% Mizar problem: t21_zf_fund1,zf_fund1,1854,48 
fof(t21_zf_fund1,conjecture,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ( ( v8_zf_fund1(B,A)
                  & r2_hidden(C,B) )
               => ! [D] : 
                    ( ( v1_zf_lang(D)
                      & m2_finseq_1(D,k5_numbers) )
                   => ! [E] : 
                        ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                       => ( r2_hidden(k10_zf_fund1(D,C),B)
                         => r2_hidden(k10_zf_fund1(k8_zf_lang(E,D),C),B) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_card_1,cc1_classes2,cc1_finset_1,cc1_funct_1,cc1_ordinal1,cc1_relset_1,cc2_card_1,cc2_classes2,cc2_finset_1,cc2_funct_1,cc2_ordinal1,cc3_card_1,cc3_classes2,cc3_ordinal1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k4_subset_1,d10_xboole_0,d1_tarski,d2_funct_2,d3_tarski,d4_xboole_0,d4_zf_fund1,d4_zf_model,d5_tarski,d5_zf_fund1,dt_k10_zf_fund1,dt_k1_card_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zf_fund1,dt_k1_zf_lang,dt_k1_zf_model,dt_k1_zfmisc_1,dt_k2_funct_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zf_lang,dt_k2_zf_model,dt_k2_zfmisc_1,dt_k3_zf_fund1,dt_k3_zf_model,dt_k4_card_1,dt_k4_subset_1,dt_k4_tarski,dt_k4_xboole_0,dt_k4_zf_fund1,dt_k4_zf_model,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k5_zf_fund1,dt_k5_zf_model,dt_k6_subset_1,dt_k6_zf_fund1,dt_k6_zf_lang,dt_k7_funct_2,dt_k7_relat_1,dt_k7_zf_fund1,dt_k8_funct_2,dt_k8_zf_fund1,dt_k8_zf_lang,dt_k9_relat_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,fc12_finset_1,fc13_finset_1,fc14_finset_1,fc1_finset_1,fc1_funct_1,fc1_ordinal2,fc1_zf_lang,fc2_card_1,fc2_finset_1,fc2_ordinal1,fc4_funct_1,fc4_zf_lang,fc6_zf_lang,fc9_finset_1,fraenkel_a_5_0_zf_fund1,fraenkel_a_5_2_zf_fund1,idempotence_k2_xboole_0,idempotence_k4_subset_1,l15_zf_fund1,l16_zf_fund1,l17_zf_fund1,l18_zf_fund1,l19_zf_fund1,l22_zf_fund1,l24_zf_fund1,l25_zf_fund1,rc1_card_1,rc1_classes2,rc1_finset_1,rc1_funct_1,rc1_ordinal1,rc1_zf_lang,rc2_card_1,rc2_classes2,rc2_finset_1,rc2_funct_1,rc2_ordinal1,rc3_finset_1,rc3_funct_1,rc3_ordinal1,rc4_finset_1,rc4_funct_1,redefinition_k2_zf_model,redefinition_k4_card_1,redefinition_k4_subset_1,redefinition_k5_numbers,redefinition_k5_zf_model,redefinition_k6_subset_1,redefinition_k6_zf_fund1,redefinition_k7_funct_2,redefinition_k7_zf_fund1,redefinition_k8_funct_2,redefinition_k8_zf_fund1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,t104_relat_1,t107_relat_1,t11_zf_fund1,t15_grfunc_1,t18_grfunc_1,t19_zf_fund1,t1_boole,t1_subset,t1_zf_fund1,t2_subset,t2_tarski,t35_grfunc_1,t36_xboole_1,t37_zfmisc_1,t3_boole,t3_subset,t45_xboole_1,t4_boole,t4_subset,t4_zf_fund1,t4_zf_model,t5_subset,t65_zf_lang1,t65_zfmisc_1,t67_zf_lang1,t6_boole,t6_zf_model,t70_funct_1,t7_boole,t84_zf_lang1,t8_boole,t8_grfunc_1,t9_funct_1,t9_zf_fund1]),
    [file(zf_fund1,t21_zf_fund1)]).

