% Mizar problem: t19_heyting2,heyting2,519,62 
fof(t19_heyting2,conjecture,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => ! [C] : 
          ( m2_subset_1(C,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B))
         => ! [D] : 
              ( m1_subset_1(D,k4_partfun1(A,B))
             => ! [E] : 
                  ( m2_subset_1(E,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B))
                 => ~ ( E = k2_setwiseo(k4_partfun1(A,B),D)
                      & k4_substlat(A,B,C,E) = k1_xboole_0
                      & ! [F] : 
                          ( v1_finset_1(F)
                         => ~ ( r2_hidden(F,k2_heyting2(A,B,C))
                              & r1_tarski(F,D) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finseq_1,cc1_finsub_1,cc1_fraenkel,cc1_funct_1,cc1_relset_1,cc1_substlat,cc2_finsub_1,cc2_funct_1,cc2_substlat,cc3_finsub_1,commutativity_k2_xboole_0,commutativity_k3_xboole_0,d1_heyting2,d1_tarski,d2_heyting1,d2_heyting2,d3_substlat,d3_tarski,d3_xboole_0,d5_partfun1,d6_partfun1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_heyting1,dt_k1_heyting2,dt_k1_relat_1,dt_k1_substlat,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_heyting2,dt_k2_relat_1,dt_k2_setwiseo,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_xboole_0,dt_k4_partfun1,dt_k4_substlat,dt_k5_finsub_1,dt_k7_relat_1,dt_k8_funct_2,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_m2_subset_1,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,existence_m2_subset_1,fc11_finseq_1,fc17_finseq_1,fc1_finsub_1,fc1_fraenkel,fc1_rfinseq,fc1_subset_1,fc1_substlat,fc1_wellfnd1,fc2_finseq_1,fc2_finsub_1,fc2_fraenkel,fc2_subset_1,fc4_funct_1,fc4_subset_1,fraenkel_a_0_0_pre_circ,fraenkel_a_3_2_heyting2,fraenkel_a_3_5_heyting2,fraenkel_a_4_0_heyting2,fraenkel_a_4_0_substlat,fraenkel_a_4_1_heyting2,fraenkel_a_4_2_heyting2,idempotence_k2_xboole_0,idempotence_k3_xboole_0,rc1_finseq_1,rc1_fraenkel,rc1_funct_1,rc1_heyting2,rc1_setwiseo,rc1_subset_1,rc1_substlat,rc2_funct_1,rc2_setwiseo,rc2_subset_1,rc2_substlat,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k1_fraenkel,redefinition_k2_setwiseo,redefinition_k8_funct_2,redefinition_m2_fraenkel,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_partfun1,reflexivity_r1_tarski,s1_pre_circ__e7_25_1_1__heyting2,s27_fraenkel__e4_25_1_1__heyting2,symmetry_r1_partfun1,t14_setwiseo,t15_heyting2,t17_xboole_1,t1_boole,t1_subset,t1_xboole_1,t2_boole,t2_heyting2,t2_subset,t2_tarski,t2_xboole_1,t3_subset,t4_subset,t5_subset,t6_boole,t70_funct_1,t7_boole,t86_relat_1,t88_relat_1,t8_boole,t90_relat_1,t99_relat_1]),
    [file(heyting2,t19_heyting2)]).

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

fof(cc1_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_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_fraenkel,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    []).

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_substlat,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_substlat(A,B))
     => v1_finset_1(C) ) ),
    file(substlat,cc1_substlat),
    []).

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(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_substlat,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_substlat(A,B))
     => ( v1_finset_1(C)
        & v1_fraenkel(C) ) ) ),
    file(substlat,cc2_substlat),
    []).

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_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(d1_heyting2,axiom,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => ! [C] : 
          ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B)))
         => ! [D] : 
              ( D = k1_heyting2(A,B,C)
            <=> ! [E] : 
                  ( r2_hidden(E,D)
                <=> ? [F] : 
                      ( v1_relat_1(F)
                      & v1_funct_1(F)
                      & v1_finset_1(F)
                      & r2_hidden(F,C)
                      & r2_hidden(E,k1_relat_1(F)) ) ) ) ) ) ),
    file(heyting2,d1_heyting2),
    []).

