% Mizar problem: t34_heyting1,heyting1,1230,30 
fof(t34_heyting1,conjecture,(
    ! [A] : k6_lattices(k12_normform(A)) = k1_tarski(k4_tarski(k1_xboole_0,k1_xboole_0)) ),
    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_k2_tarski,commutativity_k2_xboole_0,commutativity_k3_xboole_0,commutativity_k5_setwiseo,d10_heyting1,d11_heyting1,d1_binop_1,d3_heyting1,d3_lattice2,d5_tarski,d6_heyting1,d7_heyting1,d8_heyting1,d9_heyting1,dt_g3_lattices,dt_k10_heyting1,dt_k10_normform,dt_k11_heyting1,dt_k12_normform,dt_k1_binop_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_heyting1,dt_k1_mcart_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k2_domain_1,dt_k2_lattice2,dt_k2_mcart_1,dt_k2_setwiseo,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_domain_1,dt_k3_funcop_1,dt_k3_heyting1,dt_k3_xboole_0,dt_k4_filter_0,dt_k4_funcop_1,dt_k4_tarski,dt_k4_xboole_0,dt_k5_finsub_1,dt_k5_heyting1,dt_k5_lattices,dt_k5_setwiseo,dt_k6_funcop_1,dt_k6_funct_3,dt_k6_heyting1,dt_k6_lattices,dt_k6_normform,dt_k6_relat_1,dt_k7_funcop_1,dt_k7_heyting1,dt_k7_normform,dt_k7_setwiseo,dt_k8_funct_2,dt_k8_heyting1,dt_k8_normform,dt_k8_setwiseo,dt_k9_heyting1,dt_k9_normform,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,fc12_finset_1,fc13_finset_1,fc14_finset_1,fc1_finset_1,fc1_finsub_1,fc1_heyting1,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_finset_1,fc2_finsub_1,fc2_normform,fc2_subset_1,fc2_xboole_0,fc3_normform,fc3_subset_1,fc3_xboole_0,fc4_normform,fc4_subset_1,fc5_normform,fc6_normform,fc9_finset_1,fraenkel_a_2_0_heyting1,fraenkel_a_3_0_heyting1,fraenkel_a_3_1_heyting1,fraenkel_a_3_4_heyting1,free_g3_lattices,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k5_setwiseo,l8_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_binop_1,redefinition_k2_domain_1,redefinition_k2_setwiseo,redefinition_k3_domain_1,redefinition_k5_setwiseo,redefinition_k6_funcop_1,redefinition_k6_funct_3,redefinition_k7_funcop_1,redefinition_k8_funct_2,redefinition_k8_setwiseo,redefinition_m2_fraenkel,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,t18_heyting1,t19_heyting1,t1_boole,t1_subset,t1_zfmisc_1,t22_heyting1,t26_setwiseo,t27_lattice2,t29_lattice2,t2_boole,t2_subset,t2_tarski,t33_heyting1,t38_filter_0,t3_boole,t3_subset,t48_funcop_1,t4_boole,t4_subset,t5_subset,t60_funcop_1,t66_normform,t6_boole,t7_boole,t7_heyting1,t86_normform,t8_boole]),
    [file(heyting1,t34_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_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

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(commutativity_k5_setwiseo,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k5_finsub_1(A))
        & m1_subset_1(C,k5_finsub_1(A)) )
     => k5_setwiseo(A,B,C) = k5_setwiseo(A,C,B) ) ),
    file(setwiseo,k5_setwiseo),
    []).

fof(d10_heyting1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,u1_struct_0(k12_normform(A)))
     => k10_heyting1(A,B) = k1_zfmisc_1(B) ) ),
    file(heyting1,d10_heyting1),
    []).

fof(d11_heyting1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,u1_struct_0(k12_normform(A)))
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A)))
            & m2_relset_1(C,u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A))) )
         => ( C = k11_heyting1(A,B)
          <=> ! [D] : 
                ( m1_subset_1(D,u1_struct_0(k12_normform(A)))
               => k8_funct_2(u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A)),C,D) = k4_xboole_0(B,D) ) ) ) ) ),
    file(heyting1,d11_heyting1),
    []).