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

fof(cc1_card_1,axiom,(
    ! [A] : 
      ( v1_card_1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(card_1,cc1_card_1),
    []).

fof(cc1_classes2,axiom,(
    ! [A] : 
      ( v2_classes1(A)
     => v1_classes1(A) ) ),
    file(classes2,cc1_classes2),
    []).

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

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

fof(cc1_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    []).

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_card_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_card_1(A) ) ) ),
    file(card_1,cc2_card_1),
    []).

fof(cc2_classes2,axiom,(
    ! [A] : 
      ( v1_classes2(A)
     => ( v1_ordinal1(A)
        & v1_classes1(A)
        & v2_classes1(A) ) ) ),
    file(classes2,cc2_classes2),
    []).

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_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_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

fof(cc3_card_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_finset_1(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_card_1(A) ) ) ),
    file(card_1,cc3_card_1),
    []).

fof(cc3_classes2,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_classes1(A) )
     => v1_classes2(A) ) ),
    file(classes2,cc3_classes2),
    []).

fof(cc3_ordinal1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    []).

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_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ),
    file(subset_1,k4_subset_1),
    []).

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

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

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

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

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

fof(d4_zf_fund1,axiom,(
    ! [A] : 
      ( ( v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_zf_lang)) )
     => k5_zf_fund1(A) = k9_relat_1(k2_funct_1(k3_zf_fund1),A) ) ),
    file(zf_fund1,d4_zf_fund1),
    []).

fof(d4_zf_model,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] : 
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ( r1_zf_model(A,B,C)
              <=> r2_hidden(B,k5_zf_model(C,A)) ) ) ) ) ),
    file(zf_model,d4_zf_model),
    []).

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

fof(d5_zf_fund1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( C = k10_zf_fund1(A,B)
            <=> ! [D] : 
                  ( r2_hidden(D,C)
                <=> ? [E] : 
                      ( v1_funct_1(E)
                      & v1_funct_2(E,k1_zf_lang,B)
                      & m2_relset_1(E,k1_zf_lang,B)
                      & D = k7_relat_1(k7_funct_2(k5_ordinal2,k1_zf_lang,B,k3_zf_fund1,E),k5_zf_fund1(k6_zf_fund1(A)))
                      & r2_hidden(E,k5_zf_model(A,B)) ) ) ) ) ) ),
    file(zf_fund1,d5_zf_fund1),
    []).

fof(dt_k10_zf_fund1,axiom,(
    $true ),
    file(zf_fund1,k10_zf_fund1),
    []).

fof(dt_k1_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    []).

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_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

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

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zf_fund1,axiom,(
    $true ),
    file(zf_fund1,k1_zf_fund1),
    []).

fof(dt_k1_zf_lang,axiom,(
    m1_subset_1(k1_zf_lang,k1_zfmisc_1(k5_numbers)) ),
    file(zf_lang,k1_zf_lang),
    []).

fof(dt_k1_zf_model,axiom,(
    $true ),
    file(zf_model,k1_zf_model),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_1(A))
        & v1_funct_1(k2_funct_1(A)) ) ) ),
    file(funct_1,k2_funct_1),
    []).

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

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_zf_lang,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => m2_subset_1(k2_zf_lang(A),k5_numbers,k1_zf_lang) ) ),
    file(zf_lang,k2_zf_lang),
    []).

fof(dt_k2_zf_model,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => m1_subset_1(k2_zf_model(A),k1_zfmisc_1(k1_zf_lang)) ) ),
    file(zf_model,k2_zf_model),
    []).