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

fof(d2_heyting1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k1_heyting1(A) = A ) ),
    file(heyting1,d2_heyting1),
    []).

fof(d2_heyting2,axiom,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => ! [C] : 
          ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B)))
         => k2_heyting2(A,B,C) = a_3_2_heyting2(A,B,C) ) ) ),
    file(heyting2,d2_heyting2),
    []).

fof(d3_substlat,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B)))
     => ! [D] : 
          ( m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B)))
         => k4_substlat(A,B,C,D) = a_4_0_substlat(A,B,C,D) ) ) ),
    file(substlat,d3_substlat),
    []).

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

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(d5_partfun1,axiom,(
    ! [A,B,C] : 
      ( C = k4_partfun1(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & r1_tarski(k1_relat_1(E),A)
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(partfun1,d5_partfun1),
    []).

fof(d6_partfun1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_partfun1(A,B)
          <=> ! [C] : 
                ( r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B)))
               => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ),
    file(partfun1,d6_partfun1),
    []).

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_heyting2,axiom,(
    $true ),
    file(heyting2,k1_heyting2),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

fof(dt_k1_substlat,axiom,(
    ! [A,B] : m1_subset_1(k1_substlat(A,B),k1_zfmisc_1(k5_finsub_1(k4_partfun1(A,B)))) ),
    file(substlat,k1_substlat),
    []).

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_heyting2,axiom,(
    ! [A,B,C] : 
      ( ( v1_finset_1(B)
        & m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) )
     => m1_subset_1(k2_heyting2(A,B,C),k5_finsub_1(k4_partfun1(A,B))) ) ),
    file(heyting2,k2_heyting2),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_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_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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k4_partfun1,axiom,(
    $true ),
    file(partfun1,k4_partfun1),
    []).

fof(dt_k4_substlat,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B)))
        & m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B))) )
     => m1_subset_1(k4_substlat(A,B,C,D),k5_finsub_1(k4_partfun1(A,B))) ) ),
    file(substlat,k4_substlat),
    []).

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

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    []).

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

fof(dt_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(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(fc11_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    []).

fof(fc17_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_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_fraenkel,axiom,(
    ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ),
    file(fraenkel,fc1_fraenkel),
    []).

fof(fc1_rfinseq,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(B) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B))
        & v1_finset_1(k7_relat_1(A,B)) ) ) ),
    file(rfinseq,fc1_rfinseq),
    []).

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

fof(fc1_substlat,axiom,(
    ! [A,B] : ~ v1_xboole_0(k1_substlat(A,B)) ),
    file(substlat,fc1_substlat),
    []).

fof(fc1_wellfnd1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k4_partfun1(A,B))
      & v1_fraenkel(k4_partfun1(A,B)) ) ),
    file(wellfnd1,fc1_wellfnd1),
    []).

fof(fc2_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_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_fraenkel,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => ( v1_finset_1(k1_funct_2(A,B))
        & v1_fraenkel(k1_funct_2(A,B)) ) ) ),
    file(fraenkel,fc2_fraenkel),
    []).

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

fof(fc4_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B)) ) ) ),
    file(funct_1,fc4_funct_1),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fraenkel_a_0_0_pre_circ,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_0_pre_circ)
    <=> ? [B] : 
          ( m1_subset_1(B,f1_s1_pre_circ)
          & A = f2_s1_pre_circ(B)
          & p1_s1_pre_circ(B) ) ) ),
    file(pre_circ,a_0_0_pre_circ),
    []).

fof(fraenkel_a_3_2_heyting2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_finset_1(C)
        & m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C))) )
     => ( r2_hidden(A,a_3_2_heyting2(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,k4_partfun1(k1_heyting2(B,C,D),C))
            & A = E
            & ! [F] : 
                ( m1_subset_1(F,k4_partfun1(B,C))
               => ~ ( r2_hidden(F,D)
                    & r1_partfun1(E,F) ) ) ) ) ) ),
    file(heyting2,a_3_2_heyting2),
    []).