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_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_lattice2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] : 
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(B))
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => k2_lattice2(A,B,C,D) = k7_setwiseo(A,u1_struct_0(B),u2_lattices(B),C,D) ) ) ) ) ),
    file(lattice2,d3_lattice2),
    []).

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

fof(d6_heyting1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => k6_heyting1(A,B) = k3_xboole_0(k7_normform(A),a_2_0_heyting1(A,B)) ) ),
    file(heyting1,d6_heyting1),
    []).

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(d8_heyting1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A)))
        & m2_relset_1(B,u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A))) )
     => ( B = k8_heyting1(A)
      <=> ! [C] : 
            ( m1_subset_1(C,u1_struct_0(k12_normform(A)))
           => k8_funct_2(u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A)),B,C) = k9_normform(A,k6_heyting1(A,k3_heyting1(A,C))) ) ) ) ),
    file(heyting1,d8_heyting1),
    []).

fof(d9_heyting1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A))),u1_struct_0(k12_normform(A)))
        & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A))),u1_struct_0(k12_normform(A))) )
     => ( B = k9_heyting1(A)
      <=> ! [C] : 
            ( m1_subset_1(C,u1_struct_0(k12_normform(A)))
           => ! [D] : 
                ( m1_subset_1(D,u1_struct_0(k12_normform(A)))
               => k2_binop_1(u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A)),B,C,D) = k9_normform(A,k7_heyting1(A,k3_heyting1(A,C),k3_heyting1(A,D))) ) ) ) ) ),
    file(heyting1,d9_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_k10_heyting1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,u1_struct_0(k12_normform(A)))
     => m1_subset_1(k10_heyting1(A,B),k5_finsub_1(u1_struct_0(k12_normform(A)))) ) ),
    file(heyting1,k10_heyting1),
    []).

fof(dt_k10_normform,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(k10_normform(A,B,C),k5_finsub_1(k7_normform(A))) ) ),
    file(normform,k10_normform),
    []).

fof(dt_k11_heyting1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,u1_struct_0(k12_normform(A)))
     => ( v1_funct_1(k11_heyting1(A,B))
        & v1_funct_2(k11_heyting1(A,B),u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A)))
        & m2_relset_1(k11_heyting1(A,B),u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A))) ) ) ),
    file(heyting1,k11_heyting1),
    []).

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

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

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_heyting1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_heyting1(A)) ),
    file(heyting1,k1_heyting1),
    []).

fof(dt_k1_mcart_1,axiom,(
    $true ),
    file(mcart_1,k1_mcart_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_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => m1_subset_1(k2_binop_1(A,B,C,D,E,F),C) ) ),
    file(binop_1,k2_binop_1),
    []).

fof(dt_k2_domain_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B)) )
     => m1_subset_1(k2_domain_1(A,B,C),A) ) ),
    file(domain_1,k2_domain_1),
    []).

fof(dt_k2_lattice2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B)
        & m1_subset_1(C,k5_finsub_1(A))
        & v1_funct_1(D)
        & v1_funct_2(D,A,u1_struct_0(B))
        & m1_relset_1(D,A,u1_struct_0(B)) )
     => m1_subset_1(k2_lattice2(A,B,C,D),u1_struct_0(B)) ) ),
    file(lattice2,k2_lattice2),
    []).

fof(dt_k2_mcart_1,axiom,(
    $true ),
    file(mcart_1,k2_mcart_1),
    []).

fof(dt_k2_setwiseo,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k2_setwiseo(A,B),k5_finsub_1(A)) ) ),
    file(setwiseo,k2_setwiseo),
    []).