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

fof(dt_k3_zf_fund1,axiom,
    ( v1_funct_1(k3_zf_fund1)
    & v1_funct_2(k3_zf_fund1,k5_ordinal2,k1_zf_lang)
    & m2_relset_1(k3_zf_fund1,k5_ordinal2,k1_zf_lang) ),
    file(zf_fund1,k3_zf_fund1),
    []).

fof(dt_k3_zf_model,axiom,(
    $true ),
    file(zf_model,k3_zf_model),
    []).

fof(dt_k4_card_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => m2_subset_1(k4_card_1(A),k1_numbers,k5_numbers) ) ),
    file(card_1,k4_card_1),
    []).

fof(dt_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k4_subset_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_k4_zf_fund1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zf_lang)
     => m2_subset_1(k4_zf_fund1(A),k1_numbers,k5_numbers) ) ),
    file(zf_fund1,k4_zf_fund1),
    []).

fof(dt_k4_zf_model,axiom,(
    $true ),
    file(zf_model,k4_zf_model),
    []).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

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

fof(dt_k5_zf_fund1,axiom,(
    ! [A] : 
      ( ( v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_zf_lang)) )
     => ( v1_finset_1(k5_zf_fund1(A))
        & m1_subset_1(k5_zf_fund1(A),k1_zfmisc_1(k5_ordinal2)) ) ) ),
    file(zf_fund1,k5_zf_fund1),
    []).

fof(dt_k5_zf_model,axiom,(
    ! [A,B] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & ~ v1_xboole_0(B) )
     => m1_subset_1(k5_zf_model(A,B),k1_zfmisc_1(k3_zf_model(B))) ) ),
    file(zf_model,k5_zf_model),
    []).

fof(dt_k6_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k6_subset_1),
    []).

fof(dt_k6_zf_fund1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_finset_1(k6_zf_fund1(A))
        & m1_subset_1(k6_zf_fund1(A),k1_zfmisc_1(k1_zf_lang)) ) ) ),
    file(zf_fund1,k6_zf_fund1),
    []).

fof(dt_k6_zf_lang,axiom,(
    ! [A] : 
      ( m1_finseq_1(A,k5_numbers)
     => m2_finseq_1(k6_zf_lang(A),k5_numbers) ) ),
    file(zf_lang,k6_zf_lang),
    []).

fof(dt_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => ( v1_funct_1(k7_funct_2(A,B,C,D,E))
        & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C)
        & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ),
    file(funct_2,k7_funct_2),
    []).

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_k7_zf_fund1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_finset_1(k7_zf_fund1(A))
        & m1_subset_1(k7_zf_fund1(A),k1_zfmisc_1(k5_ordinal2)) ) ) ),
    file(zf_fund1,k7_zf_fund1),
    []).

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_zf_fund1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zf_lang)
     => ( v1_finset_1(k8_zf_fund1(A))
        & m1_subset_1(k8_zf_fund1(A),k1_zfmisc_1(k1_zf_lang)) ) ) ),
    file(zf_fund1,k8_zf_fund1),
    []).

fof(dt_k8_zf_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_zf_lang)
        & m1_finseq_1(B,k5_numbers) )
     => m2_finseq_1(k8_zf_lang(A,B),k5_numbers) ) ),
    file(zf_lang,k8_zf_lang),
    []).

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

fof(dt_m1_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    []).

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_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_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_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    []).

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_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    []).

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(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_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    []).

fof(fc1_ordinal2,axiom,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    []).

fof(fc1_zf_lang,axiom,(
    ~ v1_xboole_0(k1_zf_lang) ),
    file(zf_lang,fc1_zf_lang),
    []).

fof(fc2_card_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ( v1_ordinal1(k1_card_1(A))
        & v2_ordinal1(k1_card_1(A))
        & v3_ordinal1(k1_card_1(A))
        & v1_finset_1(k1_card_1(A))
        & v1_card_1(k1_card_1(A)) ) ) ),
    file(card_1,fc2_card_1),
    []).

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_ordinal1,axiom,
    ( 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_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    []).

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_zf_lang,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => ( v1_relat_1(k6_zf_lang(A))
        & v1_funct_1(k6_zf_lang(A))
        & v1_finset_1(k6_zf_lang(A))
        & v1_finseq_1(k6_zf_lang(A))
        & v1_zf_lang(k6_zf_lang(A)) ) ) ),
    file(zf_lang,fc4_zf_lang),
    []).

fof(fc6_zf_lang,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_zf_lang)
        & v1_zf_lang(B)
        & m1_finseq_1(B,k5_numbers) )
     => ( v1_relat_1(k8_zf_lang(A,B))
        & v1_funct_1(k8_zf_lang(A,B))
        & v1_finset_1(k8_zf_lang(A,B))
        & v1_finseq_1(k8_zf_lang(A,B))
        & v1_zf_lang(k8_zf_lang(A,B)) ) ) ),
    file(zf_lang,fc6_zf_lang),
    []).