fof(fraenkel_a_3_5_heyting2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_finset_1(C)
        & m2_subset_1(D,k5_finsub_1(k4_partfun1(B,C)),k1_substlat(B,C)) )
     => ( r2_hidden(A,a_3_5_heyting2(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,k4_partfun1(k1_heyting2(B,C,D),C))
            & A = E
            & ! [F] : 
                ( m1_subset_1(F,k4_partfun1(B,C))
               => ~ ( r2_hidden(F,D)
                    & r1_partfun1(E,F) ) ) ) ) ) ),
    file(heyting2,a_3_5_heyting2),
    []).

fof(fraenkel_a_4_0_heyting2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v1_finset_1(C)
        & m2_subset_1(D,k5_finsub_1(k4_partfun1(B,C)),k1_substlat(B,C))
        & m2_subset_1(E,k5_finsub_1(k4_partfun1(B,C)),k1_substlat(B,C)) )
     => ( r2_hidden(A,a_4_0_heyting2(B,C,D,E))
      <=> ? [F,G] : 
            ( m1_subset_1(F,k4_partfun1(B,C))
            & m1_subset_1(G,k4_partfun1(B,C))
            & A = k2_xboole_0(F,G)
            & r2_hidden(F,D)
            & r2_hidden(G,E)
            & r1_partfun1(F,G) ) ) ) ),
    file(heyting2,a_4_0_heyting2),
    []).

fof(fraenkel_a_4_0_substlat,axiom,(
    ! [A,B,C,D,E] : 
      ( ( m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C)))
        & m1_subset_1(E,k5_finsub_1(k4_partfun1(B,C))) )
     => ( r2_hidden(A,a_4_0_substlat(B,C,D,E))
      <=> ? [F,G] : 
            ( m1_subset_1(F,k4_partfun1(B,C))
            & m1_subset_1(G,k4_partfun1(B,C))
            & A = k2_xboole_0(F,G)
            & r2_hidden(F,D)
            & r2_hidden(G,E)
            & r1_partfun1(F,G) ) ) ) ),
    file(substlat,a_4_0_substlat),
    []).

fof(fraenkel_a_4_1_heyting2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v1_finset_1(C)
        & m2_fraenkel(D,k4_partfun1(B,C),k1_heyting1(B),k1_fraenkel(k4_partfun1(B,C),k1_heyting1(B)))
        & ~ v1_xboole_0(E)
        & v1_finset_1(E) )
     => ( r2_hidden(A,a_4_1_heyting2(B,C,D,E))
      <=> ? [F] : 
            ( m1_subset_1(F,E)
            & A = k1_funct_1(D,F) ) ) ) ),
    file(heyting2,a_4_1_heyting2),
    []).

fof(fraenkel_a_4_2_heyting2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v1_finset_1(C)
        & m2_subset_1(D,k5_finsub_1(k4_partfun1(B,C)),k1_substlat(B,C))
        & m2_fraenkel(E,k4_partfun1(B,C),k1_heyting1(B),k1_fraenkel(k4_partfun1(B,C),k1_heyting1(B))) )
     => ( r2_hidden(A,a_4_2_heyting2(B,C,D,E))
      <=> ? [F] : 
            ( m1_subset_1(F,k1_heyting1(D))
            & A = k1_funct_1(E,F) ) ) ) ),
    file(heyting2,a_4_2_heyting2),
    []).

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(rc1_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

fof(rc1_fraenkel,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    []).

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

fof(rc1_heyting2,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_fraenkel(A) ) ),
    file(heyting2,rc1_heyting2),
    []).

fof(rc1_setwiseo,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k5_finsub_1(A))
      & v1_xboole_0(B)
      & v1_finset_1(B) ) ),
    file(setwiseo,rc1_setwiseo),
    []).

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_substlat,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_subset_1(C,k1_substlat(A,B))
      & ~ v1_xboole_0(C) ) ),
    file(substlat,rc1_substlat),
    []).

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_setwiseo,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k5_finsub_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(setwiseo,rc2_setwiseo),
    []).

