_1,cc1_finsub_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_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    []).

fof(cc2_finsub_1,axiom,(
    ! [A] : 
      ( ( v1_finsub_1(A)
        & v3_finsub_1(A) )
     => v4_finsub_1(A) ) ),
    file(finsub_1,cc2_finsub_1),
    []).

fof(cc3_finsub_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(A))
     => v1_finset_1(B) ) ),
    file(finsub_1,cc3_finsub_1),
    []).

fof(commutativity_k1_normform,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & ~ v1_xboole_0(B)
        & v4_finsub_1(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B))
        & m1_subset_1(D,k2_zfmisc_1(A,B)) )
     => k1_normform(A,B,C,D) = k1_normform(A,B,D,C) ) ),
    file(normform,k1_normform),
    []).

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(d3_heyting1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,u1_struct_0(k12_normform(A)))
     => k3_heyting1(A,B) = B ) ),
    file(heyting1,d3_heyting1),
    []).

fof(d3_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    []).

fof(d7_heyting1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => ! [C] : 
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => k7_heyting1(A,B,C) = k3_xboole_0(k7_normform(A),a_3_4_heyting1(A,B,C)) ) ) ),
    file(heyting1,d7_heyting1),
    []).

fof(dt_g3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ( v3_lattices(g3_lattices(A,B,C))
        & l3_lattices(g3_lattices(A,B,C)) ) ) ),
    file(lattices,g3_lattices),
    []).

fof(dt_k12_normform,axiom,(
    ! [A] : 
      ( v3_lattices(k12_normform(A))
      & l3_lattices(k12_normform(A)) ) ),
    file(normform,k12_normform),
    []).

fof(dt_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

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_normform,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & ~ v1_xboole_0(B)
        & v4_finsub_1(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B))
        & m1_subset_1(D,k2_zfmisc_1(A,B)) )
     => m1_subset_1(k1_normform(A,B,C,D),k2_zfmisc_1(A,B)) ) ),
    file(normform,k1_normform),
    []).

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_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)) ) ),
    file(funct_2,k2_funct_2),
    []).

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

fof(dt_k3_funcop_1,axiom,(
    $true ),
    file(funcop_1,k3_funcop_1),
    []).

fof(dt_k3_heyting1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,u1_struct_0(k12_normform(A)))
     => m2_subset_1(k3_heyting1(A,B),k5_finsub_1(k7_normform(A)),k8_normform(A)) ) ),
    file(heyting1,k3_heyting1),
    []).

fof(dt_k3_normform,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & ~ v1_xboole_0(B)
        & v4_finsub_1(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B))
        & m1_subset_1(D,k2_zfmisc_1(A,B)) )
     => m1_subset_1(k3_normform(A,B,C,D),k2_zfmisc_1(A,B)) ) ),
    file(normform,k3_normform),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k5_finsub_1,axiom,(
    ! [A] : v4_finsub_1(k5_finsub_1(A)) ),
    file(finsub_1,k5_finsub_1),
    []).

fof(dt_k5_heyting1,axiom,(
    ! [A] : 
      ( v1_funct_1(k5_heyting1(A))
      & v1_funct_2(k5_heyting1(A),k2_zfmisc_1(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
      & m2_relset_1(k5_heyting1(A),k2_zfmisc_1(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) ) ),
    file(heyting1,k5_heyting1),
    []).

fof(dt_k6_funcop_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & v1_funct_2(E,B,A)
        & m1_relset_1(E,B,A) )
     => ( v1_funct_1(k6_funcop_1(A,B,C,D,E))
        & v1_funct_2(k6_funcop_1(A,B,C,D,E),B,A)
        & m2_relset_1(k6_funcop_1(A,B,C,D,E),B,A) ) ) ),
    file(funcop_1,k6_funcop_1),
    []).

fof(dt_k6_funct_3,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ( v1_funct_1(k6_funct_3(A,B))
        & v1_funct_2(k6_funct_3(A,B),B,A)
        & m2_relset_1(k6_funct_3(A,B),B,A) ) ) ),
    file(funct_3,k6_funct_3),
    []).

fof(dt_k6_normform,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,k5_finsub_1(A))
        & v1_funct_1(D)
        & v1_funct_2(D,A,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)))
        & m1_relset_1(D,A,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B))) )
     => m1_subset_1(k6_normform(A,B,C,D),k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B))) ) ),
    file(normform,k6_normform),
    []).

fof(dt_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_1),
    []).

fof(dt_k7_heyting1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
        & m1_subset_1(C,k5_finsub_1(k7_normform(A))) )
     => m1_subset_1(k7_heyting1(A,B,C),k5_finsub_1(k7_normform(A))) ) ),
    file(heyting1,k7_heyting1),
    []).

fof(dt_k7_normform,axiom,(
    ! [A] : m1_subset_1(k7_normform(A),k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))) ),
    file(normform,k7_normform),
    []).