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

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(dt_k3_domain_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B)) )
     => m1_subset_1(k3_domain_1(A,B,C),B) ) ),
    file(domain_1,k3_domain_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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k4_filter_0,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_filter_0(A,B,C),u1_struct_0(A)) ) ),
    file(filter_0,k4_filter_0),
    []).

fof(dt_k4_funcop_1,axiom,(
    $true ),
    file(funcop_1,k4_funcop_1),
    []).

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

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_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_k5_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A) )
     => m1_subset_1(k5_lattices(A),u1_struct_0(A)) ) ),
    file(lattices,k5_lattices),
    []).

fof(dt_k5_setwiseo,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k5_finsub_1(A))
        & m1_subset_1(C,k5_finsub_1(A)) )
     => m1_subset_1(k5_setwiseo(A,B,C),k5_finsub_1(A)) ) ),
    file(setwiseo,k5_setwiseo),
    []).

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_heyting1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => m1_subset_1(k6_heyting1(A,B),k5_finsub_1(k7_normform(A))) ) ),
    file(heyting1,k6_heyting1),
    []).

fof(dt_k6_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_lattices(A) )
     => m1_subset_1(k6_lattices(A),u1_struct_0(A)) ) ),
    file(lattices,k6_lattices),
    []).

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_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)
        & m1_subset_1(E,A) )
     => ( v1_funct_1(k7_funcop_1(A,B,C,D,E))
        & v1_funct_2(k7_funcop_1(A,B,C,D,E),B,A)
        & m2_relset_1(k7_funcop_1(A,B,C,D,E),B,A) ) ) ),
    file(funcop_1,k7_funcop_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_k7_setwiseo,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(B,B),B)
        & m1_relset_1(C,k2_zfmisc_1(B,B),B)
        & m1_subset_1(D,k5_finsub_1(A))
        & v1_funct_1(E)
        & v1_funct_2(E,A,B)
        & m1_relset_1(E,A,B) )
     => m1_subset_1(k7_setwiseo(A,B,C,D,E),B) ) ),
    file(setwiseo,k7_setwiseo),
    []).

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_heyting1,axiom,(
    ! [A] : 
      ( v1_funct_1(k8_heyting1(A))
      & v1_funct_2(k8_heyting1(A),u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A)))
      & m2_relset_1(k8_heyting1(A),u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A))) ) ),
    file(heyting1,k8_heyting1),
    []).

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_heyting1,axiom,(
    ! [A] : 
      ( v1_funct_1(k9_heyting1(A))
      & v1_funct_2(k9_heyting1(A),k2_zfmisc_1(u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A))),u1_struct_0(k12_normform(A)))
      & m2_relset_1(k9_heyting1(A),k2_zfmisc_1(u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A))),u1_struct_0(k12_normform(A))) ) ),
    file(heyting1,k9_heyting1),
    []).

fof(dt_k9_normform,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => m2_subset_1(k9_normform(A,B),k5_finsub_1(k7_normform(A)),k8_normform(A)) ) ),
    file(normform,k9_normform),
    []).

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(fc12_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k4_xboole_0(A,B)) ) ),
    file(finset_1,fc12_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_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_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_heyting1,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))
      & v3_filter_0(k12_normform(A)) ) ),
    file(heyting1,fc1_heyting1),
    []).

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_finset_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_tarski(A,B))
      & v1_finset_1(k2_tarski(A,B)) ) ),
    file(finset_1,fc2_finset_1),
    []).

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

fof(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

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

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

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

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(fc9_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_1),
    []).

fof(fraenkel_a_2_0_heyting1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k5_finsub_1(k7_normform(B)))
     => ( r2_hidden(A,a_2_0_heyting1(B,C))
      <=> ? [D] : 
            ( m2_fraenkel(D,k7_normform(B),k1_heyting1(B),k1_fraenkel(k7_normform(B),k1_heyting1(B)))
            & A = k4_tarski(a_3_0_heyting1(B,C,D),a_3_1_heyting1(B,C,D))
            & ! [E] : 
                ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))
               => ( r2_hidden(E,C)
                 => r2_hidden(k8_funct_2(k7_normform(B),k1_heyting1(B),D,E),k5_setwiseo(B,k2_domain_1(k5_finsub_1(B),k5_finsub_1(B),E),k3_domain_1(k5_finsub_1(B),k5_finsub_1(B),E))) ) ) ) ) ) ),
    file(heyting1,a_2_0_heyting1),
    []).