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_substlat,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_subset_1(C,k4_partfun1(A,B))
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_finset_1(C) ) ),
    file(substlat,rc2_substlat),
    []).

fof(rc3_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_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(rc4_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

fof(rc6_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

fof(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

fof(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    []).

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_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_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(redefinition_m2_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_partfun1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => r1_partfun1(A,A) ) ),
    file(partfun1,r1_partfun1),
    []).

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

fof(s1_pre_circ__e7_25_1_1__heyting2,axiom,(
    v1_finset_1(a_0_0_pre_circ) ),
    file(heyting2,s1_pre_circ__e7_25_1_1__heyting2),
    []).

fof(s27_fraenkel__e4_25_1_1__heyting2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_finset_1(B)
        & m2_subset_1(C,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B))
        & m1_subset_1(D,k4_partfun1(A,B)) )
     => ( ! [E] : 
            ( m1_subset_1(E,k4_partfun1(A,B))
           => ~ ( r2_hidden(E,C)
                & ! [F] : 
                    ( m1_subset_1(F,k1_heyting1(A))
                   => ~ ( r2_hidden(F,k3_xboole_0(k1_relat_1(E),k1_relat_1(D)))
                        & k1_funct_1(E,F) != k1_funct_1(D,F) ) ) ) )
       => ? [E] : 
            ( m2_fraenkel(E,k4_partfun1(A,B),k1_heyting1(A),k1_fraenkel(k4_partfun1(A,B),k1_heyting1(A)))
            & ! [F] : 
                ( m1_subset_1(F,k4_partfun1(A,B))
               => ( r2_hidden(F,C)
                 => ( r2_hidden(k8_funct_2(k4_partfun1(A,B),k1_heyting1(A),E,F),k3_xboole_0(k1_relat_1(F),k1_relat_1(D)))
                    & k1_funct_1(F,k8_funct_2(k4_partfun1(A,B),k1_heyting1(A),E,F)) != k1_funct_1(D,k8_funct_2(k4_partfun1(A,B),k1_heyting1(A),E,F)) ) ) ) ) ) ) ),
    file(heyting2,s27_fraenkel__e4_25_1_1__heyting2),
    []).

fof(symmetry_r1_partfun1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_partfun1(A,B)
       => r1_partfun1(B,A) ) ) ),
    file(partfun1,r1_partfun1),
    []).

fof(t14_setwiseo,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k5_finsub_1(A))
         => ! [C] : 
              ( r2_hidden(C,B)
             => m1_subset_1(C,A) ) ) ) ),
    file(setwiseo,t14_setwiseo),
    []).

fof(t15_heyting2,axiom,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => ! [C] : 
          ( m2_subset_1(C,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B))
         => ( C = k1_xboole_0
           => k2_heyting2(A,B,C) = k1_tarski(k1_xboole_0) ) ) ) ),
    file(heyting2,t15_heyting2),
    []).

fof(t17_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    []).

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

fof(t2_heyting2,axiom,(
    ! [A,B,C,D] : 
      ( ( r2_hidden(D,k1_substlat(A,B))
        & r2_hidden(C,D) )
     => ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finset_1(C) ) ) ),
    file(heyting2,t2_heyting2),
    []).

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(t2_xboole_1,axiom,(
    ! [A] : r1_tarski(k1_xboole_0,A) ),
    file(xboole_1,t2_xboole_1),
    []).

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

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(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(t70_funct_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,k1_relat_1(k7_relat_1(C,A)))
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t70_funct_1),
    []).

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

fof(t86_relat_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r2_hidden(A,k1_relat_1(k7_relat_1(C,B)))
      <=> ( r2_hidden(A,B)
          & r2_hidden(A,k1_relat_1(C)) ) ) ) ),
    file(relat_1,t86_relat_1),
    []).

fof(t88_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k7_relat_1(B,A),B) ) ),
    file(relat_1,t88_relat_1),
    []).

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

fof(t90_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A) ) ),
    file(relat_1,t90_relat_1),
    []).

fof(t99_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) ) ),
    file(relat_1,t99_relat_1),
    []).