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_5_0_zf_fund1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(B)
        & v1_classes2(B)
        & m1_subset_1(C,B)
        & m1_subset_1(D,B)
        & m1_subset_1(E,k5_ordinal2)
        & v1_finset_1(F)
        & m1_subset_1(F,k1_zfmisc_1(k5_ordinal2)) )
     => ( r2_hidden(A,a_5_0_zf_fund1(B,C,D,E,F))
      <=> ? [G] : 
            ( m1_subset_1(G,B)
            & A = G
            & r2_hidden(G,k1_funct_2(k6_subset_1(k5_ordinal2,F,k7_zf_fund1(E)),C))
            & ? [H] : r2_hidden(k2_xboole_0(k1_tarski(k4_tarski(E,H)),G),D) ) ) ) ),
    file(zf_fund1,a_5_0_zf_fund1),
    []).

fof(fraenkel_a_5_2_zf_fund1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(B)
        & v1_classes2(B)
        & v1_zf_lang(C)
        & m2_finseq_1(C,k5_numbers)
        & m2_subset_1(D,k5_numbers,k1_zf_lang)
        & m1_subset_1(E,B)
        & m1_subset_1(F,B) )
     => ( r2_hidden(A,a_5_2_zf_fund1(B,C,D,E,F))
      <=> ? [G] : 
            ( m1_subset_1(G,B)
            & A = G
            & r2_hidden(G,k1_funct_2(k6_subset_1(k5_ordinal2,k5_zf_fund1(k6_zf_fund1(C)),k7_zf_fund1(k4_zf_fund1(D))),F))
            & ? [H] : r2_hidden(k2_xboole_0(k1_tarski(k4_tarski(k4_zf_fund1(D),H)),G),E) ) ) ) ),
    file(zf_fund1,a_5_2_zf_fund1),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(idempotence_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,B) = B ) ),
    file(subset_1,k4_subset_1),
    []).

fof(l15_zf_fund1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => A = k4_zf_fund1(k2_zf_lang(k4_card_1(A))) ) ),
    file(zf_fund1,l15_zf_fund1),
    []).

fof(l16_zf_fund1,axiom,(
    ! [A] : 
      ( ( v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k5_ordinal2)) )
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,B)
                & m2_relset_1(C,k1_zf_lang,B) )
             => ( k1_relat_1(k7_relat_1(k7_funct_2(k5_ordinal2,k1_zf_lang,B,k3_zf_fund1,C),A)) = A
                & r1_tarski(k2_relat_1(k7_relat_1(k7_funct_2(k5_ordinal2,k1_zf_lang,B,k3_zf_fund1,C),A)),B)
                & r2_hidden(k7_relat_1(k7_funct_2(k5_ordinal2,k1_zf_lang,B,k3_zf_fund1,C),A),k1_funct_2(A,B))
                & k1_relat_1(k7_funct_2(k5_ordinal2,k1_zf_lang,B,k3_zf_fund1,C)) = k5_ordinal2
                & r1_tarski(k2_relat_1(k7_funct_2(k5_ordinal2,k1_zf_lang,B,k3_zf_fund1,C)),B) ) ) ) ) ),
    file(zf_fund1,l16_zf_fund1),
    []).

fof(l17_zf_fund1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zf_lang,A)
            & m2_relset_1(B,k1_zf_lang,A) )
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k1_zf_lang)
             => ( k8_funct_2(k5_numbers,k1_zf_lang,k3_zf_fund1,k4_zf_fund1(C)) = C
                & k1_funct_1(k2_funct_1(k3_zf_fund1),C) = k4_zf_fund1(C)
                & k8_funct_2(k5_numbers,A,k7_funct_2(k5_ordinal2,k1_zf_lang,A,k3_zf_fund1,B),k4_zf_fund1(C)) = k8_funct_2(k1_zf_lang,A,B,C) ) ) ) ) ),
    file(zf_fund1,l17_zf_fund1),
    []).