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_k8_normform,axiom,(
    ! [A] : m1_subset_1(k8_normform(A),k1_zfmisc_1(k5_finsub_1(k7_normform(A)))) ),
    file(normform,k8_normform),
    []).

fof(dt_k8_setwiseo,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,k5_finsub_1(A)) )
     => m1_subset_1(k8_setwiseo(A,B,C,D),k5_finsub_1(B)) ) ),
    file(setwiseo,k8_setwiseo),
    []).

fof(dt_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    []).

fof(dt_l1_lattices,axiom,(
    ! [A] : 
      ( l1_lattices(A)
     => l1_struct_0(A) ) ),
    file(lattices,l1_lattices),
    []).

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

fof(dt_l2_lattices,axiom,(
    ! [A] : 
      ( l2_lattices(A)
     => l1_struct_0(A) ) ),
    file(lattices,l2_lattices),
    []).

fof(dt_l3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( l1_lattices(A)
        & l2_lattices(A) ) ) ),
    file(lattices,l3_lattices),
    []).

fof(dt_m1_fraenkel,axiom,(
    ! [A,B,C] : 
      ( m1_fraenkel(C,A,B)
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) ),
    file(fraenkel,m1_fraenkel),
    []).

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_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) ) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(dt_u1_lattices,axiom,(
    ! [A] : 
      ( l1_lattices(A)
     => ( v1_funct_1(u1_lattices(A))
        & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattices,u1_lattices),
    []).

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

fof(dt_u2_lattices,axiom,(
    ! [A] : 
      ( l2_lattices(A)
     => ( v1_funct_1(u2_lattices(A))
        & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattices,u2_lattices),
    []).

fof(existence_l1_lattices,axiom,(
    ? [A] : l1_lattices(A) ),
    file(lattices,l1_lattices),
    []).

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

fof(existence_l2_lattices,axiom,(
    ? [A] : l2_lattices(A) ),
    file(lattices,l2_lattices),
    []).

fof(existence_l3_lattices,axiom,(
    ? [A] : l3_lattices(A) ),
    file(lattices,l3_lattices),
    []).

fof(existence_m1_fraenkel,axiom,(
    ! [A,B] : 
    ? [C] : m1_fraenkel(C,A,B) ),
    file(fraenkel,m1_fraenkel),
    []).

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_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ? [D] : m2_fraenkel(D,A,B,C) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(fc10_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc10_finset_1),
    []).

fof(fc11_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc11_finset_1),
    []).

fof(fc13_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k9_relat_1(A,B)) ) ),
    file(finset_1,fc13_finset_1),
    []).

fof(fc14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    []).

fof(fc1_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_zfmisc_1(A))
      & v1_finsub_1(k1_zfmisc_1(A))
      & v3_finsub_1(k1_zfmisc_1(A))
      & v4_finsub_1(k1_zfmisc_1(A)) ) ),
    file(finsub_1,fc1_finsub_1),
    []).

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

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

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

fof(fc2_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k5_finsub_1(A))
      & v1_finsub_1(k5_finsub_1(A))
      & v3_finsub_1(k5_finsub_1(A))
      & v4_finsub_1(k5_finsub_1(A)) ) ),
    file(finsub_1,fc2_finsub_1),
    []).

fof(fc2_normform,axiom,(
    ! [A] : 
      ( v1_relat_1(k7_normform(A))
      & ~ v1_xboole_0(k7_normform(A)) ) ),
    file(normform,fc2_normform),
    []).

fof(fc3_normform,axiom,(
    ! [A] : ~ v1_xboole_0(k8_normform(A)) ),
    file(normform,fc3_normform),
    []).

fof(fc4_normform,axiom,(
    ! [A] : 
      ( ~ v3_struct_0(k12_normform(A))
      & v3_lattices(k12_normform(A)) ) ),
    file(normform,fc4_normform),
    []).