fof(fraenkel_a_3_0_heyting1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,k5_finsub_1(k7_normform(B)))
        & m2_fraenkel(D,k7_normform(B),k1_heyting1(B),k1_fraenkel(k7_normform(B),k1_heyting1(B))) )
     => ( r2_hidden(A,a_3_0_heyting1(B,C,D))
      <=> ? [E] : 
            ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))
            & A = k8_funct_2(k7_normform(B),k1_heyting1(B),D,E)
            & r2_hidden(k8_funct_2(k7_normform(B),k1_heyting1(B),D,E),k3_domain_1(k5_finsub_1(B),k5_finsub_1(B),E))
            & r2_hidden(E,C) ) ) ) ),
    file(heyting1,a_3_0_heyting1),
    []).

fof(fraenkel_a_3_1_heyting1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,k5_finsub_1(k7_normform(B)))
        & m2_fraenkel(D,k7_normform(B),k1_heyting1(B),k1_fraenkel(k7_normform(B),k1_heyting1(B))) )
     => ( r2_hidden(A,a_3_1_heyting1(B,C,D))
      <=> ? [E] : 
            ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))
            & A = k8_funct_2(k7_normform(B),k1_heyting1(B),D,E)
            & r2_hidden(k8_funct_2(k7_normform(B),k1_heyting1(B),D,E),k2_domain_1(k5_finsub_1(B),k5_finsub_1(B),E))
            & r2_hidden(E,C) ) ) ) ),
    file(heyting1,a_3_1_heyting1),
    []).

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(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_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(idempotence_k5_setwiseo,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k5_finsub_1(A))
        & m1_subset_1(C,k5_finsub_1(A)) )
     => k5_setwiseo(A,B,B) = B ) ),
    file(setwiseo,k5_setwiseo),
    []).

fof(l8_heyting1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,u1_struct_0(k12_normform(A)))
     => ! [C] : 
          ( m1_subset_1(C,u1_struct_0(k12_normform(A)))
         => k9_normform(A,k10_normform(A,k3_heyting1(A,B),k3_heyting1(A,C))) = k2_binop_1(u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A)),u1_lattices(k12_normform(A)),B,C) ) ) ),
    file(heyting1,l8_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_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F) ) ),
    file(binop_1,k2_binop_1),
    []).

fof(redefinition_k2_domain_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B)) )
     => k2_domain_1(A,B,C) = k1_mcart_1(C) ) ),
    file(domain_1,k2_domain_1),
    []).

fof(redefinition_k2_setwiseo,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k2_setwiseo(A,B) = k1_tarski(B) ) ),
    file(setwiseo,k2_setwiseo),
    []).

fof(redefinition_k3_domain_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B)) )
     => k3_domain_1(A,B,C) = k2_mcart_1(C) ) ),
    file(domain_1,k3_domain_1),
    []).

fof(redefinition_k5_setwiseo,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k5_finsub_1(A))
        & m1_subset_1(C,k5_finsub_1(A)) )
     => k5_setwiseo(A,B,C) = k2_xboole_0(B,C) ) ),
    file(setwiseo,k5_setwiseo),
    []).

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_k7_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)
        & m1_subset_1(E,A) )
     => k7_funcop_1(A,B,C,D,E) = k4_funcop_1(C,D,E) ) ),
    file(funcop_1,k7_funcop_1),
    []).