fof(l18_zf_fund1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zf_lang)) )
     => ( r2_hidden(A,k5_zf_fund1(B))
      <=> ? [C] : 
            ( m2_subset_1(C,k5_numbers,k1_zf_lang)
            & r2_hidden(C,B)
            & A = k4_zf_fund1(C) ) ) ) ),
    file(zf_fund1,l18_zf_fund1),
    []).

fof(l19_zf_fund1,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k1_zf_lang)
     => k5_zf_fund1(k8_zf_fund1(A)) = k7_zf_fund1(k4_zf_fund1(A)) ) ),
    file(zf_fund1,l19_zf_fund1),
    []).

fof(l22_zf_fund1,axiom,(
    ! [A] : 
      ( ( v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_zf_lang)) )
     => ! [B] : 
          ( ( v1_finset_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_zf_lang)) )
         => ( k5_zf_fund1(k4_subset_1(k1_zf_lang,A,B)) = k4_subset_1(k5_ordinal2,k5_zf_fund1(A),k5_zf_fund1(B))
            & k5_zf_fund1(k6_subset_1(k1_zf_lang,A,B)) = k6_subset_1(k5_ordinal2,k5_zf_fund1(A),k5_zf_fund1(B)) ) ) ) ),
    file(zf_fund1,l22_zf_fund1),
    []).

fof(l24_zf_fund1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,A)
                & m2_relset_1(C,k1_zf_lang,A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,A)
                    & m2_relset_1(D,k1_zf_lang,A) )
                 => ( ( k7_relat_1(k7_funct_2(k5_ordinal2,k1_zf_lang,A,k3_zf_fund1,C),k5_zf_fund1(k6_zf_fund1(B))) = k7_relat_1(k7_funct_2(k5_ordinal2,k1_zf_lang,A,k3_zf_fund1,D),k5_zf_fund1(k6_zf_fund1(B)))
                      & r2_hidden(C,k5_zf_model(B,A)) )
                   => r2_hidden(D,k5_zf_model(B,A)) ) ) ) ) ) ),
    file(zf_fund1,l24_zf_fund1),
    []).

fof(l25_zf_fund1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(B)
        & m1_subset_1(B,k1_zfmisc_1(k5_ordinal2)) )
     => ! [C] : 
          ( ~ v1_xboole_0(C)
         => ~ ( r2_hidden(A,k1_funct_2(B,C))
              & ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,C)
                    & m2_relset_1(D,k1_zf_lang,C) )
                 => A != k7_relat_1(k7_funct_2(k5_ordinal2,k1_zf_lang,C,k3_zf_fund1,D),B) ) ) ) ) ),
    file(zf_fund1,l25_zf_fund1),
    []).

fof(rc1_card_1,axiom,(
    ? [A] : v1_card_1(A) ),
    file(card_1,rc1_card_1),
    []).

fof(rc1_classes2,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & ~ v1_xboole_0(A)
      & v1_classes1(A)
      & v2_classes1(A)
      & v1_classes2(A) ) ),
    file(classes2,rc1_classes2),
    []).

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

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

fof(rc1_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

fof(rc1_zf_lang,axiom,(
    ? [A] : 
      ( m1_finseq_1(A,k5_numbers)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_zf_lang(A) ) ),
    file(zf_lang,rc1_zf_lang),
    []).

fof(rc2_card_1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v1_finset_1(A)
      & v1_card_1(A) ) ),
    file(card_1,rc2_card_1),
    []).

fof(rc2_classes2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] : 
          ( m1_subset_1(B,A)
          & ~ v1_xboole_0(B) ) ) ),
    file(classes2,rc2_classes2),
    []).

fof(rc2_finset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_ordinal1(B)
      & v2_ordinal1(B)
      & v3_ordinal1(B)
      & v4_ordinal2(B)
      & v1_finset_1(B) ) ),
    file(finset_1,rc2_finset_1),
    []).

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

fof(rc2_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    []).

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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc3_ordinal1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    []).