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_normform,axiom,(
    ! [A] : 
      ( ~ v3_struct_0(k12_normform(A))
      & v3_lattices(k12_normform(A))
      & v4_lattices(k12_normform(A))
      & v5_lattices(k12_normform(A))
      & v6_lattices(k12_normform(A))
      & v7_lattices(k12_normform(A))
      & v8_lattices(k12_normform(A))
      & v9_lattices(k12_normform(A))
      & v10_lattices(k12_normform(A)) ) ),
    file(normform,fc5_normform),
    []).

fof(fc6_normform,axiom,(
    ! [A] : 
      ( ~ v3_struct_0(k12_normform(A))
      & v3_lattices(k12_normform(A))
      & v4_lattices(k12_normform(A))
      & v5_lattices(k12_normform(A))
      & v6_lattices(k12_normform(A))
      & v7_lattices(k12_normform(A))
      & v8_lattices(k12_normform(A))
      & v9_lattices(k12_normform(A))
      & v10_lattices(k12_normform(A))
      & v11_lattices(k12_normform(A))
      & v12_lattices(k12_normform(A))
      & v13_lattices(k12_normform(A)) ) ),
    file(normform,fc6_normform),
    []).

fof(fraenkel_a_3_4_heyting1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,k5_finsub_1(k7_normform(B)))
        & m1_subset_1(D,k5_finsub_1(k7_normform(B))) )
     => ( r2_hidden(A,a_3_4_heyting1(B,C,D))
      <=> ? [E] : 
            ( m2_fraenkel(E,k7_normform(B),k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k1_fraenkel(k7_normform(B),k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B))))
            & A = k6_normform(k7_normform(B),B,C,k6_funcop_1(k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B),k5_heyting1(B),E,k6_funct_3(k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))))
            & r1_tarski(k8_setwiseo(k7_normform(B),k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),E,C),D) ) ) ) ),
    file(heyting1,a_3_4_heyting1),
    []).

fof(fraenkel_a_3_8_heyting1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,u1_struct_0(k12_normform(B)))
        & m1_subset_1(D,u1_struct_0(k12_normform(B))) )
     => ( r2_hidden(A,a_3_8_heyting1(B,C,D))
      <=> ? [E] : 
            ( m2_fraenkel(E,k7_normform(B),k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k1_fraenkel(k7_normform(B),k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B))))
            & A = k6_normform(k7_normform(B),B,k3_heyting1(B,C),k6_funcop_1(k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B),k5_heyting1(B),E,k6_funct_3(k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))))
            & r1_tarski(k8_setwiseo(k7_normform(B),k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),E,k3_heyting1(B,C)),D) ) ) ) ),
    file(heyting1,a_3_8_heyting1),
    []).

fof(free_g3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ! [D,E,F] : 
          ( g3_lattices(A,B,C) = g3_lattices(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(lattices,g3_lattices),
    []).

fof(idempotence_k1_normform,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & ~ v1_xboole_0(B)
        & v4_finsub_1(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B))
        & m1_subset_1(D,k2_zfmisc_1(A,B)) )
     => k1_normform(A,B,C,C) = C ) ),
    file(normform,k1_normform),
    []).

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(l38_heyting1,axiom,(
    ! [A,B] : 
      ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A))
     => ! [C] : 
          ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
         => ! [D] : 
              ( m2_fraenkel(D,k7_normform(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k1_fraenkel(k7_normform(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))))
             => k8_funct_2(k7_normform(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k6_funcop_1(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A),k5_heyting1(A),D,k6_funct_3(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))),C) = k3_normform(k5_finsub_1(A),k5_finsub_1(A),k8_funct_2(k7_normform(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),D,C),C) ) ) ) ),
    file(heyting1,l38_heyting1),
    []).

fof(rc1_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

fof(rc1_heyting1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k8_normform(A))
      & ~ v1_xboole_0(B) ) ),
    file(heyting1,rc1_heyting1),
    []).

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

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

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

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

fof(rc3_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    []).

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

fof(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    []).