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

fof(t18_heyting1,axiom,(
    ! [A,B] : 
      ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A))
     => ( B = k1_xboole_0
       => k6_heyting1(A,B) = k1_tarski(k4_tarski(k1_xboole_0,k1_xboole_0)) ) ) ),
    file(heyting1,t18_heyting1),
    []).

fof(t19_heyting1,axiom,(
    ! [A,B] : 
      ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A))
     => ! [C] : 
          ( m2_subset_1(C,k5_finsub_1(k7_normform(A)),k8_normform(A))
         => ( ( B = k1_xboole_0
              & C = k1_xboole_0 )
           => k7_heyting1(A,B,C) = k1_tarski(k4_tarski(k1_xboole_0,k1_xboole_0)) ) ) ) ),
    file(heyting1,t19_heyting1),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

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

fof(t1_zfmisc_1,axiom,(
    k1_zfmisc_1(k1_xboole_0) = k1_tarski(k1_xboole_0) ),
    file(zfmisc_1,t1_zfmisc_1),
    []).

fof(t22_heyting1,axiom,(
    ! [A] : m2_subset_1(k1_tarski(k4_tarski(k1_xboole_0,k1_xboole_0)),k5_finsub_1(k7_normform(A)),k8_normform(A)) ),
    file(heyting1,t22_heyting1),
    []).

fof(t26_setwiseo,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ( ( v1_binop_1(C,A)
                      & v2_binop_1(C,A) )
                   => ! [E] : 
                        ( m1_subset_1(E,B)
                       => k7_setwiseo(B,A,C,k2_setwiseo(B,E),D) = k8_funct_2(B,A,D,E) ) ) ) ) ) ) ),
    file(setwiseo,t26_setwiseo),
    []).

fof(t27_lattice2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A) )
     => v1_binop_1(u2_lattices(A),u1_struct_0(A)) ) ),
    file(lattice2,t27_lattice2),
    []).

fof(t29_lattice2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v5_lattices(A)
        & l2_lattices(A) )
     => v2_binop_1(u2_lattices(A),u1_struct_0(A)) ) ),
    file(lattice2,t29_lattice2),
    []).

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(t33_heyting1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,u1_struct_0(k12_normform(A)))
     => ! [C] : 
          ( m1_subset_1(C,u1_struct_0(k12_normform(A)))
         => k4_filter_0(k12_normform(A),B,C) = k2_lattice2(u1_struct_0(k12_normform(A)),k12_normform(A),k10_heyting1(A,B),k6_funcop_1(u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A)),u1_lattices(k12_normform(A)),k8_heyting1(A),k7_funcop_1(u1_struct_0(k12_normform(A)),u1_struct_0(k12_normform(A)),k9_heyting1(A),k11_heyting1(A,B),C))) ) ) ),
    file(heyting1,t33_heyting1),
    []).

fof(t38_filter_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v3_filter_0(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k4_filter_0(A,B,B) = k6_lattices(A) ) ) ),
    file(filter_0,t38_filter_0),
    []).

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(t48_funcop_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ! [F] : 
                          ( m1_subset_1(F,B)
                         => k8_funct_2(B,A,k6_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),k8_funct_2(B,A,E,F)) ) ) ) ) ) ) ),
    file(funcop_1,t48_funcop_1),
    []).

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

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(t60_funcop_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] : 
                      ( m1_subset_1(E,A)
                     => ! [F] : 
                          ( m1_subset_1(F,B)
                         => k8_funct_2(B,A,k7_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),E) ) ) ) ) ) ) ),
    file(funcop_1,t60_funcop_1),
    []).

fof(t66_normform,axiom,(
    ! [A,B] : 
      ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A))
     => k9_normform(A,B) = B ) ),
    file(normform,t66_normform),
    []).

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(t7_heyting1,axiom,(
    ! [A,B] : 
      ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A))
     => k9_normform(A,k10_normform(A,B,B)) = B ) ),
    file(heyting1,t7_heyting1),
    []).

fof(t86_normform,axiom,(
    ! [A] : k5_lattices(k12_normform(A)) = k1_xboole_0 ),
    file(normform,t86_normform),
    []).

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