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

fof(redefinition_k2_zf_model,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => k2_zf_model(A) = k1_zf_model(A) ) ),
    file(zf_model,k2_zf_model),
    []).

fof(redefinition_k4_card_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => k4_card_1(A) = k1_card_1(A) ) ),
    file(card_1,k4_card_1),
    []).

fof(redefinition_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(redefinition_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(redefinition_k5_zf_model,axiom,(
    ! [A,B] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers)
        & ~ v1_xboole_0(B) )
     => k5_zf_model(A,B) = k4_zf_model(A,B) ) ),
    file(zf_model,k5_zf_model),
    []).

fof(redefinition_k6_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ),
    file(subset_1,k6_subset_1),
    []).

fof(redefinition_k6_zf_fund1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m1_finseq_1(A,k5_numbers) )
     => k6_zf_fund1(A) = k1_zf_model(A) ) ),
    file(zf_fund1,k6_zf_fund1),
    []).

fof(redefinition_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ),
    file(funct_2,k7_funct_2),
    []).

fof(redefinition_k7_zf_fund1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => k7_zf_fund1(A) = k1_tarski(A) ) ),
    file(zf_fund1,k7_zf_fund1),
    []).

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_zf_fund1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zf_lang)
     => k8_zf_fund1(A) = k1_tarski(A) ) ),
    file(zf_fund1,k8_zf_fund1),
    []).

fof(redefinition_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(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(t104_relat_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => r1_tarski(k7_relat_1(C,A),k7_relat_1(C,B)) ) ) ),
    file(relat_1,t104_relat_1),
    []).

fof(t107_relat_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => k7_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) ) ),
    file(relat_1,t107_relat_1),
    []).

fof(t11_zf_fund1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( ( ~ v1_xboole_0(D)
                    & m1_subset_1(D,k1_zfmisc_1(A)) )
                 => ! [E] : 
                      ( m1_subset_1(E,k5_ordinal2)
                     => ! [F] : 
                          ( ( v1_finset_1(F)
                            & m1_subset_1(F,k1_zfmisc_1(k5_ordinal2)) )
                         => ( ( v8_zf_fund1(D,A)
                              & r2_hidden(E,F)
                              & r2_hidden(B,D)
                              & r2_hidden(C,D)
                              & r1_tarski(C,k1_funct_2(F,B)) )
                           => r2_hidden(a_5_0_zf_fund1(A,B,C,E,F),D) ) ) ) ) ) ) ) ),
    file(zf_fund1,t11_zf_fund1),
    []).

fof(t15_grfunc_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k1_tarski(k4_tarski(A,B)))
      & v1_funct_1(k1_tarski(k4_tarski(A,B))) ) ),
    file(grfunc_1,t15_grfunc_1),
    []).

fof(t18_grfunc_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( k1_relat_1(B) = k1_tarski(A)
       => B = k1_tarski(k4_tarski(A,k1_funct_1(B,A))) ) ) ),
    file(grfunc_1,t18_grfunc_1),
    []).

fof(t19_zf_fund1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ( ( v8_zf_fund1(B,A)
                  & r2_hidden(C,B) )
               => ! [D] : 
                    ( ( v1_zf_lang(D)
                      & m2_finseq_1(D,k5_numbers) )
                   => ( r2_hidden(k10_zf_fund1(D,C),B)
                     => r2_hidden(k10_zf_fund1(k6_zf_lang(D),C),B) ) ) ) ) ) ) ),
    file(zf_fund1,t19_zf_fund1),
    []).

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_zf_fund1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C,D] : 
              ( r1_tarski(B,A)
              & ( r2_hidden(C,B)
               => m1_subset_1(C,A) )
              & ( ( r2_hidden(C,D)
                  & r2_hidden(D,B) )
               => m1_subset_1(C,A) ) ) ) ) ),
    file(zf_fund1,t1_zf_fund1),
    []).

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(t35_grfunc_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( ( r2_hidden(A,k1_relat_1(B))
                  & C = k2_xboole_0(D,B) )
               => k1_funct_1(C,A) = k1_funct_1(B,A) ) ) ) ) ),
    file(grfunc_1,t35_grfunc_1),
    []).

fof(t36_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    []).

fof(t37_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    []).