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

fof(redefinition_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

fof(redefinition_k2_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ) ),
    file(funct_2,k2_funct_2),
    []).

fof(redefinition_k6_funcop_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & v1_funct_2(E,B,A)
        & m1_relset_1(E,B,A) )
     => k6_funcop_1(A,B,C,D,E) = k3_funcop_1(C,D,E) ) ),
    file(funcop_1,k6_funcop_1),
    []).

fof(redefinition_k6_funct_3,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k6_funct_3(A,B) = k6_relat_1(B) ) ),
    file(funct_3,k6_funct_3),
    []).

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_k8_setwiseo,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,k5_finsub_1(A)) )
     => k8_setwiseo(A,B,C,D) = k9_relat_1(C,D) ) ),
    file(setwiseo,k8_setwiseo),
    []).

fof(redefinition_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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(redefinition_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(reflexivity_r1_normform,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & ~ v1_xboole_0(B)
        & v4_finsub_1(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B))
        & m1_subset_1(D,k2_zfmisc_1(A,B)) )
     => r1_normform(A,B,C,C) ) ),
    file(normform,r1_normform),
    []).

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

fof(s27_fraenkel__e4_33__heyting1,axiom,(
    ! [A,B,C,D] : 
      ( ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
        & m1_subset_1(C,u1_struct_0(k12_normform(A)))
        & m1_subset_1(D,u1_struct_0(k12_normform(A))) )
     => ( ! [E] : 
            ( m1_subset_1(E,k7_normform(A))
           => ~ ( r2_hidden(E,k3_heyting1(A,C))
                & ! [F] : 
                    ( m1_subset_1(F,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
                   => ~ ( r2_hidden(F,k3_heyting1(A,D))
                        & r1_normform(k5_finsub_1(A),k5_finsub_1(A),F,k1_normform(k5_finsub_1(A),k5_finsub_1(A),E,B)) ) ) ) )
       => ? [E] : 
            ( m2_fraenkel(E,k7_normform(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k1_fraenkel(k7_normform(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))))
            & ! [F] : 
                ( m1_subset_1(F,k7_normform(A))
               => ( r2_hidden(F,k3_heyting1(A,C))
                 => ( r2_hidden(k8_funct_2(k7_normform(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),E,F),k3_heyting1(A,D))
                    & r1_normform(k5_finsub_1(A),k5_finsub_1(A),k8_funct_2(k7_normform(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),E,F),k1_normform(k5_finsub_1(A),k5_finsub_1(A),F,B)) ) ) ) ) ) ) ),
    file(heyting1,s27_fraenkel__e4_33__heyting1),
    []).

fof(t15_setwiseo,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [D,E] : 
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,A,B)
                    & m2_relset_1(E,A,B) )
                 => ( ! [F] : 
                        ( m1_subset_1(F,A)
                       => ( r2_hidden(F,C)
                         => r2_hidden(k8_funct_2(A,B,E,F),D) ) )
                   => r1_tarski(k2_funct_2(A,B,E,C),D) ) ) ) ) ) ),
    file(setwiseo,t15_setwiseo),
    []).

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

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

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(t31_normform,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] : 
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ! [E] : 
                      ( m1_subset_1(E,k2_zfmisc_1(A,B))
                     => ( r1_normform(A,B,C,k1_normform(A,B,D,E))
                       => r1_normform(A,B,k3_normform(A,B,C,E),D) ) ) ) ) ) ) ),
    file(normform,t31_normform),
    []).

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

fof(t40_normform,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
            & m2_relset_1(C,B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) )
         => ! [D] : 
              ( m1_subset_1(D,k5_finsub_1(B))
             => ! [E] : 
                  ( m1_subset_1(E,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
                 => ( ! [F] : 
                        ( m1_subset_1(F,B)
                       => ( r2_hidden(F,D)
                         => r1_normform(k5_finsub_1(A),k5_finsub_1(A),k8_funct_2(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),C,F),E) ) )
                   => r1_normform(k5_finsub_1(A),k5_finsub_1(A),k6_normform(B,A,D,C),E) ) ) ) ) ) ),
    file(normform,t40_normform),
    []).

fof(t45_normform,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
     => ! [C] : 
          ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
         => ( r1_normform(k5_finsub_1(A),k5_finsub_1(A),B,C)
           => m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) ) ) ) ),
    file(normform,t45_normform),
    []).

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(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),
    []).