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

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

fof(t45_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => B = k2_xboole_0(A,k4_xboole_0(B,A)) ) ),
    file(xboole_1,t45_xboole_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(t4_zf_fund1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(A)) )
         => ! [C,D] : 
              ( ( v8_zf_fund1(B,A)
                & r2_hidden(C,B)
                & r2_hidden(D,B) )
             => ( r2_hidden(k2_xboole_0(C,D),B)
                & r2_hidden(k4_xboole_0(C,D),B)
                & r2_hidden(k1_zf_fund1(C,D),B) ) ) ) ) ),
    file(zf_fund1,t4_zf_fund1),
    []).

fof(t4_zf_model,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_zf_lang(B)
            & m2_finseq_1(B,k5_numbers) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,A)
                & m2_relset_1(C,k1_zf_lang,A) )
             => ( ~ r2_hidden(C,k5_zf_model(B,A))
              <=> r2_hidden(C,k5_zf_model(k6_zf_lang(B),A)) ) ) ) ) ),
    file(zf_model,t4_zf_model),
    []).

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(t65_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => k2_zf_model(k6_zf_lang(A)) = k2_zf_model(A) ) ),
    file(zf_lang1,t65_zf_lang1),
    []).

fof(t65_zfmisc_1,axiom,(
    ! [A,B] : 
      ( k4_xboole_0(A,k1_tarski(B)) = A
    <=> ~ r2_hidden(B,A) ) ),
    file(zfmisc_1,t65_zfmisc_1),
    []).

fof(t67_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => k2_zf_model(k8_zf_lang(B,A)) = k4_xboole_0(k2_zf_model(A),k1_tarski(B)) ) ) ),
    file(zf_lang1,t67_zf_lang1),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t6_zf_model,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k1_zf_lang)
         => ! [C] : 
              ( ( v1_zf_lang(C)
                & m2_finseq_1(C,k5_numbers) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,A)
                    & m2_relset_1(D,k1_zf_lang,A) )
                 => ( ( r2_hidden(D,k5_zf_model(C,A))
                      & ! [E] : 
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,k1_zf_lang,A)
                            & m2_relset_1(E,k1_zf_lang,A) )
                         => ( ! [F] : 
                                ( m2_subset_1(F,k5_numbers,k1_zf_lang)
                               => ( k8_funct_2(k1_zf_lang,A,E,F) != k8_funct_2(k1_zf_lang,A,D,F)
                                 => B = F ) )
                           => r2_hidden(E,k5_zf_model(C,A)) ) ) )
                  <=> r2_hidden(D,k5_zf_model(k8_zf_lang(B,C),A)) ) ) ) ) ) ),
    file(zf_model,t6_zf_model),
    []).

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(t84_zf_lang1,axiom,(
    ! [A] : 
      ( ( v1_zf_lang(A)
        & m2_finseq_1(A,k5_numbers) )
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_zf_lang,B)
                & m2_relset_1(C,k1_zf_lang,B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_zf_lang,B)
                    & m2_relset_1(D,k1_zf_lang,B) )
                 => ( ( ! [E] : 
                          ( m2_subset_1(E,k5_numbers,k1_zf_lang)
                         => ( r2_hidden(E,k2_zf_model(A))
                           => k8_funct_2(k1_zf_lang,B,D,E) = k8_funct_2(k1_zf_lang,B,C,E) ) )
                      & r1_zf_model(B,C,A) )
                   => r1_zf_model(B,D,A) ) ) ) ) ) ),
    file(zf_lang1,t84_zf_lang1),
    []).

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

fof(t8_grfunc_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
          <=> ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) ),
    file(grfunc_1,t8_grfunc_1),
    []).

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

fof(t9_zf_fund1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(A)) )
             => ! [D] : 
                  ( ( v1_finset_1(D)
                    & m1_subset_1(D,k1_zfmisc_1(k5_ordinal2)) )
                 => ( ( v8_zf_fund1(C,A)
                      & r2_hidden(B,C) )
                   => r2_hidden(k1_funct_2(D,B),C) ) ) ) ) ) ),
    file(zf_fund1,t9_zf_fund1),
    []).